LCGT

Common files

Initial input

include files

<<"BarCharts`";<<"Histograms`";<<"PieCharts`"

Text style

(*$TextStyle ={FontFamily -> Papyrus,FontSize -> 24}*)

$TextStyle ={FontFamily -> Times,FontSize -> 24}

Options

SpellingOptions -> {AlwaysSkip};

Misc. information

X: light axis
Y: parpendiculer to the light axis
Z: vertical direction

Units

kg = 1;

g = 0.001 kg;

m = 1;

mm = 0.001 m;

cm = 0.01 m;

micron = 10^(-6) m;

W = 1;

mW = 0.001 W;

K=1;

second =1;

hz = Hz= 1/second;

ppm = 10^-6;

J =1;

Physical constants

gaccel = 9.8 m/second^2; (*acceleration of gravity [m/sec^2]*)

sb = 5.7 10^(-8) W/m^2/K^4; (*Stefan-Boltzmann constant*)

kb = 1.39 10^(-23) J/second; (*Boltzmann's constant [J/K]*)

hbar= 1.055*10^(-34);(* reduced Planck constant (J*s) *)

c=2.9979*10^8;(* speed of light (m/s) *)

Functions

Geometrical

Area

sACyl[r_,l_]:=2*r^2*Pi+2*Pi*r*l (*function to calculate surface aria of cylinder.r_:radius of column,l_:length of column*)

sAPipe[r_,l_]:=2 Pi r l(*function to calculate surface aria of pipe.r_:radius of column,l_:length of column*)

sACube[x_,y_,z_]:=2*(x y+y z+z x) (*function to calculate surface aria of cubu.*)

aC[r_]:=Pi r^2(*circle area*)

aS[x_,y_]:=x y (*square area*)

Volume

vCyl[r_,l_]:=r^2 Pi l (*volume of cylinder[m^3]*)

vCube[x_,y_,z_]:=x  y  z

vCage[x_,y_,z_,d_]:= 2 z d (x-2 d+y)

Mass

mCyl[dens_,r_,l_] := dens vCyl[r,l]

mCube[dens_,x_,y_,z_] := dens vCube[x,y,z]

mCage[dens_,x_,y_,z_,d_]:=dens 2 z d (x-2 d+y)

Solid angle

sAngle[r_,l_] := ((r^2 Pi)/(l^2)) (*function to calculate solid angle. r_: radius of window, l_: distance to window*)

sAArea[s_,l_] := (s/(l^2)) (*function to calculate solid angle. s_: area, l_: distance to window*)

moment of inertia

mIRollCube[dens_,x_,y_,z_]:= x y z dens (y^2+z^2)/12 (*M. I. for Roll(rotation round X axis).*)

mIPitchCube[dens_,x_,y_,z_]:= x y z dens (x^2+z^2)/12 (*M. I. for Pitch(rotation round Y axis).*)

mIYawCube[dens_,x_,y_,z_]:= x y z dens (x^2+y^2)/12 (*M. I. for Yaw(rotation round Z axis).*)

mIRCyl[dens_,r_,l_]:= dens vCyl[r,l] (r^2/4+l^2/12) (*r: radius of cylinder, l: length of cylinder*)

mILCyl[dens_,r_,l_] :=dens vCyl[r,l] r^2/2(*r: radius of cylinder, l: length of cylinder*)

mIRollCage[dens_,x_,y_,z_,d_]:= 2 dens z d(((y^2+z^2)/12) y+(((z^2+d^2)/12)+(((y-d)^2)/4))(x-2 d))(*see note 2003/07/23*)

mIPitchCage[dens_,x_,y_,z_,d_]:= 2 dens z d((((z^2+d^2)/12)+(((x-d)^2)/4))y+(((x-4d)^2+z^2)/12)(x-2 d))(*see note 2003/07/23*)

mIYawCage[dens_,x_,y_,z_,d_]:= 2 dens z d((((y^2+d^2)/12)+(((x-d)^2)/4)) y+((((x-4 d)^2+d^2)/12)+(((y-d)^2)/4))(x-2 d))(*see note 2003/07/23*)

Length

lU[deg_,rad_] := rad  deg;(*length of U shape*)

Heat

radiation heat

hRadHole[HTemp_,LTemp_,emis_,r_] := sb*(HTemp^4-LTemp^4)*(emis/(2-emis))*r^2*Pi(*Radiation heat throgh hole [W]*)

hRadArea[HTemp_,LTemp_,emis_,area__] := sb*(HTemp^4-LTemp^4)*(emis/(2-emis))*area (*Radiation heat throgh hole [W]*)

hRadMass[ht_,lt_,saria_,sangle_,emiss_] := ((sb saria emiss)/(4 Pi))sangle (ht^4 - lt^4) (*radiation to mass. ht_:higher temperature,lt_:lower temperature, saria_:surface aria of mass, sangle_:solid angle of window, emiss_:emissivity of mass.*)

hRadRoom[s_] := 2W/m^2 s m^2 (*radiation from 300K to shield covered by 60 SI.*)

thermal ocnduction of sapphire

hSa[num_,ht_,lt_,d_,l_] := 3.49*10^(-6)*(((25 cm)/l))*((d/(0.5 mm)))^3*((num/4))*(ht^3.2-lt^3.2)  (*thermal conduction of sapphire. ht_:higher temperature,lt_:lower temperature, d_: diameter of fiber, l_: length,num_:number of fiber*)

hSa[4,20,10,0.1 mm, 0.25]

Plot[hSa[4,20,lt,1.8 mm, 0.5 m],{lt, 8,17}]

thermal conduction through G10 support

hG10300[num_,r_,l_]:=(103.1-14.1)*r^2*Pi/l*num(*heat due to thermal conduction of G10 support rod from 300K to 100K*)

hG104[num_,r_,l_]:=14.1*r^2*Pi/l*num (*heat due to thermal conduction of G10 support rod from 100K to 4K*)

thermal conduction through coaxial cable (Lake shore coaxial cable cc-ss)

rSusInCC=0.2 mm/2;(*radius of inner sus part of coaxial cable*)

rTefInCC=0.406 mm/2;(*radius of inner tefron part of coaxial cable*)

rSusOutCC=0.71 mm/2;(*radius of outer sus part of coaxial cable*)

rTefOutCC=1 mm/2;(*radius of outer tefron part of coaxial cable*)

ariaSusCC=Pi*(rSusInCC^2+rSusOutCC^2-rTefInCC^2);(*aria of sus part in CC[m^2]*)

ariaTefCC=Pi*rTefOutCC^2-ariaSusCC;(*aria of sus part in CC[m^2]*)

hSig300[num_,l_]:=((30.6*10^2-5.28*10^2)*ariaSusCC+(702*10^-1-187*10^-1)*ariaTefCC)/l*num (*heat due to thermal conduction of coaxial cable from 300K to 100K[W]*)

hSig4[num_,l_]:=(5.28*10^2*ariaSusCC+187*10^-1*ariaTefCC)/l*num (*heat due to thermal conduction of coaxial cable from 100K to 4K[W]*)

thermal conduction of Aluminum

kAl[rrr_,t_]:=(1/(1.83 10^(-7)t^2+(1.09/(rrr t))))(*thermal confuctivity of aluminum[W/m/K]*)

hAl[thigh_,tlow_,rrr_,r_,l_] :=((r^2 Pi)/l)(∫_tlow^thigh)kAl[rrr,x]\[DifferentialD]x

hAlU[thigh_,tlow_,rrr_,dia_,r_,deg_] :=((dia^2 Pi)/(4 r deg))(∫_tlow^thigh)kAl[rrr,x]\[DifferentialD]x

hAl2[thigh_,tlow_,rrr_,sl_] :=sl*(∫_tlow^thigh)kAl[rrr,x]\[DifferentialD]x(*sl_; S/l*)

4*hAl[13.5,13.,6000,2 mm,0.4m]

7*hAlU[13,7,6000,1mm,25 cm,Pi]

thermal conduction of SUS

hSUS[num_,r_,l_]=num*(30.6-0.0293)*100*r^2 Pi/l W;(*thermal conduction between 300K-10K.*)(*低温工学概論P.272*)

thermal resistance effect

tDelta[h_]:=0.25*(h)^0.6 (*temperature increase due to thermal contact resistance[K].heat[W]*)

laser absorption

hLAMass[p_,abs_,l_] :=2*(p/2)*abs*l (*laser absorption in mirror[W].p:effective laser power at BS[W],abs:laser absorption[ppm/cm],l:length of mirror[cm]*)

hLACoat[p_,abs_,finesse_]:=2*(p/2)(finesse/Pi)abs (*laser absorption in coating[W].p:effective laser power at BS[W],abs:laser absorption in coating[ppm]*)

Spring constant & torque

U shape

scUZ[young_,deg_,dia_,r_] :=  ((4 Pi young dia^4)/(64 r^3))*(6*deg+Sin[2 deg]-8Sin[deg])^-1 (*spring constant of U shape thermal conductor of circular cross section fiber. 
Z direction. (vertical)
young:young's modulus[N/m^2],
 dia:diameter of fiber[m], 
deg:degree of U shape[rad], 
r:radius of U shape [m]*)

scUX[young_,deg_,dia_,r_]:= ((4 Pi young dia^4)/(64 r^3))*(2*deg-Sin[2 deg])^-1 (*spring constant of U shape thermal conductor of circular cross section fiber. 
X direction. (light axis)
young:young's modulus[N/m^2],
 dia:diameter of fiber[m], 
deg:degree of U shape[rad], 
r:radius of U shape [m]*)

scUY[shear_,dia_,r_]:= ((shear dia^4)/(32 r^3))(*spring constant of U shape thermal conductor of circular cross section fiber. 
Y direction. (perpendicular to light axis)
shere:shere modulus[N/m^2],
 dia:diameter of fiber[m], 
r:radius of U shape [m]*)

torque for pitch, yaw and roll. (see note 03/05/26. At present not use. 2003/08/18.)

tRoll[x_,y_,z_,kh_,dh_,kv_,dv_] :=  (y^2 kv(1+I dv)+z^2 kh (1+I dh))(*torque for Roll motion(rotation around X-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

tPitch[x_,y_,z_,kh_,dh_,kv_,dv_] := (z^2 kh (1+I dh)+x^2 kv (1+I dv))(*torque for Roll motion(rotation around Y-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

tYaw[x_,y_,z_,kh_,dh_,kv_,dv_] := (y^2 kh (1+I dh)+x^2 kh (1+I dh) )(*torque for Roll motion(rotation around Z-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

tURoll[x_,y_,z_,kx_,ky_,kz_,du_] :=  (y^2 kz(1+I du)+z^2 ky (1+I du))(*torque for Roll motion(rotation around X-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

tUPitch[x_,y_,z_,kx_,ky_,kz_,du_] := (z^2 kx (1+I du)+x^2 kz (1+I du))(*torque for Roll motion(rotation around Y-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

tUYaw[x_,y_,z_,kx_,ky_,kz_,du_] := (y^2 kx (1+I du)+x^2 ky (1+I du) )(*torque for Roll motion(rotation around Z-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

torque caused by next mass rotation for pitch, yaw and roll. (see note 03/06/20, All torques are calculated by these functions.2003/08/18. )

ctRoll[x1_,y1_,z1_,x2_,y2_,z2_,kh_,dh_,kv_,dv_] :=  (y1 y2 kv(1+I dv)+z1 z2 kh (1+I dh))(*torque for Roll motion(rotation around X-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

ctPitch[x1_,y1_,z1_,x2_,y2_,z2_,kh_,dh_,kv_,dv_] := (z1 z2 kh (1+I dh)+x1 x2 kv (1+I dv))(*torque for Roll motion(rotation around Y-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

ctYaw[x1_,y1_,z1_,x2_,y2_,z2_,kh_,dh_,kv_,dv_] := (y1 y2 kh (1+I dh)+x1 x2 kh (1+I dh) )(*torque for Roll motion(rotation around Z-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

ctURoll[x1_,y1_,z1_,x2_,y2_,z2_,kx_,ky_,kz_,du_] :=  (y1 y2 kz(1+I du)+z1 z2 ky (1+I du))(*torque for Roll motion(rotation around X-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

ctUPitch[x1_,y1_,z1_,x2_,y2_,z2_,kx_,ky_,kz_,du_] := (z1 z2 kx (1+I du)+x1 x2 kz (1+I du))(*torque for Roll motion(rotation around Y-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

ctUYaw[x1_,y1_,z1_,x2_,y2_,z2_,kx_,ky_,kz_,du_] := (y1 y2 kx (1+I du)+x1 x2 ky (1+I du) )(*torque for Roll motion(rotation around Z-axis.),
x, y, z: position from clamp from COM[m],
kh: spring constant of wire in horizontal direction[N/m],
kv: spring constant of wire in vertical direction[N/m],
dh: disspation angle of horizontal spring,
dv: dissipation angle of vertical spring*)

square shape vertical spring

scSV[young_,poisson_,width_,thick_,hori_,vert_] := ((3 width thick^3 young)/(12 (1-poisson^2)))(1/(2*hori^3 +3 hori^2 vert)) (*spring constant of square shape vertical spring in vertical direction. 
young: young's modulus,
poisson: poisson ratio,
width: width of plate,
thick: thickness of balde,
hori: horizontal length of square,
vertical length of square.
ばねの設計, p204, (7.46)*)

cbYoung

scSV[cbYoung,0.3,10 mm,0.5 mm,3cm,1 cm]

6 4 cm/(1 cm)/(0.5 mm)^2

blade vertical spring

scBV[young_,poisson_,dens_,width_,length_,thick_,force_] := (1/(length^3))((young width thick^3)/(4 (1-poisson^2))) (*spring constant of blade vertical spring in vertical direction. 
young: young's modulus,
poisson: poisson ratio,
width: width of blade,
length: length of blade,
thick: thickness of blade,
ばねの設計, p198, (7.6).*)

fiBV[young_,poisson_,dens_,width_,length_,thick_,force_]:=0.56 (1/(length^2))(Sqrt[((young thick^2)/dens)]) (*the lowest resonant frequency of internal mode.*)

stMaxBV[young_,poisson_,dens_,width_,length_,thick_,force_]:=((6 length (1-poisson^2))/(width thick^2))force (*maximum stress due to the force*)

bBV[young_,poisson_,dens_,width_,length_,thick_,force_]:=((width thick^3 young)/(12 (1-poisson^2)))

etc.

scPend[m_,l_] := ((m gaccel)/l)

scVert[young_,d_,l_] := ((young (d/2)^2 Pi)/l)

scFreq[m_,f_]:=m (2 Pi f)^2

Damping

(*Damp[f_,f0_,q_] := Which[

((2 Pi f0)/q)f<0.5,((2 Pi f0)/q),
True,0.5] *)

Damp[f_,f0_,q_] := ((2 Pi f0)/q)

Rot-displacement conversion

covRotDisp[offset_,rad_] := rad offset (*rotation-displacement conversion: offset: offset of beam centering, rad: angle of rotation*)

Seismic motion

seisK[f_] := Which[f<50,3*10^-9/f^2,
f<200,3*10^-9/50^2,
True,3*10^-9/50^2*(200/f)^2]m/Sqrt[hz](*seismic motion at KAMiOKA [m/rtHz]*)

seisKRot[f_] :=  Which[f<50,3*10^-9/f^2 (4 f/5000),
f<200,3*10^-9/50^2 (4 f/5000),
True,3*10^-9/50^2*(200/f)^2 (4 f/5000)]m/Sqrt[hz](*seismic rotation motion at KAMiOKA. [rad/rtHZ]*)

seisTAMA[f_]:=10^-7/f^2m/Sqrt[hz](*seismic motion at TAMA site*)

seisTAMARot[f_]:=10^-7/f^2 (4 f/1000) (*seismic motion at TAMA site*)

trfHSAS[f_]:= Which[f<0.03,1,True,(0.03/f)^2] Which[f<0.7,1,True,(0.7/f)^2]  Which[f<0.7,1,True,(0.7/f)^2](*TRF of SAS in horizontal direction*)

trfVSAS[f_]:= Which[f<0.5,1,True,(0.5/f)^4] (*TRF of SAS in vertical direction*)

LogLogPlot[{seisK[f],seisTAMA[f]},{f,0.1,1000},PlotRange -> All]

LogLogPlot[{trfHSAS[f] ,trfVSAS[f]},{f,0.01,10},PlotRange -> All]

LogLogPlot[{seisK[f],trfHSAS[f] seisK[f],trfVSAS[f] seisK[f]},{f,0.1,1},PlotRange -> All]

LogLogPlot[{seisKRot[f],seisTAMARot[f]},{f,0.1,1000},PlotRange -> All]

Pendulum thermal noise

dilution factor

dilutionFactor[mass_,num_,length_,dia_,young_]:=num Sqrt[mass gaccel/num young (Pi dia^4/64)]/(2 length^2)/(mass gaccel/length)

pThermal[f_,temp_,mass_,pFreq_,qPend_] :=((4 kb (2 Pi pFreq)^2)/(mass (2 Pi f)^5))(temp/qPend);(*Pendulum thermal noise. mass[kg],pFreq[Hz]:pendulum frequency, temp[K], qPend:Qfacor of pendulum*)

Sqrt[pThermal[20,10 K,30 kg,0.8Hz,10^8]]*2

Mirror thermal noise

Coating thermal noise

mirrorcoa[f_,tm_,dcoa_,phicoa_,w1_,w2_,E0_]:=5.5*10^(-19)*(dcoa/(15*10^(-6)))^(1/2)*(phicoa/(1.2*10^(-2)))^(1/2)*Sqrt[(10^(-2)/w1)^2*2+(10^(-2)/w2)^2*2]*(tm/300)^(1/2)*(7.24*10^10/E0)^(1/2)*(100/f)^(1/2);(*coating thermal noise.l:length of cavity[m],dcoa:thickness of coating[m],phicoa:loss angle of coating,w1:beam radius of front mirror[m],w2:beam radius of end mirror[m],tm:temperature[K],E0:Young's modulus[N/m^2]*)

Mirror (structure)

mirrorhomo[f_,tm_,sigma_,phimir_,w1_,w2_,E0_]:=Sqrt[4*kb*tm*(1-sigma^2)*phimir/(Sqrt[Pi]*E0*2*Pi*f)]*Sqrt[1/w1*2+1/w2*2];
(*Mirror thermal noise (structure).l:length of cavity[m],sigma:poisson ratio,phimir:loss angle of mirror material,w1:beam radius of front mirror[m],w2:beam radius of end mirror[m],tm:temperature[K],E0:Young's modulus[N/m^2]*)

Mirror thermoelastic

thelasticRoom[f_,t_,alpha_,sigma_,kappa_,spheat_,w_] :=((8/(Sqrt[2 Pi])))alpha^2 (1+sigma)^2 ((kb t^2 kappa)/((2 Pi f)^2 spheat^2))(((Sqrt[2])/w))^3(*thermoelastic noise of mirror [m/rtHz].
t: temperature [K],
alpha: linerar expansion ratio,
sigma: poisson ratio,
kappa: thermal conductivity [W/K/m],
spheat: specific heat [J/K/m^3,
w: beam radius of front mirror [m]
*)

thelasticCryo[f_,t_,alpha_,sigma_,kappa_,spheat_] :=((8/(Sqrt[2 Pi])))alpha^2 (1+sigma)^2 ((kb t^2 )/kappa)((kappa/(2 Pi f spheat  )))^0.5(*thermoelastic noise of mirror [m/rtHz].
t: temperature [K],
alpha: linerar expansion ratio,
sigma: poisson ratio,
kappa: thermal conductivity [W/K/m],
spheat: specific heat [J/K/m^3
*)

thelasticFreq[w_,kappa_,spheat_] := (kappa/(spheat w^2/2)) (1/(2 Pi))(*cut off frequency of thermoelastic noise. [Hz].
w: beam radius [m],
kappa: thermal ocnductivity [W/K/m],
spheat: specific heat [J/K/m^3]*)

thelastic[f_,t_,alpha_,sigma_,kappa_,spheat_,w_]:=If[f>thelasticFreq[w,kappa,spheat],thelasticRoom[f,t,alpha,sigma,kappa,spheat,w],thelasticCryo[f,t,alpha,sigma,kappa,spheat]]

Shot noise

(*hshot[f_,p_,tau_]:=Sqrt[hbar*lambda/(4*Pi*c*p)*(1/tau^2+(2*Pi*f)^2)];(*shot noise limit.p:laser power at BS[W],tau:storage time[sec].*)*)

sTime[l_,f_]:=2*l*f/(Pi*c)
(*storage time[sec].l:length of cavity[m],f:finesse.*)

hshot[f_,pcav_,fcut_]:=Sqrt[hbar*lambda*fcut/(2*l*pcav)*(1+(f/fcut)^2)];(*shot noise limit.p:laser power at BS[W],tau:storage time[sec].*)

Radiation pressure noise

(*hradia[f_,p_,fcut_,l_,finesse_,mass_]:=1/l*(4*finesse/Pi)/(mass*(2*Pi*f)^2)*Sqrt[16*Pi*hbar*p/(c*lambda)]/Sqrt[1+(f/fcut)^2];*)

fCut[l_,f_]:=1/(2*Pi*2*l*f/(Pi*c))
(*cut off frequency time[Hz].l:length of cavity[m],f:finesse.*)

hradia[f_,pcav_,fcut_,l_,finesse_,mass_]:=2/l*2/(mass*(2*Pi*f)^2)*Sqrt[2*hbar*pcav/(lambda l fcut)]/Sqrt[1+(f/fcut)^2];(*pcav; power in cavity*)

pcav[p_,finesse_,gRecycle_]:= gRecycle (2 finesse/Pi)p;

Single pendulum

nTotalsingle = 1;

single pendulim (X - Pitch, Y - Roll) : for Test (OLD)

matrix

matXPYRtest[f_,m1_,i1_,g10_,tg10_,ctg10_,zg01_,zg10_,d1_] := -(2 Pi f)^2*(({{m1, 0}, {0, i1}}))+(({{g10, g10 zg10}, {g10 zg10, tg10}}))

{f,m1,i1,g10,tg10,ctg10,zg01,zg10,d1}

+2 Pi f I (({{m1 d1, 0}, {0, i1 d1}}))

transfer function

trfXYtest[n_,
f_,m1_,i1_,g10_,tg10_,ctg10_,zg01_,zg10_,d1_] :=

Abs[Part[Inverse[matXPYRtest[
f,m1,i1,g10,tg10,ctg10,zg01,zg10,d1]].{g10, g10 zg01},n]]
 (*transfer function from cryostat. *)

trfPRtest[n_,
f_,m1_,i1_,g10_,tg10_,ctg10_,zg01_,zg10_,d1_] :=

Abs[Part[Inverse[matXPYRtest[
f,m1,i1,g10,tg10,ctg10,zg01,zg10,d1]].{g10 zg01, ctg10},n]]
 (*transfer function from cryostat. *)

displacement

dispXYtest[n_,
f_,m1_,i1_,g10_,tg10_,ctg10_,zg01_,zg10_,d1_] := 

Sqrt[(seisK[f]*trfXYtest[n,f,m1,i1,g10,tg10,ctg10,zg01,zg10,d1])^2]

radPRtest[n_,
f_,m1_,i1_,g10_,tg10_,ctg10_,zg01_,zg10_,d1_] := 

Sqrt[(seisKRot[f]*trfPRtest[n,f,m1,i1,g10,tg10,ctg10,zg01,zg10,d1])^2]

dispPRtest[offset_,n_,f_,m1_,i1_,g10_,tg10_,ctg10_,zg01_,zg10_,d1_] := 

covRotDisp[offset,
radPRtest[n,f,m1,i1,g10,tg10,ctg10,zg01,zg10,d1]]

thermal noise

tNoiseXYtest[n_,
f_,m1_,i1_,g10_,tg10_,ctg10_,zg01_,zg10_,d1_]:=

Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matXPYRtest[f,m1,i1,g10,tg10,ctg10,zg01,zg10,d1]]],n,n]]

tNoisePRtest[offset_,n_,f_,m1_,i1_,g10_,tg10_,ctg10_,zg01_,zg10_,d1_]:=

covRotDisp[offset,
Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matXPYRtest[f,m1,i1,g10,tg10,ctg10,zg01,zg10,d1]]],n,n]]]

single pendulum (all 6 deg.)

matrix

mat6single[f_,
m_,ix_,iy_,iz_,
kh_,kv_,
tx_,ty_,tz_,
ctx_,cty_,ctz_,
x_,y_,z_,
dx_,dy_,dz_,
x0_,y0_,z0_,
dx0_,dy0_,dz0_,
l_
]:= -(2 Pi f)^2(({{m, 0, 0, 0, 0, 0}, {0, m, 0, 0, 0, 0}, {0, 0, m, 0, 0, 0}, {0, 0, 0, ix, 0, 0}, {0, 0, 0, 0, iy, 0}, {0, 0, 0, 0, 0, iz}}))+(({{kh, 0, 0, 0, z kh, -dy kh}, {0, kh, 0, -z kh, 0, dx kh}, {0, 0, kv, dy kv, -dx kv, 0}, {0, -z kh, dy kv, tx, -{y, dy}.{dx,x} kv, -{z+l,dz}.{dx,x} kh}, {z kh, 0, -dx kv, -{x,dx}.{dy,y} kv, ty, -{z+l,dz}.{dy,y} kh}, {-dy kh, dx kh, 0, -{x,dx}.{dz,z} kh, -{y,dy}.{dz,z} kh, tz}}))

{f,
m,ix,iy,iz,
kh,kv,
tx,ty,tz,
ctx,cty,ctz,
x,y,z,
dx,dy,dz,
x0,y0,z0,
dx0,dy0,dz0,
l};

trf

matForce[f_,
m_,ix_,iy_,iz_,
kh_,kv_,
tx_,ty_,tz_,
ctx_,cty_,ctz_,
x_,y_,z_,
dx_,dy_,dz_,
x0_,y0_,z0_,
dx0_,dy0_,dz0_,
l_
]:=(({{kh, 0, 0, 0, z0 kh, -dy0 kh}, {0, kh, 0, -z0 kh, 0, dx0 kh}, {0, 0, kv, dy0 kv, -dx0 kv, 0}, {0, -z0 kh, dy0 kv, ctx, -{y,dy}.{dx0,x0} kv, -{z+l,dz}.{dx0,x0} kh}, {z0 kh, 0, -dx0 kv, -{x,dx}.{dy0,y0} kv, cty, -{z+l,dz}.{dy0,y0} kh}, {-dy0 kh, dx0 kh, 0, -{x,dx}.{dz0,z0} kh, -{y,dy}.{dz0,z0} kh, ctz}}))

matSeis[f_]:=(({{seisK[f]}, {seisK[f]}, {seisK[f]}, {seisKRot[f]}, {seisKRot[f]}, {seisKRot[f]}}))

trfAmpsingle[a_,b_,c_,d_,f_,
m_,ix_,iy_,iz_,
kh_,kv_,
tx_,ty_,tz_,
ctx_,cty_,ctz_,
x_,y_,z_,
dx_,dy_,dz_,
x0_,y0_,z0_,
dx0_,dy0_,dz0_,
l_

] := Abs[Part
[Inverse[mat6single[
f,
m,ix,iy,iz,
kh,kv,
tx,ty,tz,
ctx,cty,ctz,
x,y,z,
dx,dy,dz,
x0,y0,z0,
dx0,dy0,dz0,
l]],(6(d-1)+c),(6(b-1)+a)]] /Abs[Part
[Inverse[mat6single[
f,
m,ix,iy,iz,
kh,kv,
tx,ty,tz,
ctx,cty,ctz,
x,y,z,
dx,dy,dz,
x0,y0,z0,
dx0,dy0,dz0,
l]],(6(b-1)+a),(6(b-1)+a)]]




(*amplitude to amplitude trf from direction "a" of mass "b" to direction "c" of mass "d".*)

trfSeissingle[a_,b_,c_,f_,
m_,ix_,iy_,iz_,
kh_,kv_,
tx_,ty_,tz_,
ctx_,cty_,ctz_,
x_,y_,z_,
dx_,dy_,dz_,
x0_,y0_,z0_,
dx0_,dy0_,dz0_,
l_

] :=Abs[Part
[Inverse[mat6single[
f,
m,ix,iy,iz,
kh,kv,
tx,ty,tz,
ctx,cty,ctz,
x,y,z,
dx,dy,dz,
x0,y0,z0,
dx0,dy0,dz0,
l]].

Part[matForce[f,
m,ix,iy,iz,
kh,kv,
tx,ty,tz,
ctx,cty,ctz,
x,y,z,
dx,dy,dz,
x0,y0,z0,
dx0,dy0,dz0,
l],a],(6(c-1)+b)]]

(*transfer function a to b.
c: interesting item.
a, b= 1 -> X to X*)

seissingle[a_,b_,c_,f_,
m_,ix_,iy_,iz_,
kh_,kv_,
tx_,ty_,tz_,
ctx_,cty_,ctz_,
x_,y_,z_,
dx_,dy_,dz_,
x0_,y0_,z0_,
dx0_,dy0_,dz0_,
l_]:=trfSeissingle[a,b,c,f,
m,ix,iy,iz,
kh,kv,
tx,ty,tz,
ctx,cty,ctz,
x,y,z,
dx,dy,dz,
x0,y0,z0,
dx0,dy0,dz0,
l] *Part[matSeis[f],a]

tNoisesingle[a_,b_,f_,
m_,ix_,iy_,iz_,
kh_,kv_,
tx_,ty_,tz_,
ctx_,cty_,ctz_,
x_,y_,z_,
dx_,dy_,dz_,
x0_,y0_,z0_,
dx0_,dy0_,dz0_,
l_]:=

Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[mat6single[f,
m,ix,iy,iz,
kh,kv,
tx,ty,tz,
ctx,cty,ctz,
x,y,z,
dx,dy,dz,
x0,y0,z0,
dx0,dy0,dz0,
l]]],6(b-1)+a,6(b-1)+a]] (*thermal noise of direction "a" of mass "b".*)

Part[(({{1, 2}, {4, 3}})),1,2]

Double pendulum

nTotalDouble = 3;

matrix

mat6Double[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
md1_,ixd1_,iyd1_,izd1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,khd10_,kvd10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,txd10_,tyd10_,tzd10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctxd10_,ctyd10_,ctzd10_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,xd01_,yd01_,zd01_,xd10_,yd10_,zd10_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dxd01_,dyd01_,dzd01_,dxd10_,dyd10_,dzd10_,
l1_,l2_,ld1_,
d1_
]:= -(2 Pi f)^2(({{m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, ix1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, iy1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, iz1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, ix2, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy2, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz2, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixd1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyd1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izd1}}))+(({{kh10+kh12, 0, 0, 0, {z10,z12}.{kh10,kh12}, -{dy10,dy12}.{kh10,kh12}, -kh12, 0, 0, 0, -z21 kh12, dy21 kh12, 0, 0, 0, 0, 0, 0}, {0, kh10+kh12, 0, -{z10,z12}.{kh10,kh12}, 0, {dx10,dx12}.{kh10,kh12}, 0, -kh12, 0, z21 kh12, 0, -dx21 kh12, 0, 0, 0, 0, 0, 0}, {0, 0, kv10+kv12, {dy10,dy12}.{kv10,kv12}, -{dx10,dx12}.{kv10,kv12}, 0, 0, 0, -kv12, -dy21 kv12, dx21 kv12, 0, 0, 0, 0, 0, 0, 0}, {0, -{z10,z12}.{kh10,kh12}, {dy10,dy12}.{kv10,kv12}, tx10+tx12, -{{y01,dy01}.{dx10,x10},{y21,dy21}.{dx12,x12}}.{kv10,kv12}, -{{z10+l1,dz01}.{dx10,x10},{z12-l2,dz21}.{dx12,x12}}.{kh10,kh12}, 0, z21 kh12, -dy21 kv12, -ctx12, {y21,dy21}.{dx21,x21} kv12, {z12-l2,dz21}.{dx21,x21} kh12, 0, 0, 0, 0, 0, 0}, {{z10,z12}.{kh10,kh12}, 0, -{dx10,dx12}.{kv10,kv12}, -{{x01,dx01}.{dy10,y10},{x21,dx21}.{dy12,y12}}.{kv10,kv12}, ty10+ty12, -{{z10+l1,dz01}.{dy10,y10},{z12-l2,dz21}.{dy12,y12}}.{kh10,kh12}, -z21 kh12, 0, dx21 kv12, {x21,dx21}.{dy21,y21} kv12, -cty12, {z12-l2,dz21}.{dy21,y21} kh12, 0, 0, 0, 0, 0, 0}, {-{dy10,dy12}.{kh10,kh12}, {dx10,dx12}.{kh10,kh12}, 0, -{{x01,dx01}.{dz10,z10},{x21,dx21}.{dz12,z12}}.{kh10,kh12}, -{{y01,dy01}.{dz10,z10},{y21,dy21}.{dz12,z12}}.{kh10,kh12}, tz10+tz12, dy21 kh12, -dx21 kh12, 0, {x21,dx21}.{dz21,z21} kh12, {y21,dy21}.{dz21,z21} kh12, -ctz12, 0, 0, 0, 0, 0, 0}, {-kh21, 0, 0, 0, -z12 kh21, dy12 kh21, kh21, 0, 0, 0, {z21}.{kh21}, -{dy21}.{kh21}, 0, 0, 0, 0, 0, 0}, {0, -kh21, 0, z12 kh21, 0, -dx12 kh21, 0, kh21, 0, -{z21}.{kh21}, 0, {dx21}.{kh21}, 0, 0, 0, 0, 0, 0}, {0, 0, -kv21, -dy12 kv21, dx12 kv21, 0, 0, 0, kv21, {dy21}.{kv21}, -{dx21}.{kv21}, 0, 0, 0, 0, 0, 0, 0}, {0, z12 kh21, -dy12 kv21, -ctx21, {y12,dy12}.{dx12,x12} kv21, {z21+l2,dz12}.{dx12,x12} kh21, 0, -{z21}.{kh21}, {dy21}.{kv21}, tx21, -{y12,dy12}.{dx21,x21} kv21, -{z21+l2,dz12}.{dx21,x21} kh21, 0, 0, 0, 0, 0, 0}, {-z12 kh21, 0, dx12 kv21, {x12,dx12}.{dy12,y12} kv21, -cty21, {z21+l2,dz12}.{dy12,y12} kh21, {z21}.{kh21}, 0, -{dx21}.{kv21}, -{x12,dx12}.{dy21,y21} kv21, ty21, -{z21+l2,dz12}.{dy21,y21} kh21, 0, 0, 0, 0, 0, 0}, {dy12 kh21, -dx12 kh21, 0, {x12,dx12}.{dz12,z12} kh21, {y12,dy12}.{dz12,z12} kh21, -ctz21, -{dy12}.{kh12}, {dx21}.{kh21}, 0, -{x12,dx12}.{dz21,z21} kh21, -{y12,dy12}.{dz21,z21} kh21, tz21, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd10, 0, 0, 0, {zd10}.{khd10}, -{dyd10}.{khd10}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd10, 0, -{zd10}.{khd10}, 0, {dxd10}.{khd10}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd10, {dyd10}.{kvd10}, -{dxd10}.{kvd10}, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd10}.{khd10}, {dyd10}.{kvd10}, txd10, -{yd01,dyd01}.{dxd10,xd10} kvd10, -{zd10+ld1,dzd10}.{dxd10,xd10} khd10}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd10}.{khd10}, 0, -{dxd10}.{kvd10}, -{xd01,dxd01}.{dyd10,yd10} kvd10, tyd10, -{zd10+ld1,dzd10}.{dyd10,yd10} khd10}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{dyd10}.{khd10}, {dxd10}.{khd10}, 0, -{xd01,dxd01}.{dzd10,zd10} khd10, -{yd01,dyd01}.{dzd10,zd10} khd10, tzd10}}))+I 2 Pi f (({{m1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -md1 d1, 0, 0, 0, 0, 0}, {0, m1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -md1 d1, 0, 0, 0, 0}, {0, 0, m1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -md1 d1, 0, 0, 0}, {0, 0, 0, ix1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ixd1 d1, 0, 0}, {0, 0, 0, 0, iy1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iyd1 d1, 0}, {0, 0, 0, 0, 0, iz1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -izd1 d1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-m1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md1 d1, 0, 0, 0, 0, 0}, {0, -m1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md1 d1, 0, 0, 0, 0}, {0, 0, -m1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md1 d1, 0, 0, 0}, {0, 0, 0, -ix1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixd1 d1, 0, 0}, {0, 0, 0, 0, -iy1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyd1 d1, 0}, {0, 0, 0, 0, 0, -iz1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izd1 d1}}))

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
md1,ixd1,iyd1,izd1,
kh10,kv10,kh12,kv12,kh21,kv21,khd10,kvd10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,txd10,tyd10,tzd10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctxd10,ctyd10,ctzd10,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,xd01,yd01,zd01,xd10,yd10,zd10,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dxd01,dyd01,dzd01,dxd10,dyd10,dzd10,
l1,l2,ld1,
d1};

matForceDouble[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
md1_,ixd1_,iyd1_,izd1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,khd10_,kvd10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,txd10_,tyd10_,tzd10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctxd10_,ctyd10_,ctzd10_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,xd01_,yd01_,zd01_,xd10_,yd10_,zd10_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dxd01_,dyd01_,dzd01_,dxd10_,dyd10_,dzd10_,
l1_,l2_,ld1_,
d1_]:=(({{kh10, 0, 0, 0, z01 kh10, -dy01 kh10, 0, 0, 0, 0, 0, 0, khd10, 0, 0, 0, zd01 khd10, -dyd01 khd10}, {0, kh10, 0, -z01 kh10, 0, dx01 kh10, 0, 0, 0, 0, 0, 0, 0, khd10, 0, -zd01 khd10, 0, dxd01 khd10}, {0, 0, kv10, dy01 kv10, -dx01 kv10, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd10, dyd01 kvd10, -dxd01 kvd10, 0}, {0, -z01 kh10, dy01 kv10, ctx10, -{y01,dy01}.{dx01,x01} kv10, -{z10+l1,dz01}.{dx01,x01} kh10, 0, 0, 0, 0, 0, 0, 0, -zd01 khd10, dyd01 kvd10, ctxd10, -{yd01,dyd01}.{dxd01,xd01} kvd10, -{zd10+ld1,dzd01}.{dxd01,xd01} khd10}, {z01 kh10, 0, -dx01 kv10, -{x01,dx01}.{dy01,y01} kv10, cty10, -{z10+l1,dz01}.{dy01,y01} kh10, 0, 0, 0, 0, 0, 0, zd01 khd10, 0, -dxd01 kvd10, -{xd01,dxd01}.{dyd01,yd01} kvd10, ctyd10, -{zd10+ld1,dzd01}.{dyd01,yd01} khd10}, {-dy01 kh10, dx01 kh10, 0, -{x01,dx01}.{dz01,z01} kh10, -{y01,dy01}.{dz01,z01} kh10, ctz10, 0, 0, 0, 0, 0, 0, -dyd01 khd10, dxd01 khd10, 0, -{xd01,dxd01}.{dzd01,zd01} khd10, -{yd01,dyd01}.{dzd01,zd01} khd10, ctzd10}}))

matSeisDouble[f_]:=(({{seisK[f]}, {seisK[f]}, {seisK[f]}, {seisKRot[f]}, {seisKRot[f]}, {seisKRot[f]}, {0}, {0}, {0}, {0}, {0}, {seisK[f]}, {seisK[f]}, {seisK[f]}, {seisKRot[f]}, {seisKRot[f]}, {seisKRot[f]}}))

(*matSeisDouble[f_]:=(({{seisTAMA[f]}, {seisTAMA[f]}, {seisTAMA[f]}, {seisTAMARot[f]}, {seisTAMARot[f]}, {seisTAMARot[f]}, {0}, {0}, {0}, {0}, {0}, {seisTAMA[f]}, {seisTAMA[f]}, {seisTAMA[f]}, {seisTAMARot[f]}, {seisTAMARot[f]}, {seisTAMARot[f]}}))*)

trf, seismic noise & thermal noise

trfAmpDouble[a_,b_,c_,d_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
md1_,ixd1_,iyd1_,izd1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,khd10_,kvd10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,txd10_,tyd10_,tzd10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctxd10_,ctyd10_,ctzd10_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,xd01_,yd01_,zd01_,xd10_,yd10_,zd10_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dxd01_,dyd01_,dzd01_,dxd10_,dyd10_,dzd10_,
l1_,l2_,ld1_,
d1_] :=

Abs[Part
[Inverse[mat6Double[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
md1,ixd1,iyd1,izd1,
kh10,kv10,kh12,kv12,kh21,kv21,khd10,kvd10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,txd10,tyd10,tzd10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctxd10,ctyd10,ctzd10,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,xd01,yd01,zd01,xd10,yd10,zd10,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dxd01,dyd01,dzd01,dxd10,dyd10,dzd10,
l1,l2,ld1,
d1]],(6(d-1)+c),(6(b-1)+a)]]/

Abs[Part
[Inverse[mat6Double[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
md1,ixd1,iyd1,izd1,
kh10,kv10,kh12,kv12,kh21,kv21,khd10,kvd10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,txd10,tyd10,tzd10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctxd10,ctyd10,ctzd10,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,xd01,yd01,zd01,xd10,yd10,zd10,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dxd01,dyd01,dzd01,dxd10,dyd10,dzd10,
l1,l2,ld1,
d1]],(6(b-1)+a),(6(b-1)+a)]]

(*amplitude to amplitude trf from direction "a" of mass "b" to direction "c" of mass "d".*)

trfSeisDouble[a_,b_,c_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
md1_,ixd1_,iyd1_,izd1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,khd10_,kvd10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,txd10_,tyd10_,tzd10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctxd10_,ctyd10_,ctzd10_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,xd01_,yd01_,zd01_,xd10_,yd10_,zd10_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dxd01_,dyd01_,dzd01_,dxd10_,dyd10_,dzd10_,
l1_,l2_,ld1_,
d1_] :=Abs[Part
[Inverse[mat6Double[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
md1,ixd1,iyd1,izd1,
kh10,kv10,kh12,kv12,kh21,kv21,khd10,kvd10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,txd10,tyd10,tzd10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctxd10,ctyd10,ctzd10,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,xd01,yd01,zd01,xd10,yd10,zd10,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dxd01,dyd01,dzd01,dxd10,dyd10,dzd10,
l1,l2,ld1,
d1]].

Part[matForceDouble[f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
md1,ixd1,iyd1,izd1,
kh10,kv10,kh12,kv12,kh21,kv21,khd10,kvd10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,txd10,tyd10,tzd10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctxd10,ctyd10,ctzd10,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,xd01,yd01,zd01,xd10,yd10,zd10,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dxd01,dyd01,dzd01,dxd10,dyd10,dzd10,
l1,l2,ld1,
d1],a],(6(c-1)+b)]]

(*transfer function a to b.
c: interesting item.
a, b= 1 -> X to X*)

seisDouble[a_,b_,c_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
md1_,ixd1_,iyd1_,izd1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,khd10_,kvd10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,txd10_,tyd10_,tzd10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctxd10_,ctyd10_,ctzd10_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,xd01_,yd01_,zd01_,xd10_,yd10_,zd10_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dxd01_,dyd01_,dzd01_,dxd10_,dyd10_,dzd10_,
l1_,l2_,ld1_,
d1_]:=

trfSeisDouble[a,b,c,f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
md1,ixd1,iyd1,izd1,
kh10,kv10,kh12,kv12,kh21,kv21,khd10,kvd10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,txd10,tyd10,tzd10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctxd10,ctyd10,ctzd10,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,xd01,yd01,zd01,xd10,yd10,zd10,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dxd01,dyd01,dzd01,dxd10,dyd10,dzd10,
l1,l2,ld1,
d1] *

Part[matSeisDouble[f],a]

tNoiseDouble[a_,b_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
md1_,ixd1_,iyd1_,izd1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,khd10_,kvd10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,txd10_,tyd10_,tzd10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctxd10_,ctyd10_,ctzd10_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,xd01_,yd01_,zd01_,xd10_,yd10_,zd10_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dxd01_,dyd01_,dzd01_,dxd10_,dyd10_,dzd10_,
l1_,l2_,ld1_,
d1_]:=

Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[mat6Double[f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
md1,ixd1,iyd1,izd1,
kh10,kv10,kh12,kv12,kh21,kv21,khd10,kvd10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,txd10,tyd10,tzd10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctxd10,ctyd10,ctzd10,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,xd01,yd01,zd01,xd10,yd10,zd10,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dxd01,dyd01,dzd01,dxd10,dyd10,dzd10,
l1,l2,ld1,
d1]]],6(b-1)+a,6(b-1)+a]] (*thermal noise of direction "a" of mass "b".*)

Quad pendulum

matrix

nTotalQuad = 5;

matQuad[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,x23_,y23_,z23_,x32_,y32_,z32_,x34_,y34_,z34_,x43_,y43_,z43_,
xd02_,yd02_,zd02_,
xd20_,yd20_,zd20_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dx23_,dy23_,dz23_,dx32_,dy32_,dz32_,dx34_,dy34_,dz34_,dx43_,dy43_,dz43_,
dxd02_,dyd02_,dzd02_,
dxd20_,dyd20_,dzd20_,
l1_,l2_,l3_,l4_,ld2_,
d2_
]:= -(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, ix1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, iy1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, iz1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, ix2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ix3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ix4, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz4, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixd2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyd2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izd2}}))+(({{kh10+kh12, 0, 0, 0, {z10,z12}.{kh10,kh12}, -{dy10,dy12}.{kh10,kh12}, -kh12, 0, 0, 0, -z21 kh12, dy21 kh12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, kh10+kh12, 0, -{z10,z12}.{kh10,kh12}, 0, {dx10,dx12}.{kh10,kh12}, 0, -kh12, 0, z21 kh12, 0, -dx21 kh12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, kv10+kv12, {dy10,dy12}.{kv10,kv12}, -{dx10,dx12}.{kv10,kv12}, 0, 0, 0, -kv12, -dy21 kv12, dx21 kv12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -{z10,z12}.{kh10,kh12}, {dy10,dy12}.{kv10,kv12}, tx10+tx12, -{{y01,dy01}.{dx10,x10},{y21,dy21}.{dx12,x12}}.{kv10,kv12}, -{{z10+l1,dz01}.{dx10,x10},{z12-l2,dz21}.{dx12,x12}}.{kh10,kh12}, 0, z21 kh12, -dy21 kv12, -ctx12, {y21,dy21}.{dx21,x21} kv12, {z12-l2,dz21}.{dx21,x21} kh12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {{z10,z12}.{kh10,kh12}, 0, -{dx10,dx12}.{kv10,kv12}, -{{x01,dx01}.{dy10,y10}, {x21,dx21}.{dy12,y12}}.{kv10,kv12}, ty10+ty12, -{{z10+l1,dz01}.{dy10,y10},{z12-l2,dz21}.{dy12,y12}}.{kh10,kh12}, -z21 kh12, 0, dx21 kv12, {x21,dx21}.{dy21,y21} kv12, -cty12, {z12-l2,dz21}.{dy21,y21} kh12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-{dy10,dy12}.{kh10,kh12}, {dx10,dx12}.{kh10,kh12}, 0, -{{x01,dx01}.{dz10,z10}, {x21,dx21}.{dz12,z12}}.{kh10,kh12}, -{{y01,dy01}.{dz10,z10},{y21,dy21}.{dz12,z12}}.{kh10,kh12}, tz10+tz12, dy21 kh12, -dx21 kh12, 0, {x21,dx21}.{dz21,z21} kh12, {y21,dy21}.{dz21,z21} kh12, -ctz12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-kh21, 0, 0, 0, -z12 kh21, dy12 kh21, kh21+kh23, 0, 0, 0, {z21,z23}.{kh21,kh23}, -{dy21,dy23}.{kh21,kh23}, -kh23, 0, 0, 0, -z32 kh23, dy32 kh23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -kh21, 0, z12 kh21, 0, -dx12 kh21, 0, kh21+kh23, 0, -{z21,z23}.{kh21,kh23}, 0, {dx21,dx23}.{kh21,kh23}, 0, -kh23, 0, z32 kh23, 0, -dx32 kh23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -kv21, -dy12 kv21, dx12 kv21, 0, 0, 0, kv21+kv23, {dy21,dy23}.{kv21,kv23}, -{dx21,dx23}.{kv21,kv23}, 0, 0, 0, -kv23, -dy32 kv23, dx32 kv23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, z12 kh21, -dy12 kv21, -ctx21, {y12,dy12}.{dx12,x12} kv21, {z21+l2,dz12}.{dx12,x12} kh21, 0, -{z21,z23}.{kh21,kh23}, {dy21,dy23}.{kv21,kv23}, tx21+tx23, -{{y12,dy12}.{dx21,x21} ,{y32,dy32}.{dx23,x23}}.{kv21,kv23}, -{{z21+l2,dz12}.{dx21,x21},{z23-l3,dz32}.{dx23,x23}}.{kh21,kh23}, 0, z32 kh23, -dy32 kv23, -ctx23, {y32,dy32}.{dx32,x32} kv23, {z23-l3,dz32}.{dx32,x32} kh23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-z12 kh21, 0, dx12 kv21, {x12,dx12}.{dy12,y12} kv21, -cty21, {z21+l2,dz12}.{dy12,y12} kh21, {z21,z23}.{kh21,kh23}, 0, -{dx21,dx23}.{kv21,kv23}, -{{x12,dx12}.{dy21,y21},{x32,dx32}.{dy23,y23}}.{kv21,kv23}, ty21+ty23, -{{z21+l2,dz12}.{dy21,y21},{z23-l3,dz32}.{dy23,y23}}.{kh21,kh23}, -z32 kh23, 0, dx32 kv23, {x32,dx32}.{dy32,y32} kv23, -cty23, {z23-l3,dz32}.{dy32,y32} kh23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {dy12 kh21, -dx12 kh21, 0, {x12,dx12}.{dz12,z12} kh21, {y12,dy12}.{dz12,z12} kh21, -ctz21, -{dy21,dy23}.{kh21,kh23}, {dx21,dx23}.{kh21,kh23}, 0, -{{x12,dx12}.{dz21,z21},{x32,dx32}.{dz23,z23}}.{kh21,kh23}, -{{y12,dy12}.{dz21,z21} ,{y32,dy32}.{dz23,z23}}.{kh21,kh23}, tz21+tz23, dy32 kh23, -dx32 kh23, 0, {x32,dx32}.{dz32,z32} kh23, {y32,dy32}.{dz32,z32} kh23, -ctz23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -kh32, 0, 0, 0, -z23 kh32, dy23 kh32, kh32+kh34, 0, 0, 0, {z32,z34}.{kh32,kh34}, -{dy32,dy34}.{kh32,kh34}, -kh34, 0, 0, 0, -z43 kh34, dy43 kh34, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, -kh32, 0, z23 kh32, 0, -dx23 kh32, 0, kh32+kh34, 0, -{z32,z34}.{kh32,kh34}, 0, {dx32,dx34}.{kh32,kh34}, 0, -kh34, 0, z43 kh34, 0, -dx43 kh34, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -kv32, -dy23 kv32, dx23 kv32, 0, 0, 0, kv32+kv34, {dy32,dy34}.{kv32,kv34}, -{dx32,dx34}.{kv32,kv34}, 0, 0, 0, -kv34, -dy43 kv34, dx43 kv34, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, z23 kh32, -dy23 kv32, -ctx32, {y23,dy23}.{dx23,x23} kv32, {z32+l3,dz23}.{dx23,x23} kh32, 0, -{z32,z34}.{kh32,kh34}, {dy32,dy34}.{kv32,kv34}, tx32+tx34, -{{y23,dy23}.{dx32,x32},{y43,dy43}.{dx34,x34}}.{kv32,kv34}, -{{z32+l3,dz23}.{dx32,x32},{z34-l4,dz43}.{dx34,x34}}.{kh32,kh34}, 0, z43 kh34, -dy43 kv34, -ctx34, {y43,dy43}.{dx43,x43} kv34, {z34-l4,dz43}.{dx43,x43} kh34, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -z23 kh32, 0, dx23 kv32, {x23,dx23}.{dy23,y23} kv32, -cty32, {z32+l3,dz23}.{dy23,y23} kh32, {z32,z34}.{kh32,kh34}, 0, -{dx32,dx34}.{kv32,kv34}, -{{x23,dx23}.{dy32,y32},{x43,dx43}.{dy34,y34}}.{kv32,kv34}, ty32+ty34, -{{z32+l3,dz23}.{dy32,y32},{z34-l4,dz43}.{dy34,y34}}.{kh32,kh34}, -z43 kh34, 0, dx43 kv34, {x43,dx43}.{dy43,y43} kv34, -cty34, {z34-l4,dz43}.{dx43,x43} kh34, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, dy23 kh32, -dx23 kh32, 0, {x23,dx23}.{dz23,z23} kh32, {y23,dy23}.{dz23,z23} kh32, -ctz32, -{dy32,dy34}.{kh32,kh34}, {dx32,dx34}.{kh32,kh34}, 0, -{{x23,dx23}.{dz32,z32},{x43,dx43}.{dz34,z34}}.{kh32,kh34}, -{{y23,dy23}.{dz32,z32},{y43,dy43}.{dz34,z34}}.{kh32,kh34}, tz32+tz34, dy43 kh34, -dx43 kh34, 0, {x43,dx43}.{dz43,z43} kh34, {y43,dy43}.{dz43,z43} kh34, -ctz34, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kh43, 0, 0, 0, -z34 kh43, dy34 kh43, kh43, 0, 0, 0, {z43}.{kh43}, -{dy43}.{kh43}, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kh43, 0, z34 kh43, 0, -dx34 kh43, 0, kh43, 0, -{z43}.{kh43}, 0, {dx43}.{kh43}, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kv43, -dy34 kv43, dx34 kv43, 0, 0, 0, kv43, {dy43}.{kv43}, -{dx43}.{kv43}, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z34 kh43, -dy34 kv43, -ctx43, {y34,dy34}.{dx34,x34} kv43, {z43+l4,dz34}.{dx34,x34} kh43, 0, -{z43}.{kh43}, {dy43}.{kv43}, tx43, -{y34,dy34}.{dx43,x43} kv43, -{z43+l4,dz34}.{dx43,x43} kh43, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -z34 kh43, 0, dx34 kv43, {x34,dx34}.{dy34,y34} kv43, -cty43, {z43+l4,dz34}.{dy34,y34} kh43, {z43}.{kh43}, 0, -{dx43}.{kv43}, -{x34,dx34}.{dy43,y43} kv43, ty43, -{z43+l4,dz34}.{dx43,x43} kh43, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, dy34 kh43, -dx34 kh43, 0, {x34,dx34}.{dz34,z34} kh43, {y34,dy34}.{dz34,z34} kh43, -ctz43, -{dy43}.{kh43}, {dx43}.{kh43}, 0, -{x34,dx34}.{dz43,z43} kh43, -{y34,dy34}.{dz43,z43} kh43, tz43, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd20}.{khd20}, -{dyd20}.{khd20}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd20}.{khd20}, 0, {dxd20}.{khd20}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, {dyd20}.{kvd20}, -{dxd20}.{kvd20}, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd20}.{khd20}, {dyd20}.{kvd20}, txd20, -{yd02,dyd02}.{dxd20,xd20} kvd20, -{zd20+ld2,dzd02}.{dxd20,xd20} khd20}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd20}.{khd20}, 0, -{dxd20}.{kvd20}, -{xd02,dxd02}.{dyd20,yd20} kvd20, tyd20, -{zd20+ld2,dzd02}.{dyd20,yd20} khd20}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{dyd20}.{khd20}, {dxd20}.{khd20}, 0, -{xd02,dxd02}.{dzd20,zd20} khd20, -{yd02,dyd02}.{dxd20,xd20} khd20, tzd20}}))+I 2 Pi f(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, ix2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ix2 d2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iy2 d2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iz2 d2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, -ixd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixd2 d2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iyd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyd2 d2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -izd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izd2 d2}}))

(({{kh10+kh12, 0, 0, 0, {z10,z12}.{kh10,kh12}, -{dy10,dy12}.{kh10,kh12}, -kh12, 0, 0, 0, -z21 kh12, dy21 kh12}, {0, kh10+kh12, 0, -{z10,z12}.{kh10,kh12}, 0, {dx10,dx12}.{kh10,kh12}, 0, -kh12, 0, z21 kh12, 0, -dx21 kh12}, {0, 0, kv10+kv12, {dy10,dy12}.{kv10,kv12}, -{dx10,dx12}.{kv10,kv12}, 0, 0, 0, -kv12, -dy21 kv12, dx21 kv12, 0}, {0, -{z10,z12}.{kh10,kh12}, {dy10,dy12}.{kv10,kv12}, tx10+tx12, -{{y01,dy01}.{dx10,x10},{y21,dy21}.{dx12,x12}}.{kv10,kv12}, -{{z10+l1,dz01}.{dx10,x10},{z12-l2,dz21}.{dx12,x12}}.{kh10,kh12}, 0, z21 kh12, -dy21 kv12, -ctx12, {y21,dy21}.{dx21,x21} kv12, {z12-l2,dz21}.{dx21,x21} kh12}, {{z10,z12}.{kh10,kh12}, 0, -{dx10,dx12}.{kv10,kv12}, -{{x01,dx01}.{dy10,y10}, {x21,dx21}.{dy12,y12}}.{kv10,kv12}, ty10+ty12, -{{z10+l1,dz01}.{dy10,y10},{z12-l2,dz21}.{dy12,y12}}.{kh10,kh12}, -z21 kh12, 0, dx21 kv12, {x21,dx21}.{dy21,y21} kv12, -cty12, {z12-l2,dz21}.{dy21,y21} kh12}, {-{dy10,dy12}.{kh10,kh12}, {dx10,dx12}.{kh10,kh12}, 0, -{{x01,dx01}.{dz10,z10}, {x21,dx21}.{dz12,z12}}.{kh10,kh12}, -{{y01,dy01}.{dz10,z10},{y21,dy21}.{dz12,z12}}.{kh10,kh12}, tz10+tz12, dy21 kh12, -dx21 kh12, 0, {x21,dx21}.{dz21,z21} kh12, {y21,dy21}.{dz21,z21} kh12, -ctz12}, {-kh21, 0, 0, 0, -z12 kh21, dy12 kh21, kh21+kh23, 0, 0, 0, {z21,z23}.{kh21,kh23}, -{dy21,dy23}.{kh21,kh23}}, {0, -kh21, 0, z12 kh21, 0, -dx12 kh21, 0, kh21+kh23, 0, -{z21,z23}.{kh21,kh23}, 0, {dx21,dx23}.{kh21,kh23}}, {0, 0, -kv21, -dy12 kv21, dx12 kv21, 0, 0, 0, kv21+kv23, {dy21,dy23}.{kv21,kv23}, -{dx21,dx23}.{kv21,kv23}, 0}, {0, z12 kh21, -dy12 kv21, -ctx21, {y12,dy12}.{dx12,x12} kv21, {z21+l2,dz12}.{dx12,x12} kh21, 0, -{z21,z23}.{kh21,kh23}, {dy21,dy23}.{kv21,kv23}, tx21+tx23, -{{y12,dy12}.{dx21,x21} ,{y32,dy32}.{dx23,x23}}.{kv21,kv23}, -{{z21+l2,dz12}.{dx21,x21},{z23-l3,dz32}.{dx23,x23}}.{kh21,kh23}}, {-z12 kh21, 0, dx12 kv21, {x12,dx12}.{dy12,y12} kv21, -cty21, {z21+l2,dz12}.{dy12,y12} kh21, {z21,z23}.{kh21,kh23}, 0, -{dx21,dx23}.{kv21,kv23}, -{{x12,dx12}.{dy21,y21},{x32,dx32}.{dy23,y23}}.{kv21,kv23}, ty21+ty23, -{{z21+l2,dz12}.{dy21,y21},{z23-l3,dz32}.{dy23,y23}}.{kh21,kh23}}, {dy12 kh21, -dx12 kh21, 0, {x12,dx12}.{dz12,z12} kh21, {y12,dy12}.{dz12,z12} kh21, -ctz21, -{dy21,dy23}.{kh21,kh23}, {dx21,dx23}.{kh21,kh23}, 0, -{{x12,dx12}.{dz21,z21},{x32,dx32}.{dz23,z23}}.{kh21,kh23}, -{{y12,dy12}.{dz21,z21} ,{y32,dy32}.{dz23,z23}}.{kh21,kh23}, tz21+tz23}, {0, 0, 0, 0, 0, 0, -kh32, 0, 0, 0, -z23 kh32, dy23 kh32}, {0, 0, 0, 0, 0, 0, 0, -kh32, 0, z23 kh32, 0, -dx23 kh32}, {0, 0, 0, 0, 0, 0, 0, 0, -kv32, -dy23 kv32, dx23 kv32, 0}, {0, 0, 0, 0, 0, 0, 0, z23 kh32, -dy23 kv32, -ctx32, {y23,dy23}.{dx23,x23} kv32, {z32+l3,dz23}.{dx23,x23} kh32}, {0, 0, 0, 0, 0, 0, -z23 kh32, 0, dx23 kv32, {x23,dx23}.{dy23,y23} kv32, -cty32, {z32+l3,dz23}.{dy23,y23} kh32}, {0, 0, 0, 0, 0, 0, dy23 kh32, -dx23 kh32, 0, {x23,dx23}.{dz23,z23} kh32, {y23,dy23}.{dz23,z23} kh32, -ctz32}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}));

(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-kh23, 0, 0, 0, -z32 kh23, dy32 kh23, 0, 0, 0, 0, 0, 0}, {0, -kh23, 0, z32 kh23, 0, -dx32 kh23, 0, 0, 0, 0, 0, 0}, {0, 0, -kv23, -dy32 kv23, dx32 kv23, 0, 0, 0, 0, 0, 0, 0}, {0, z32 kh23, -dy32 kv23, -ctx23, {y32,dy32}.{dx32,x32} kv23, {z23-l3,dz32}.{dx32,x32} kh23, 0, 0, 0, 0, 0, 0}, {-z32 kh23, 0, dx32 kv23, {x32,dx32}.{dy32,y32} kv23, -cty23, {z23-l3,dz32}.{dy32,y32} kh23, 0, 0, 0, 0, 0, 0}, {dy32 kh23, -dx32 kh23, 0, {x32,dx32}.{dz32,z32} kh23, {y32,dy32}.{dz32,z32} kh23, -ctz23, 0, 0, 0, 0, 0, 0}, {kh32+kh34, 0, 0, 0, {z32,z34}.{kh32,kh34}, -{dy32,dy34}.{kh32,kh34}, -kh34, 0, 0, 0, -z43 kh34, dy43 kh34}, {0, kh32+kh34, 0, -{z32,z34}.{kh32,kh34}, 0, {dx32,dx34}.{kh32,kh34}, 0, -kh34, 0, z43 kh34, 0, -dx43 kh34}, {0, 0, kv32+kv34, {dy32,dy34}.{kv32,kv34}, -{dx32,dx34}.{kv32,kv34}, 0, 0, 0, -kv34, -dy43 kv34, dx43 kv34, 0}, {0, -{z32,z34}.{kh32,kh34}, {dy32,dy34}.{kv32,kv34}, tx32+tx34, -{{y23,dy23}.{dx32,x32},{y43,dy43}.{dx34,x34}}.{kv32,kv34}, -{{z32+l3,dz23}.{dx32,x32},{z34-l4,dz43}.{dx34,x34}}.{kh32,kh34}, 0, z43 kh34, -dy43 kv34, -ctx34, {y43,dy43}.{dx43,x43} kv34, {z34-l4,dz43}.{dx43,x43} kh34}, {{z32,z34}.{kh32,kh34}, 0, -{dx32,dx34}.{kv32,kv34}, -{{x23,dx23}.{dy32,y32},{x43,dx43}.{dy34,y34}}.{kv32,kv34}, ty32+ty34, -{{z32+l3,dz23}.{dy32,y32},{z34-l4,dz43}.{dy34,y34}}.{kh32,kh34}, -z43 kh34, 0, dx43 kv34, {x43,dx43}.{dy43,y43} kv34, -cty34, {z34-l4,dz43}.{dx43,x43} kh34}, {-{dy32,dy34}.{kh32,kh34}, {dx32,dx34}.{kh32,kh34}, 0, -{{x23,dx23}.{dz32,z32},{x43,dx43}.{dz34,z34}}.{kh32,kh34}, -{{y23,dy23}.{dz32,z32},{y43,dy43}.{dz34,z34}}.{kh32,kh34}, tz32+tz34, dy43 kh34, -dx43 kh34, 0, {x43,dx43}.{dz43,z43} kh34, {y43,dy43}.{dz43,z43} kh34, -ctz34}, {-kh43, 0, 0, 0, -z34 kh43, dy34 kh43, kh43, 0, 0, 0, {z43}.{kh43}, -{dy43}.{kh43}}, {0, -kh43, 0, z34 kh43, 0, -dx34 kh43, 0, kh43, 0, -{z43}.{kh43}, 0, {dx43}.{kh43}}, {0, 0, -kv43, -dy34 kv43, dx34 kv43, 0, 0, 0, kv43, {dy43}.{kv43}, -{dx43}.{kv43}, 0}, {0, z34 kh43, -dy34 kv43, -ctx43, {y34,dy34}.{dx34,x34} kv43, {z43+l4,dz34}.{dx34,x34} kh43, 0, -{z43}.{kh43}, {dy43}.{kv43}, tx43, -{y34,dy34}.{dx43,x43} kv43, -{z43+l4,dz34}.{dx43,x43} kh43}, {-z34 kh43, 0, dx34 kv43, {x34,dx34}.{dy34,y34} kv43, -cty43, {z43+l4,dz34}.{dy34,y34} kh43, {z43}.{kh43}, 0, -{dx43}.{kv43}, -{x34,dx34}.{dy43,y43} kv43, ty43, -{z43+l4,dz34}.{dx43,x43} kh43}, {dy34 kh43, -dx34 kh43, 0, {x34,dx34}.{dz34,z34} kh43, {y34,dy34}.{dz34,z34} kh43, -ctz43, -{dy43}.{kh43}, {dx43}.{kh43}, 0, -{x34,dx34}.{dz43,z43} kh43, -{y34,dy34}.{dz43,z43} kh43, tz43}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}));

(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd20}.{khd20}, -{dyd20}.{khd20}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd20}.{khd20}, 0, {dxd20}.{khd20}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, {dyd20}.{kvd20}, -{dxd20}.{kvd20}, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd20}.{khd20}, {dyd20}.{kvd20}, txd20, -{yd02,dyd02}.{dxd20,xd20} kvd20, -{zd20+ld2,dzd02}.{dxd20,xd20} khd20}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd20}.{khd20}, 0, -{dxd20}.{kvd20}, -{xd02,dxd02}.{dyd20,yd20} kvd20, tyd20, -{zd20+ld2,dzd02}.{dyd20,yd20} khd20}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{dyd20}.{khd20}, {dxd20}.{khd20}, 0, -{xd02,dxd02}.{dzd20,zd20} khd20, -{yd02,dyd02}.{dxd20,xd20} khd20, tzd20}}));

parameter set

{f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,x23_,y23_,z23_,x32_,y32_,z32_,x34_,y34_,z34_,x43_,y43_,z43_,
xd02_,yd02_,zd02_,
xd20_,yd20_,zd20_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dx23_,dy23_,dz23_,dx32_,dy32_,dz32_,dx34_,dy34_,dz34_,dx43_,dy43_,dz43_,
dxd02_,dyd02_,dzd02_,
dxd20_,dyd20_,dzd20_,
l1_,l2_,l3_,l4_,ld2_,
d2_}

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,x23,y23,z23,x32,y32,z32,x34,y34,z34,x43,y43,z43,
xd02,yd02,zd02,
xd20,yd20,zd20,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dx23,dy23,dz23,dx32,dy32,dz32,dx34,dy34,dz34,dx43,dy43,dz43,
dxd02,dyd02,dzd02,
dxd20,dyd20,dzd20,
l1,l2,l3,l4,ld2,
d2}

TRF, seismoc noise & thermal noise

matForceQuad[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,x23_,y23_,z23_,x32_,y32_,z32_,x34_,y34_,z34_,x43_,y43_,z43_,
xd02_,yd02_,zd02_,
xd20_,yd20_,zd20_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dx23_,dy23_,dz23_,dx32_,dy32_,dz32_,dx34_,dy34_,dz34_,dx43_,dy43_,dz43_,
dxd02_,dyd02_,dzd02_,
dxd20_,dyd20_,dzd20_,
l1_,l2_,l3_,l4_,ld2_,
d2_]:=(({{kh10, 0, 0, 0, z01 kh10, -dy01 kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd02}.{khd20}, -{dyd02}.{khd20}}, {0, kh10, 0, -z01 kh10, 0, dx01 kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd02}.{khd20}, 0, {dxd02}.{khd20}}, {0, 0, kv10, dy01 kv10, -dx01 kv10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, {dyd02}.{kvd20}, -{dxd02}.{kvd20}, 0}, {0, -z01 kh10, dy01 kv10, ctx10, -{y01,dy01}.{dx01,x01} kv10, -{z10+l1,dz01}.{dx01,x01} kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd02}.{khd20}, {dyd02}.{kvd20}, txd20, -{yd02,dyd02}.{dxd02,xd02} kvd20, -{zd20+ld2,dzd02}.{dxd02,xd02} khd20}, {z01 kh10, 0, -dx01 kv10, -{x01,dx01}.{dy01,y01} kv10, cty10, -{z10+l1,dz01}.{dy01,y01} kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd02}.{khd20}, 0, -{dxd02}.{kvd20}, -{xd02,dxd02}.{dyd02,yd02} kvd20, tyd20, -{zd20+ld2,dzd02}.{dyd02,yd02} khd20}, {-dy01 kh10, dx01 kh10, 0, -{x01,dx01}.{dz01,z01} kh10, -{y01,dy01}.{dz01,z01} kh10, ctz10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{dyd02}.{khd20}, {dxd02}.{khd20}, 0, -{xd02,dxd02}.{dzd02,zd02} khd20, -{yd02,dyd02}.{dzd02,zd02} khd20, tzd20}}))

matSeisQuad[f_]:=(({{seisK[f]}, {seisK[f]}, {seisK[f]}, {seisKRot[f]}, {seisKRot[f]}, {seisKRot[f]}}))

trfAmpQuad[a_,b_,c_,d_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,x23_,y23_,z23_,x32_,y32_,z32_,x34_,y34_,z34_,x43_,y43_,z43_,
xd02_,yd02_,zd02_,
xd20_,yd20_,zd20_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dx23_,dy23_,dz23_,dx32_,dy32_,dz32_,dx34_,dy34_,dz34_,dx43_,dy43_,dz43_,
dxd02_,dyd02_,dzd02_,
dxd20_,dyd20_,dzd20_,
l1_,l2_,l3_,l4_,ld2_,
d2_

] :=Abs[Part[Inverse[matQuad[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,x23,y23,z23,x32,y32,z32,x34,y34,z34,x43,y43,z43,
xd02,yd02,zd02,
xd20,yd20,zd20,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dx23,dy23,dz23,dx32,dy32,dz32,dx34,dy34,dz34,dx43,dy43,dz43,
dxd02,dyd02,dzd02,
dxd20,dyd20,dzd20,
l1,l2,l3,l4,ld2,
d2]],(6(d-1)+c),(6(b-1)+a)]]/Abs[Part[Inverse[matQuad[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,x23,y23,z23,x32,y32,z32,x34,y34,z34,x43,y43,z43,
xd02,yd02,zd02,
xd20,yd20,zd20,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dx23,dy23,dz23,dx32,dy32,dz32,dx34,dy34,dz34,dx43,dy43,dz43,
dxd02,dyd02,dzd02,
dxd20,dyd20,dzd20,
l1,l2,l3,l4,ld2,
d2]],(6(b-1)+a),(6(b-1)+a)]]

(*amplitude to amplitude trf from direction "a" of mass "b" to direction "c" of mass "d".*)

trfSeisQuad[a_,b_,c_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,x23_,y23_,z23_,x32_,y32_,z32_,x34_,y34_,z34_,x43_,y43_,z43_,
xd02_,yd02_,zd02_,
xd20_,yd20_,zd20_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dx23_,dy23_,dz23_,dx32_,dy32_,dz32_,dx34_,dy34_,dz34_,dx43_,dy43_,dz43_,
dxd02_,dyd02_,dzd02_,
dxd20_,dyd20_,dzd20_,
l1_,l2_,l3_,l4_,ld2_,
d2_

] :=Abs[Part[Inverse[matQuad[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,x23,y23,z23,x32,y32,z32,x34,y34,z34,x43,y43,z43,
xd02,yd02,zd02,
xd20,yd20,zd20,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dx23,dy23,dz23,dx32,dy32,dz32,dx34,dy34,dz34,dx43,dy43,dz43,
dxd02,dyd02,dzd02,
dxd20,dyd20,dzd20,
l1,l2,l3,l4,ld2,
d2]].

Part[matForceQuad[f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,x23,y23,z23,x32,y32,z32,x34,y34,z34,x43,y43,z43,
xd02,yd02,zd02,
xd20,yd20,zd20,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dx23,dy23,dz23,dx32,dy32,dz32,dx34,dy34,dz34,dx43,dy43,dz43,
dxd02,dyd02,dzd02,
dxd20,dyd20,dzd20,
l1,l2,l3,l4,ld2,
d2],a],(6(c-1)+b)]]

(*transfer function a to b.
c: interesting item.
a, b= 1 -> X to X*)

seisQuad[a_,b_,c_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,x23_,y23_,z23_,x32_,y32_,z32_,x34_,y34_,z34_,x43_,y43_,z43_,
xd02_,yd02_,zd02_,
xd20_,yd20_,zd20_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dx23_,dy23_,dz23_,dx32_,dy32_,dz32_,dx34_,dy34_,dz34_,dx43_,dy43_,dz43_,
dxd02_,dyd02_,dzd02_,
dxd20_,dyd20_,dzd20_,
l1_,l2_,l3_,l4_,ld2_,
d2_

]:=trfSeisQuad[a,b,c,f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,x23,y23,z23,x32,y32,z32,x34,y34,z34,x43,y43,z43,
xd02,yd02,zd02,
xd20,yd20,zd20,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dx23,dy23,dz23,dx32,dy32,dz32,dx34,dy34,dz34,dx43,dy43,dz43,
dxd02,dyd02,dzd02,
dxd20,dyd20,dzd20,
l1,l2,l3,l4,ld2,
d2] *Part[matSeisQuad[f],a] 

(*seismicnoise: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

tNoiseQuad[a_,b_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
x01_,y01_,z01_,
x10_,y10_,z10_,x12_,y12_,z12_,x21_,y21_,z21_,x23_,y23_,z23_,x32_,y32_,z32_,x34_,y34_,z34_,x43_,y43_,z43_,
xd02_,yd02_,zd02_,
xd20_,yd20_,zd20_,
dx01_,dy01_,dz01_,
dx10_,dy10_,dz10_,dx12_,dy12_,dz12_,dx21_,dy21_,dz21_,dx23_,dy23_,dz23_,dx32_,dy32_,dz32_,dx34_,dy34_,dz34_,dx43_,dy43_,dz43_,
dxd02_,dyd02_,dzd02_,
dxd20_,dyd20_,dzd20_,
l1_,l2_,l3_,l4_,ld2_,
d2_
]:=Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matQuad[f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,x23,y23,z23,x32,y32,z32,x34,y34,z34,x43,y43,z43,
xd02,yd02,zd02,
xd20,yd20,zd20,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dx23,dy23,dz23,dx32,dy32,dz32,dx34,dy34,dz34,dx43,dy43,dz43,
dxd02,dyd02,dzd02,
dxd20,dyd20,dzd20,
l1,l2,l3,l4,ld2,
d2]]],6(b-1)+a,6(b-1)+a]]

(*thermal noise: thermal noise in "b" direction caused by flctuation force in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

Matrix & displacement of full suspension (OLD)

heat link suspension + main suspension (X - Pitch, Y - Roll)

matrix

matXPYR[f_,
m1_,i1_,m2_,i2_,m3_,i3_,m4_,i4_,m5_,i5_,m6_,i6_,m7_,i7_,md2_,id2_,md5_,id5_,
k10_,k13_,k31_,k36_,k63_,
g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
tk10_,tk13_,tk31_,tk36_,tk63_,
tg10_,tg20_,tg23_,tg32_,tg40_,tg45_,tg54_,tg56_,tg65_,tg67_,tg76_,tgm20_,tgm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
zk01_,zk10_,zk13_,zk31_,zk36_,zk63_,
zg01_,zg10_,zg02_,zg20_,zg23_,zg32_,zg04_,zg40_,zg45_,zg54_,zg56_,zg65_,zg67_,zg76_,zgm02_,zgm20_,zgm05_,zgm50_,
d1_,d2_,d3_,d4_,d5_] :=
-(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, i1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, i2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, i3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, i4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m5, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, i5, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m6, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, i6, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m7, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, i7, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, id2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md5, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, id5}}))+(({{g10+k10+k13, {g10,k10,k13}.{zg10,zk10,zk13}, 0, 0, -k13, -k13 zk31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {{g10,k10,k13}.{zg10,zk10,zk13}, tg10+tk10+tk13, 0, 0, -k13 zk31, -ctk13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, g20+g23, {g20,g23}.{zg20,zg23}, -g23, -g23 zg32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, {g20,g23}.{zg20,zg23}, tg20+tg23, -g23 zg32, -ctg23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-k31, -k31 zk13, -g32, -g32 zg23, g32+k31+k36, {g32,k31,k36}.{zg32,zk31,zk36}, 0, 0, 0, 0, -k36, -k36 zk63, 0, 0, 0, 0, 0, 0}, {-k31 zk13, -ctk31, -g32 zg23, -ctg32, {g32,k31,k36}.{zg32,zk31,zk36}, tg32+tk31+tk36, 0, 0, 0, 0, -k36 zk63, -ctk36, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, g40+g45, {g40,g45}.{zg40,zg45}, -g45, -g45 zg54, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, {g40,g45}.{zg40,zg45}, tg40+tg45, -g45 zg54, -ctg45, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -g54, -g54 zg45, g54+g56, {g54,g56}.{zg54,zg56}, -g56, -g56 zg65, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -g54 zg45, -ctg54, {g54,g56}.{zg54,zg56}, tg54+tg56, -g56 zg65, -ctg56, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, -k63, -k63 zk36, 0, 0, -g65, -g65 zg56, g65+g67+k63, {g65,g67,k63}.{zg65,zg67,zk63}, -g67, -g67 zg76, 0, 0, 0, 0}, {0, 0, 0, 0, -k63 zk36, -ctk63, 0, 0, -g65 zg56, -ctg65, {g65,g67,k63}.{zg65,zg67,zk63}, tg65+tg67+tk63, -g67 zg76, -ctg67, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -g76, -g76 zg67, g76, g76 zg67, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -g76 zg67, -ctg76, g76 zg67, tg76, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, gm20, gm20 zgm20, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, gm20 zgm20, tgm20, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, gm50, gm50 zgm50}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, gm50 zgm50, tgm50}}))+I 2 Pi f* (({{m1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, i1 d1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0}, {0, 0, 0, i2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -i2 d2, 0, 0}, {0, 0, 0, 0, m3 d3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, i3 d3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m4 d4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, i4 d4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m5 d5, 0, 0, 0, 0, 0, 0, 0, -m5 d5, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, i5 d5, 0, 0, 0, 0, 0, 0, 0, -i5 d5}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0}, {0, 0, 0, -id2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, id2 d2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -md5 d5, 0, 0, 0, 0, 0, 0, 0, md5 d5, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, -id5 d5, 0, 0, 0, 0, 0, 0, 0, id5 d5}}))(*matrix of full suspension model of CLIO. see note at 6/2.
f: frequency,
 m1,i1....md5,id5: mass [kg] & moment of inertia [kg m^2],
 k10....k63: spring constant of heat link [N/m],
 g10...gd50: spring constant of wire(horizontal) or vertical spring (vertical) [N/m],
 tg10..tgd50: torque [N m],
 zg10..zgd50: Z position from COM of clamp,
 ckA...: toruque caused by next mass rotation (see note 6/20), 
 d1...d5: velocity damping factor = ω0*phi [rad/sec],
 *)

{f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5};

iMatXPYR[f_,
m1_,i1_,m2_,i2_,m3_,i3_,m4_,i4_,m5_,i5_,m6_,i6_,m7_,i7_,md2_,id2_,md5_,id5_,
k10_,k13_,k31_,k36_,k63_,
g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
tk10_,tk13_,tk31_,tk36_,tk63_,
tg10_,tg20_,tg23_,tg32_,tg40_,tg45_,tg54_,tg56_,tg65_,tg67_,tg76_,tgm20_,tgm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
zk01_,zk10_,zk13_,zk31_,zk36_,zk63_,
zg01_,zg10_,zg02_,zg20_,zg23_,zg32_,zg04_,zg40_,zg45_,zg54_,zg56_,zg65_,zg67_,zg76_,zgm02_,zgm20_,zgm05_,zgm50_,
d1_,d2_,d3_,d4_,d5_] :=

Inverse[matXPYR[f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5]]

transfer function

trfCryoXY[n_,f_,
m1_,i1_,m2_,i2_,m3_,i3_,m4_,i4_,m5_,i5_,m6_,i6_,m7_,i7_,md2_,id2_,md5_,id5_,
k10_,k13_,k31_,k36_,k63_,
g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
tk10_,tk13_,tk31_,tk36_,tk63_,
tg10_,tg20_,tg23_,tg32_,tg40_,tg45_,tg54_,tg56_,tg65_,tg67_,tg76_,tgm20_,tgm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
zk01_,zk10_,zk13_,zk31_,zk36_,zk63_,
zg01_,zg10_,zg02_,zg20_,zg23_,zg32_,zg04_,zg40_,zg45_,zg54_,zg56_,zg65_,zg67_,zg76_,zgm02_,zgm20_,zgm05_,zgm50_,
d1_,d2_,d3_,d4_,d5_] :=

Abs[Part[iMatXPYR[f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5].{k10+I 2 Pi m1  d1 f,k10 zk01,0,0,I 2 Pi m3  d3 f,0,0,0,0,0,0,0,0,0,0,0,0,0},n]]
 (*transfer function from cryostat. *)

trfStageXY[n_,f_,
m1_,i1_,m2_,i2_,m3_,i3_,m4_,i4_,m5_,i5_,m6_,i6_,m7_,i7_,md2_,id2_,md5_,id5_,
k10_,k13_,k31_,k36_,k63_,
g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
tk10_,tk13_,tk31_,tk36_,tk63_,
tg10_,tg20_,tg23_,tg32_,tg40_,tg45_,tg54_,tg56_,tg65_,tg67_,tg76_,tgm20_,tgm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
zk01_,zk10_,zk13_,zk31_,zk36_,zk63_,
zg01_,zg10_,zg02_,zg20_,zg23_,zg32_,zg04_,zg40_,zg45_,zg54_,zg56_,zg65_,zg67_,zg76_,zgm02_,zgm20_,zgm05_,zgm50_,
d1_,d2_,d3_,d4_,d5_] :=

Abs[Part[iMatXPYR[f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5].{g10,g10 zg01,g20,g20 zg02,0,0,g40+I 2 Pi m4  d4 f,g40 zg04,0,0,0,0,0,0,gm20,gm20 zgm02,gm50,gm50 zgm05},n]] 
(*transfer function from stage.*)

trfCryoPR[n_,f_,
m1_,i1_,m2_,i2_,m3_,i3_,m4_,i4_,m5_,i5_,m6_,i6_,m7_,i7_,md2_,id2_,md5_,id5_,
k10_,k13_,k31_,k36_,k63_,
g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
tk10_,tk13_,tk31_,tk36_,tk63_,
tg10_,tg20_,tg23_,tg32_,tg40_,tg45_,tg54_,tg56_,tg65_,tg67_,tg76_,tgm20_,tgm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
zk01_,zk10_,zk13_,zk31_,zk36_,zk63_,
zg01_,zg10_,zg02_,zg20_,zg23_,zg32_,zg04_,zg40_,zg45_,zg54_,zg56_,zg65_,zg67_,zg76_,zgm02_,zgm20_,zgm05_,zgm50_,
d1_,d2_,d3_,d4_,d5_] :=

Abs[Part[iMatXPYR[f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5].{k10 zk01,ctk10 + I 2 Pi i1 d1 f,0,0,0,I 2 Pi i3 d3 f,0,0,0,0,0,0,0,0,0,0,0,0},n]]
 (*transfer function from cryostat. *)

trfStagePR[n_,f_,
m1_,i1_,m2_,i2_,m3_,i3_,m4_,i4_,m5_,i5_,m6_,i6_,m7_,i7_,md2_,id2_,md5_,id5_,
k10_,k13_,k31_,k36_,k63_,
g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
tk10_,tk13_,tk31_,tk36_,tk63_,
tg10_,tg20_,tg23_,tg32_,tg40_,tg45_,tg54_,tg56_,tg65_,tg67_,tg76_,tgm20_,tgm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
zk01_,zk10_,zk13_,zk31_,zk36_,zk63_,
zg01_,zg10_,zg02_,zg20_,zg23_,zg32_,zg04_,zg40_,zg45_,zg54_,zg56_,zg65_,zg67_,zg76_,zgm02_,zgm20_,zgm05_,zgm50_,
d1_,d2_,d3_,d4_,d5_] :=

Abs[Part[iMatXPYR[f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5].{g10 zg01,ctg10,g20 zg02,ctg20,0,0,g40 zg04,ctg40+I 2 Pi i4  d4 f,0,0,0,0,0,0,gm20 zgm02,ctgm20,gm50 zgm05,ctgm50},n]] 
(*transfer function from stage.*)

displacement

dispXY[a_,b_,n_,f_,
m1_,i1_,m2_,i2_,m3_,i3_,m4_,i4_,m5_,i5_,m6_,i6_,m7_,i7_,md2_,id2_,md5_,id5_,
k10_,k13_,k31_,k36_,k63_,
g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
tk10_,tk13_,tk31_,tk36_,tk63_,
tg10_,tg20_,tg23_,tg32_,tg40_,tg45_,tg54_,tg56_,tg65_,tg67_,tg76_,tgm20_,tgm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
zk01_,zk10_,zk13_,zk31_,zk36_,zk63_,
zg01_,zg10_,zg02_,zg20_,zg23_,zg32_,zg04_,zg40_,zg45_,zg54_,zg56_,zg65_,zg67_,zg76_,zgm02_,zgm20_,zgm05_,zgm50_,
d1_,d2_,d3_,d4_,d5_] := 

Sqrt[(a*seisK[f]*trfCryoXY[n,f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5])^2+

(b*seisK[f]*trfStageXY[n,f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5])^2]

radPR[a_,b_,n_,f_,
m1_,i1_,m2_,i2_,m3_,i3_,m4_,i4_,m5_,i5_,m6_,i6_,m7_,i7_,md2_,id2_,md5_,id5_,
k10_,k13_,k31_,k36_,k63_,
g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
tk10_,tk13_,tk31_,tk36_,tk63_,
tg10_,tg20_,tg23_,tg32_,tg40_,tg45_,tg54_,tg56_,tg65_,tg67_,tg76_,tgm20_,tgm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
zk01_,zk10_,zk13_,zk31_,zk36_,zk63_,
zg01_,zg10_,zg02_,zg20_,zg23_,zg32_,zg04_,zg40_,zg45_,zg54_,zg56_,zg65_,zg67_,zg76_,zgm02_,zgm20_,zgm05_,zgm50_,
d1_,d2_,d3_,d4_,d5_] := 

Sqrt[(a*seisKRot[f]*trfCryoPR[n,f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5])^2+

(b*seisKRot[f]*trfStagePR[n,f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5])^2]

dispPR[offset_,a_,b_,n_,f_,
m1_,i1_,m2_,i2_,m3_,i3_,m4_,i4_,m5_,i5_,m6_,i6_,m7_,i7_,md2_,id2_,md5_,id5_,
k10_,k13_,k31_,k36_,k63_,
g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
tk10_,tk13_,tk31_,tk36_,tk63_,
tg10_,tg20_,tg23_,tg32_,tg40_,tg45_,tg54_,tg56_,tg65_,tg67_,tg76_,tgm20_,tgm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
zk01_,zk10_,zk13_,zk31_,zk36_,zk63_,
zg01_,zg10_,zg02_,zg20_,zg23_,zg32_,zg04_,zg40_,zg45_,zg54_,zg56_,zg65_,zg67_,zg76_,zgm02_,zgm20_,zgm05_,zgm50_,
d1_,d2_,d3_,d4_,d5_] := 

covRotDisp[offset,
radPR[a,b,n,f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5]]

thermal noise

tNoiseXY[n_,f_,
m1_,i1_,m2_,i2_,m3_,i3_,m4_,i4_,m5_,i5_,m6_,i6_,m7_,i7_,md2_,id2_,md5_,id5_,
k10_,k13_,k31_,k36_,k63_,
g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
tk10_,tk13_,tk31_,tk36_,tk63_,
tg10_,tg20_,tg23_,tg32_,tg40_,tg45_,tg54_,tg56_,tg65_,tg67_,tg76_,tgm20_,tgm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
zk01_,zk10_,zk13_,zk31_,zk36_,zk63_,
zg01_,zg10_,zg02_,zg20_,zg23_,zg32_,zg04_,zg40_,zg45_,zg54_,zg56_,zg65_,zg67_,zg76_,zgm02_,zgm20_,zgm05_,zgm50_,
d1_,d2_,d3_,d4_,d5_]:=

Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[iMatXPYR[f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5]],n,n]]

tNoisePR[offset_,n_,f_,
m1_,i1_,m2_,i2_,m3_,i3_,m4_,i4_,m5_,i5_,m6_,i6_,m7_,i7_,md2_,id2_,md5_,id5_,
k10_,k13_,k31_,k36_,k63_,
g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
tk10_,tk13_,tk31_,tk36_,tk63_,
tg10_,tg20_,tg23_,tg32_,tg40_,tg45_,tg54_,tg56_,tg65_,tg67_,tg76_,tgm20_,tgm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
zk01_,zk10_,zk13_,zk31_,zk36_,zk63_,
zg01_,zg10_,zg02_,zg20_,zg23_,zg32_,zg04_,zg40_,zg45_,zg54_,zg56_,zg65_,zg67_,zg76_,zgm02_,zgm20_,zgm05_,zgm50_,
d1_,d2_,d3_,d4_,d5_]:=

covRotDisp[offset,
Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[iMatXPYR[f,
m1,i1,m2,i2,m3,i3,m4,i4,m5,i5,m6,i6,m7,i7,md2,id2,md5,id5,
k10,k13,k31,k36,k63,
g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
tk10,tk13,tk31,tk36,tk63,
tg10,tg20,tg23,tg32,tg40,tg45,tg54,tg56,tg65,tg67,tg76,tgm20,tgm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
zk01,zk10,zk13,zk31,zk36,zk63,
zg01,zg10,zg02,zg20,zg23,zg32,zg04,zg40,zg45,zg54,zg56,zg65,zg67,zg76,zgm02,zgm20,zgm05,zgm50,
d1,d2,d3,d4,d5]],n,n]]]

heat link suspension + main suspension (Z)

matrix

matZ[f_,
m1_,m2_,m3_,m4_,m5_,m6_,m7_,md2_,md5_,
k10_,k13_,k31_,k36_,k63_,g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
d1_,d2_,d3_,d4_,d5_] :=
-(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m2, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m3, 0, 0, 0, 0, 0, 0}, {0, 0, 0, m4, 0, 0, 0, 0, 0}, {0, 0, 0, 0, m5, 0, 0, 0, 0}, {0, 0, 0, 0, 0, m6, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m7, 0, 0}, {0, 0, 0, 0, 0, 0, 0, md2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, md5}}))+(({{g10+k10+k13, 0, -k13, 0, 0, 0, 0, 0, 0}, {0, g20+g23, -g23, 0, 0, 0, 0, 0, 0}, {-k31, -g32, g32+k31+k36, 0, 0, -k36, 0, 0, 0}, {0, 0, 0, g40+g45, -g45, 0, 0, 0, 0}, {0, 0, 0, -g54, g54+g56, -g56, 0, 0, 0}, {0, 0, -k63, 0, -g65, g65+g67+k63, -g67, 0, 0}, {0, 0, 0, 0, 0, -g76, g76, 0, 0}, {0, 0, 0, 0, 0, 0, 0, gm20, 0}, {0, 0, 0, 0, 0, 0, 0, 0, gm50 }}))+I 2 Pi f (({{m1 d1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m2 d2, 0, 0, 0, 0, 0, -m2 d2, 0}, {0, 0, m3 d3, 0, 0, 0, 0, 0, 0}, {0, 0, 0, m4 d4, 0, 0, 0, 0, 0}, {0, 0, 0, 0, m5 d5, 0, 0, 0, -m5 d5}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -md2 d2, 0, 0, 0, 0, 0, md2 d2, 0}, {0, 0, 0, 0, -md5 d5, 0, 0, 0, md5 d5}}))
(*matrix of full suspension model of CLIO. see note at 6/2.
f: frequency,
 m1,i1....md5,id5: mass [kg] & moment of inertia [kg m^2],
 k10....k63: spring constant of heat link [N/m],
 g10...gd50: spring constant of wire(horizontal) or vertical spring (vertical) [N/m],
 d1...d5: velocity damping factor = ω0*phi [rad/sec],
 *)

{f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
d1,d2,d3,d4,d5};

transfer function

trfCryoZ[n_,
f_,
m1_,m2_,m3_,m4_,m5_,m6_,m7_,md2_,md5_,
k10_,k13_,k31_,k36_,k63_,g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
d1_,d2_,d3_,d4_,d5_] :=

Abs[Part[Inverse[matZ[f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
d1,d2,d3,d4,d5]].{k10+I 2 Pi m1  d1 f,0,I 2 Pi m3  d3 f,0,0,0,0,0,0},n]] (*transfer function from cryostat*)

trfStageZ[n_,
f_,
m1_,m2_,m3_,m4_,m5_,m6_,m7_,md2_,md5_,
k10_,k13_,k31_,k36_,k63_,g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
d1_,d2_,d3_,d4_,d5_] :=

Abs[Part[Inverse[matZ[f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
d1,d2,d3,d4,d5]].{g10,g20,0,g40+I 2 Pi m4  d4 f,0,0,0,gm20,gm50},n]] (*transfer function from stage*)

displacement

dispZ[a_,b_,n_,
f_,
m1_,m2_,m3_,m4_,m5_,m6_,m7_,md2_,md5_,
k10_,k13_,k31_,k36_,k63_,g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
d1_,d2_,d3_,d4_,d5_] := 

Sqrt[(a*seisK[f]*trfCryoZ[n,f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
d1,d2,d3,d4,d5])^2+

(b*seisK[f]*trfStageZ[n,f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
d1,d2,d3,d4,d5])^2]

thermal noise

tNoiseZ[n_,
f_,
m1_,m2_,m3_,m4_,m5_,m6_,m7_,md2_,md5_,
k10_,k13_,k31_,k36_,k63_,g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
d1_,d2_,d3_,d4_,d5_]:=

Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matZ[f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
d1,d2,d3,d4,d5]]],n,n]]

heat link suspension + main suspension (Yaw)

matrix

matYaw[f_,
m1_,m2_,m3_,m4_,m5_,m6_,m7_,md2_,md5_,
k10_,k13_,k31_,k36_,k63_,g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
d1_,d2_,d3_,d4_,d5_] :=
-(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m2, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m3, 0, 0, 0, 0, 0, 0}, {0, 0, 0, m4, 0, 0, 0, 0, 0}, {0, 0, 0, 0, m5, 0, 0, 0, 0}, {0, 0, 0, 0, 0, m6, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m7, 0, 0}, {0, 0, 0, 0, 0, 0, 0, md2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, md5}}))+(({{g10+k10+k13, 0, -ctk13, 0, 0, 0, 0, 0, 0}, {0, g20+g23, -ctg23, 0, 0, 0, 0, 0, 0}, {-ctk31, -ctg32, g32+k31+k36, 0, 0, -ctk36, 0, 0, 0}, {0, 0, 0, g40+g45, -ctg45, 0, 0, 0, 0}, {0, 0, 0, -ctg54, g54+g56, -ctg56, 0, 0, 0}, {0, 0, -ctk63, 0, -ctg65, g65+g67+k63, -ctg67, 0, 0}, {0, 0, 0, 0, 0, -ctg76, g76, 0, 0}, {0, 0, 0, 0, 0, 0, 0, gm20, 0}, {0, 0, 0, 0, 0, 0, 0, 0, gm50 }}))+I 2 Pi f (({{m1 d1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m2 d2, 0, 0, 0, 0, 0, -m2 d2, 0}, {0, 0, m3 d3, 0, 0, 0, 0, 0, 0}, {0, 0, 0, m4 d4, 0, 0, 0, 0, 0}, {0, 0, 0, 0, m5 d5, 0, 0, 0, -m5 d5}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -md2 d2, 0, 0, 0, 0, 0, md2 d2, 0}, {0, 0, 0, 0, -md5 d5, 0, 0, 0, md5 d5}}))
(*matrix of full suspension model of CLIO. see note at 6/2.
f: frequency,
 m1,i1....md5,id5: mass [kg] & moment of inertia [kg m^2],
 k10....k63: spring constant of heat link [N/m],
 g10...gd50: spring constant of wire(horizontal) or vertical spring (vertical) [N/m],
 ckA...: toruque caused by next mass rotation (see note 6/20), 
 d1...d5: velocity damping factor = ω0*phi [rad/sec],
 *)

{f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
d1,d2,d3,d4,d5};

transfer function

trfCryoYaw[n_,
f_,
m1_,m2_,m3_,m4_,m5_,m6_,m7_,md2_,md5_,
k10_,k13_,k31_,k36_,k63_,g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
d1_,d2_,d3_,d4_,d5_] :=

Abs[Part[Inverse[matYaw[f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
d1,d2,d3,d4,d5]].{ctk10+I 2 Pi m1  d1 f,0,I 2 Pi m3  d3 f,0,0,0,0,0,0},n]] (*transfer function from cryostat*)

trfStageYaw[n_,
f_,
m1_,m2_,m3_,m4_,m5_,m6_,m7_,md2_,md5_,
k10_,k13_,k31_,k36_,k63_,g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
d1_,d2_,d3_,d4_,d5_] :=

Abs[Part[Inverse[matYaw[f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
d1,d2,d3,d4,d5]].{ctg10,ctg20,0,ctg40+I 2 Pi m4  d4 f,0,0,0,ctgm20,ctgm50},n]] (*transfer function from stage*)

displacement

radYaw[a_,b_,n_,
f_,
m1_,m2_,m3_,m4_,m5_,m6_,m7_,md2_,md5_,
k10_,k13_,k31_,k36_,k63_,g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
d1_,d2_,d3_,d4_,d5_] := 

Sqrt[(a*seisKRot[f]*trfCryoYaw[n,f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
d1,d2,d3,d4,d5])^2+

(b*seisKRot[f]*trfStageYaw[n,f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
d1,d2,d3,d4,d5])^2]

dispYaw[offset_,a_,b_,n_,
f_,
m1_,m2_,m3_,m4_,m5_,m6_,m7_,md2_,md5_,
k10_,k13_,k31_,k36_,k63_,g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
d1_,d2_,d3_,d4_,d5_] := 

covRotDisp[offset,
radYaw[a,b,n,f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
d1,d2,d3,d4,d5]]

thermal noise

tNoiseYaw[offset_,n_,
f_,
m1_,m2_,m3_,m4_,m5_,m6_,m7_,md2_,md5_,
k10_,k13_,k31_,k36_,k63_,g10_,g20_,g23_,g32_,g40_,g45_,g54_,g56_,g65_,g67_,g76_,gm20_,gm50_,
ctk10_,ctk13_,ctk31_,ctk36_,ctk63_,
ctg10_,ctg20_,ctg23_,ctg32_,ctg40_,ctg45_,ctg54_,ctg56_,ctg65_,ctg67_,ctg76_,ctgm20_,ctgm50_,
d1_,d2_,d3_,d4_,d5_]:=

covRotDisp[offset,
Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matYaw[f,
m1,m2,m3,m4,m5,m6,m7,md2,md5,
k10,k13,k31,k36,k63,g10,g20,g23,g32,g40,g45,g54,g56,g65,g67,g76,gm20,gm50,
ctk10,ctk13,ctk31,ctk36,ctk63,
ctg10,ctg20,ctg23,ctg32,ctg40,ctg45,ctg54,ctg56,ctg65,ctg67,ctg76,ctgm20,ctgm50,
d1,d2,d3,d4,d5]]],n,n]]]

Matrix & displacement of triple suspension (OLD)

triple suspension (X - Pitch, Y - Roll)

matrix

matXPYR3Pend[f_,
m1_,i1_,m2_,i2_,m3_,i3_,
g10_,g12_,g21_,g23_,g32_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_,
zg01_,zg10_,zg12_,zg21_,zg23_,zg32_
] :=
-(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0}, {0, i1, 0, 0, 0, 0}, {0, 0, m2, 0, 0, 0}, {0, 0, 0, i2, 0, 0}, {0, 0, 0, 0, m3, 0}, {0, 0, 0, 0, 0, i3}}))+(({{g10+g12, {g10,g12}.{zg10,zg12}, -g12, -g12 zg21, 0, 0}, {{g10,g12}.{zg10,zg12}, tg10+tg12, -g12 zg21, -ctg12, 0, 0}, {-g21, -g21 zg12, g21+g23, {g21,g23}.{zg21,zg23}, -g23, -g23 zg32}, {-g21 zg12, -ctg21, {g21,g23}.{zg21,zg23}, tg21+tg23, -g23 zg32, -ctg23}, {0, 0, -g32, -g32 zg23, g32, g32 zg32}, {0, 0, -g32 zg23, -ctg32, g32 zg32, tg32}}))
(*matrix of triple suspension for LCGT thermal noise estimation.
f: frequency,
 m1,i1....: mass [kg] & moment of inertia [kg m^2],

 g10..: spring constant of wire(horizontal) or vertical spring (vertical) [N/m],
 tg10..: torque [N m],
 zg10..: Z position from COM of clamp
 *)

{f,
m1,i1,m2,i2,m3,i3,
g10,g12,g21,g23,g32,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32,
zg01,zg10,zg12,zg21,zg23,zg32};

transfer function

trfXY3Pend[n_,
f_,
m1_,i1_,m2_,i2_,m3_,i3_,
g10_,g12_,g21_,g23_,g32_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_,
zg01_,zg10_,zg12_,zg21_,zg23_,zg32_] :=

Abs[Part[Inverse[matXPYR3Pend[f,
m1,i1,m2,i2,m3,i3,
g10,g12,g21,g23,g32,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32,
zg01,zg10,zg12,zg21,zg23,zg32]].{g10,g10 zg01 ,0,0,0,0},n]]
 (*transfer function from cryostat. *)

trfPR3Pend[n_,
f_,
m1_,i1_,m2_,i2_,m3_,i3_,
g10_,g12_,g21_,g23_,g32_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_,
zg01_,zg10_,zg12_,zg21_,zg23_,zg32_] :=

Abs[Part[Inverse[matXPYR3Pend[f,
m1,i1,m2,i2,m3,i3,
g10,g12,g21,g23,g32,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32,
zg01,zg10,zg12,zg21,zg23,zg32]].{g10 zg01,tg10 ,0,0,0,0},n]]
 (*transfer function from cryostat. *)

displacement

dispXY3Pend[n_,
f_,
m1_,i1_,m2_,i2_,m3_,i3_,
g10_,g12_,g21_,g23_,g32_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_,
zg01_,zg10_,zg12_,zg21_,zg23_,zg32_] := 

Sqrt[(seisK[f]*trfXY3Pend[n,f,
m1,i1,m2,i2,m3,i3,
g10,g12,g21,g23,g32,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32,
zg01,zg10,zg12,zg21,zg23,zg32])^2]

radPR3Pend[n_,
f_,
m1_,i1_,m2_,i2_,m3_,i3_,
g10_,g12_,g21_,g23_,g32_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_,
zg01_,zg10_,zg12_,zg21_,zg23_,zg32_] := 

Sqrt[(seisKRot[f]*trfPR3Pend[n,f,
m1,i1,m2,i2,m3,i3,
g10,g12,g21,g23,g32,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32,
zg01,zg10,zg12,zg21,zg23,zg32])^2]

dispPR3Pend[offset_,n_,
f_,
m1_,i1_,m2_,i2_,m3_,i3_,
g10_,g12_,g21_,g23_,g32_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_,
zg01_,zg10_,zg12_,zg21_,zg23_,zg32_] := 

covRotDisp[offset,
radPR3Pend[n,f,
m1,i1,m2,i2,m3,i3,
g10,g12,g21,g23,g32,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32,
zg01,zg10,zg12,zg21,zg23,zg32]]

thermal noise

tNoiseXY3Pend[n_,
f_,
m1_,i1_,m2_,i2_,m3_,i3_,
g10_,g12_,g21_,g23_,g32_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_,
zg01_,zg10_,zg12_,zg21_,zg23_,zg32_]:=

Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matXPYR3Pend[f,
m1,i1,m2,i2,m3,i3,
g10,g12,g21,g23,g32,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32,
zg01,zg10,zg12,zg21,zg23,zg32]]],n,n]]

tNoisePR3Pend[offset_,n_,
f_,
m1_,i1_,m2_,i2_,m3_,i3_,
g10_,g12_,g21_,g23_,g32_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_,
zg01_,zg10_,zg12_,zg21_,zg23_,zg32_]:=

covRotDisp[offset,
Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matXPYR3Pend[f,
m1,i1,m2,i2,m3,i3,
g10,g12,g21,g23,g32,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32,
zg01,zg10,zg12,zg21,zg23,zg32]]],n,n]]]

triple suspension (Z )

matrix

matZ3Pend[f_,
m1_,m2_,m3_,g10_,g12_,g21_,g23_,g32_] :=
-(2 Pi f)^2*(({{m1, 0, 0}, {0, m2, 0}, {0, 0, m3}}))+(({{g10+g12, -g12, 0}, {-g21, g21+g23, -g23}, {0, -g32, g32}}))
(*matrix of triple suspension for LCGT thermal noise estimation.
f: frequency,
 m1,....: mass [kg] & moment of inertia [kg m^2],
 g10..: spring constant of wire(horizontal) or vertical spring (vertical) [N/m]
 *)

{f,
m1,m2,m3,g10,g12,g21,g23,g32};

transfer function

trfZ3Pend[n_,
f_,
m1_,m2_,m3_,g10_,g12_,g21_,g23_,g32_] :=

Abs[Part[Inverse[matZ3Pend[f,
m1,m2,m3,g10,g12,g21,g23,g32]].{g10,0,0},n]] (*transfer function from cryostat*)

displacement

dispZ3Pend[n_,
f_,
m1_,m2_,m3_,g10_,g12_,g21_,g23_,g32_]:=
 
Sqrt[(seisK[f]*trfZ3Pend[n,f,
m1,m2,m3,g10,g12,g21,g23,g32])^2]

thermal noise

tNoiseZ3Pend[n_,
f_,
m1_,m2_,m3_,g10_,g12_,g21_,g23_,g32_]:=

Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matZ3Pend[f,
m1,m2,m3,g10,g12,g21,g23,g32]]],n,n]]

triple suspension (Yaw)

matrix

matYaw3Pend[f_,
i1_,i2_,i3_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_] :=
-(2 Pi f)^2*(({{i1, 0, 0}, {0, i2, 0}, {0, 0, i3}}))+(({{tg10+tg12, -ctg12, 0}, {-ctg21, tg21+tg23, -ctg23}, {0, -tg32, ctg32}}))
(*matrix of triple suspension for LCGT thermal noise estimation.
f: frequency,
 m1,....: mass [kg] & moment of inertia [kg m^2],
 g10..: spring constant of wire(horizontal) or vertical spring (vertical) [N/m]
 *)

{f,
i1,i2,i3,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32};

transfer function

trfYaw3Pend[n_,
f_,
i1_,i2_,i3_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_] :=

Abs[Part[Inverse[matYaw3Pend[f,
i1,i2,i3,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32]].{ctg10,0,0},n]] (*transfer function from cryostat*)

displacement

radYaw3Pend[n_,
f_,
i1_,i2_,i3_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_] := 

Sqrt[(seisKRot[f]*trfYaw3Pend[n,f,
i1,i2,i3,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32])^2]

dispYaw3Pend[offset_,n_,
f_,
i1_,i2_,i3_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_] := 

covRotDisp[offset,
radYaw3Pend[n,f,
i1,i2,i3,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32]]

thermal noise

tNoiseYaw3Pend[offset_,n_,
f_,
i1_,i2_,i3_,
tg10_,tg12_,tg21_,tg23_,tg32_,
ctg10_,ctg12_,ctg21_,ctg23_,ctg32_]:=

covRotDisp[offset,
Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matYaw3Pend[f,
i1,i2,i3,
tg10,tg12,tg21,tg23,tg32,
ctg10,ctg12,ctg21,ctg23,ctg32]]],n,n]]]

Matrix & displacement of LISM suspension (OLD)

triple suspension (Z - Yaw)

matrix

matZYLISM[f_,
m1_,m2_,m3_,m4_,g10_,g12_,g21_,g23_,g32_,g34_,g43_] :=
-(2 Pi f)^2*(({{m1, 0, 0, 0}, {0, m2, 0, 0}, {0, 0, m3, 0}, {0, 0, 0, m4}}))+(({{g10+g12, -g12, 0, 0}, {-g21, g21+g23, -g23, 0}, {0, -g32, g32+g34, -g34}, {0, 0, -g43, g43}}))
(*matrix of triple suspension for LCGT thermal noise estimation.
f: frequency,
 m1,....: mass [kg] & moment of inertia [kg m^2],
 g10..: spring constant of wire(horizontal) or vertical spring (vertical) [N/m]
 *)

{f,
m1,m2,m3,m4,g10,g12,g21,g23,g32,g34,g43};

transfer function

trfZYLISM[n_,
f_,
m1_,m2_,m3_,m4_,g10_,g12_,g21_,g23_,g32_,g34_,g43_] :=

Abs[Part[Inverse[matZYLISM[f,
m1,m2,m3,m4,g10,g12,g21,g23,g32,g34,g43]].{g10,0,0,0},n]] (*transfer function from cryostat*)

displacement

dispZLISM[n_,
f_,
m1_,m2_,m3_,m4_,g10_,g12_,g21_,g23_,g32_,g34_,g43_]:=
 
Sqrt[(seisK[f]*trfZYLISM[n,f,
m1,m2,m3,m4,g10,g12,g21,g23,g32,g34,g43])^2]

thermal noise

tNoiseZLISM[n_,
f_,
m1_,m2_,m3_,m4_,g10_,g12_,g21_,g23_,g32_,g34_,g43_]:=

Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matZYLISM[f,
m1,m2,m3,m4,g10,g12,g21,g23,g32,g34,g43]]],n,n]]

Quad pendulum simplified (2004/01)

matrix

nTotalQuadS = 5;

matQuadS[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
d2_
]:= -(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, ix1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, iy1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, iz1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, ix2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ix3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ix4, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz4, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixd2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyd2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izd2}}))+(({{kh10+kh12, 0, 0, 0, {z01,z21}.{kh10,kh12}, 0, -kh21, 0, 0, 0, -z21 kh21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, kh10+kh12, 0, -{z01,z21}.{kh10,kh12}, 0, 0, 0, -kh21, 0, z21 kh21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, kv10+kv12, 0, 0, 0, 0, 0, -kv21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -{z01,z21}.{kh10,kh12}, 0, tx10+tx12, 0, 0, 0, z12 kh21, 0, -ctx21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {{z01,z21}.{kh10,kh12}, 0, 0, 0, ty10+ty12, 0, -z12 kh21, 0, 0, 0, -cty21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, tz10+tz12, 0, 0, 0, 0, 0, -ctz21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-kh12, 0, 0, 0, -z12 kh12, 0, kh21+kh23, 0, 0, 0, {z12,z32}.{kh21,kh23}, 0, -kh32, 0, 0, 0, -z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -kh21, 0, z12 kh12, 0, 0, 0, kh21+kh23, 0, -{z12,z32}.{kh21,kh23}, 0, 0, 0, -kh32, 0, z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -kv12, 0, 0, 0, 0, 0, kv21+kv23, 0, 0, 0, 0, 0, -kv32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, z21 kh12, 0, -ctx12, 0, 0, 0, -{z12,z32}.{kh21,kh23}, 0, tx21+tx23, 0, 0, 0, z23 kh32, 0, -ctx32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-z21 kh12, 0, 0, 0, -cty12, 0, {z12,z32}.{kh21,kh23}, 0, 0, 0, ty21+ty23, 0, -z23 kh32, 0, 0, 0, -cty32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -ctz12, 0, 0, 0, 0, 0, tz21+tz23, 0, 0, 0, 0, 0, -ctz32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -kh23, 0, 0, 0, -z23 kh23, 0, kh32+kh34, 0, 0, 0, {z23,z43}.{kh32,kh34}, 0, -kh43, 0, 0, 0, -z34 kh43, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, -kh23, 0, z23 kh23, 0, 0, 0, kh32+kh34, 0, -{z23,z43}.{kh32,kh34}, 0, 0, 0, -kh43, 0, z43 kh43, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -kv23, 0, 0, 0, 0, 0, kv32+kv34, 0, 0, 0, 0, 0, -kv43, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, z32 kh23, 0, -ctx23, 0, 0, 0, -{z23,z43}.{kh32,kh34}, 0, tx32+tx34, 0, 0, 0, z34 kh43, 0, -ctx43, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -z32 kh23, 0, 0, 0, -cty23, 0, {z23,z43}.{kh32,kh34}, 0, 0, 0, ty32+ty34, 0, -z34 kh43, 0, 0, 0, -cty43, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz23, 0, 0, 0, 0, 0, tz32+tz34, 0, 0, 0, 0, 0, -ctz43, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kh34, 0, 0, 0, -z34 kh34, 0, kh43, 0, 0, 0, {z43}.{kh43}, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kh34, 0, z34 kh34, 0, 0, 0, kh43, 0, -{z43}.{kh43}, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kv34, 0, 0, 0, 0, 0, kv43, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z43 kh34, 0, -ctx34, 0, 0, 0, -{z43}.{kh43}, 0, tx43, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -z43 kh34, 0, 0, 0, -cty34, 0, {z43}.{kh43}, 0, 0, 0, ty43, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz34, 0, 0, 0, 0, 0, tz43, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd02}.{khd20}, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd02}.{khd20}, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd02}.{khd20}, 0, txd20, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd02}.{khd20}, 0, 0, 0, tyd20, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, tzd20}}))+I 2 Pi f(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, ix2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ix2 d2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iy2 d2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iz2 d2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, -ixd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixd2 d2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iyd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyd2 d2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -izd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izd2 d2}}))

(({{kh10+kh12, 0, 0, 0, {z01,z21}.{kh10,kh12}, 0, -kh21, 0, 0, 0, -z21 kh21, 0}, {0, kh10+kh12, 0, -{z01,z21}.{kh10,kh12}, 0, 0, 0, -kh21, 0, z21 kh21, 0, 0}, {0, 0, kv10+kv12, 0, 0, 0, 0, 0, -kv21, 0, 0, 0}, {0, -{z01,z21}.{kh10,kh12}, 0, tx10+tx12, 0, 0, 0, z12 kh21, 0, -ctx21, 0, 0}, {{z01,z21}.{kh10,kh12}, 0, 0, 0, ty10+ty12, 0, -z12 kh21, 0, 0, 0, -cty21, 0}, {0, 0, 0, 0, 0, tz10+tz12, 0, 0, 0, 0, 0, -ctz21}, {-kh12, 0, 0, 0, -z12 kh12, 0, kh21+kh23, 0, 0, 0, {z12,z32}.{kh21,kh23}, 0}, {0, -kh21, 0, z12 kh12, 0, 0, 0, kh21+kh23, 0, -{z12,z32}.{kh21,kh23}, 0, 0}, {0, 0, -kv12, 0, 0, 0, 0, 0, kv21+kv23, 0, 0, 0}, {0, z21 kh12, 0, -ctx12, 0, 0, 0, -{z12,z32}.{kh21,kh23}, 0, tx21+tx23, 0, 0}, {-z21 kh12, 0, 0, 0, -cty12, 0, {z12,z32}.{kh21,kh23}, 0, 0, 0, ty21+ty23, 0}, {0, 0, 0, 0, 0, -ctz12, 0, 0, 0, 0, 0, tz21+tz23}, {0, 0, 0, 0, 0, 0, -kh23, 0, 0, 0, -z23 kh23, 0}, {0, 0, 0, 0, 0, 0, 0, -kh23, 0, z23 kh23, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -kv23, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, z32 kh23, 0, -ctx23, 0, 0}, {0, 0, 0, 0, 0, 0, -z32 kh23, 0, 0, 0, -cty23, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz23}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}));

(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-kh32, 0, 0, 0, -z32 kh32, 0, 0, 0, 0, 0, 0, 0}, {0, -kh32, 0, z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -kv32, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, z23 kh32, 0, -ctx32, 0, 0, 0, 0, 0, 0, 0, 0}, {-z23 kh32, 0, 0, 0, -cty32, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -ctz32, 0, 0, 0, 0, 0, 0}, {kh32+kh34, 0, 0, 0, {z23,z43}.{kh32,kh34}, 0, -kh43, 0, 0, 0, -z34 kh43, 0}, {0, kh32+kh34, 0, -{z23,z43}.{kh32,kh34}, 0, 0, 0, -kh43, 0, z43 kh43, 0, 0}, {0, 0, kv32+kv34, 0, 0, 0, 0, 0, -kv43, 0, 0, 0}, {0, -{z23,z43}.{kh32,kh34}, 0, tx32+tx34, 0, 0, 0, z34 kh43, 0, -ctx43, 0, 0}, {{z23,z43}.{kh32,kh34}, 0, 0, 0, ty32+ty34, 0, -z34 kh43, 0, 0, 0, -cty43, 0}, {0, 0, 0, 0, 0, tz32+tz34, 0, 0, 0, 0, 0, -ctz43}, {-kh34, 0, 0, 0, -z34 kh34, 0, kh43, 0, 0, 0, {z43}.{kh43}, 0}, {0, -kh34, 0, z34 kh34, 0, 0, 0, kh43, 0, -{z43}.{kh43}, 0, 0}, {0, 0, -kv34, 0, 0, 0, 0, 0, kv43, 0, 0, 0}, {0, z43 kh34, 0, -ctx34, 0, 0, 0, -{z43}.{kh43}, 0, tx43, 0, 0}, {-z43 kh34, 0, 0, 0, -cty34, 0, {z43}.{kh43}, 0, 0, 0, ty43, 0}, {0, 0, 0, 0, 0, -ctz34, 0, 0, 0, 0, 0, tz43}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}));

(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd02}.{khd20}, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd02}.{khd20}, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd02}.{khd20}, 0, txd20, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd02}.{khd20}, 0, 0, 0, tyd20, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, tzd20}}));

parameter set

{f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
d2_}

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
d2}

TRF, seismoc noise & thermal noise

matForceQuadS[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
d2_]:=(({{kh10, 0, 0, 0, z10 kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd20}.{khd20}, 0}, {0, kh10, 0, -z10 kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd20}.{khd20}, 0, 0}, {0, 0, kv10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, 0, 0, 0}, {0, -z10 kh10, 0, ctx10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd20}.{khd20}, 0, txd20, 0, 0}, {z10 kh10, 0, 0, 0, cty10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd20}.{khd20}, 0, 0, 0, tyd20, 0}, {0, 0, 0, 0, 0, ctz10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, tzd20}}))

matSeisQuadS[f_]:=(({{seisK[f]}, {seisK[f]}, {seisK[f]}, {seisKRot[f]}, {seisKRot[f]}, {seisKRot[f]}}))

trfAmpQuadS[a_,b_,c_,d_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
d2_
] :=Abs[Part[Inverse[matQuadS[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
d2

]],(6(d-1)+c),(6(b-1)+a)]]/Abs[Part[Inverse[matQuadS[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
d2

]],(6(b-1)+a),(6(b-1)+a)]]

(*amplitude to amplitude trf from direction "a" of mass "b" to direction "c" of mass "d".*)

trfSeisQuadS[a_,b_,c_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
d2_
] :=Abs[Part[Inverse[matQuadS[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
d2
]].

Part[matForceQuadS[f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
d2
],a],(6(c-1)+b)]]

(*transfer function a to b.
c: interesting item.
a, b= 1 -> X to X*)

seisQuadS[a_,b_,c_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
d2_
]:=trfSeisQuadS[a,b,c,f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
d2
] *Part[matSeisQuadS[f],a] 

(*seismicnoise: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

tNoiseQuadS[a_,b_,f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd20_,kvd20_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
d2_
]:=Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matQuadS[f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
d2
]]],6(b-1)+a,6(b-1)+a]]

(*thermal noise: thermal noise in "b" direction caused by flctuation force in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

Quad pendulum simplified + heat link(2004/01)

matrix

nTotalQuadSa = 5;

matQuadSa[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,
kxu10_,kyu10_,kzu10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
txu10_,tyu10_,tzu10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,
ctxd20_,ctyd20_,ctzd20_,ctxu10_,ctyu10_,ctzu10_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,
d2_
]:= -(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, ix1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, iy1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, iz1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, ix2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ix3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ix4, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz4, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixd2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyd2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izd2}}))+(({{kh10+kh12, 0, 0, 0, {z10,z12}.{kh10,kh12}, 0, -kh21, 0, 0, 0, -z21 kh21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, kh10+kh12, 0, -{z10,z12}.{kh10,kh12}, 0, 0, 0, -kh21, 0, z21 kh21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, kv10+kv12, 0, 0, 0, 0, 0, -kv21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -{z10,z12}.{kh10,kh12}, 0, tx10+tx12, 0, 0, 0, z12 kh21, 0, -ctx21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {{z10,z12}.{kh10,kh12}, 0, 0, 0, ty10+ty12, 0, -z12 kh21, 0, 0, 0, -cty21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, tz10+tz12, 0, 0, 0, 0, 0, -ctz21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-kh12, 0, 0, 0, -z12 kh12, 0, kh21+kh23, 0, 0, 0, {z21,z23}.{kh21,kh23}, 0, -kh32, 0, 0, 0, -z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -kh12, 0, z12 kh12, 0, 0, 0, kh21+kh23, 0, -{z21,z23}.{kh21,kh23}, 0, 0, 0, -kh32, 0, z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -kv12, 0, 0, 0, 0, 0, kv21+kv23, 0, 0, 0, 0, 0, -kv32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, z21 kh12, 0, -ctx12, 0, 0, 0, -{z21,z23}.{kh21,kh23}, 0, tx21+tx23, 0, 0, 0, z23 kh32, 0, -ctx32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-z21 kh12, 0, 0, 0, -cty12, 0, {z21,z23}.{kh21,kh23}, 0, 0, 0, ty21+ty23, 0, -z23 kh32, 0, 0, 0, -cty32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -ctz12, 0, 0, 0, 0, 0, tz21+tz23, 0, 0, 0, 0, 0, -ctz32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -kh23, 0, 0, 0, -z23 kh23, 0, kh32+kh34+kxu10, 0, 0, 0, {z32,z34,zu10}.{kh32,kh34,kxu10}, -yu10 kxu10, -kh43, 0, 0, 0, -z43 kh43, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, -kh23, 0, z23 kh23, 0, 0, 0, kh32+kh34+kyu10, 0, -{z32,z34,zu10}.{kh32,kh34,kyu10}, 0, -xu10 kyu10, 0, -kh43, 0, z43 kh43, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -kv23, 0, 0, 0, 0, 0, kv32+kv34+kzu10, -yu10 kzu10, -xu10 kzu10 , 0, 0, 0, -kv43, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, z32 kh23, 0, -ctx23, 0, 0, 0, -{z32,z34,zu10}.{kh32,kh34,kxu10}, 0, tx32+tx34+txu10, -yu10 xu10 kzu10 , -zu10 xu10 kyu10, 0, z34 kh43, 0, -ctx43, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -z32 kh23, 0, 0, 0, -cty23, 0, {z32,z34,zu10}.{kh32,kh34,kyu10}, 0, yu10 kzu10, -xu10 yu10 kzu10, ty32+ty34+tyu10, -zu10 yu10 kxu10, -z34 kh43, 0, 0, 0, -cty43, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz23, -yu10 kxu10, xu10 kyu10, -xu10 kzu10, -xu10 zu10 kyu10, -yu10 zu10 kxu10, tz32+tz34+tzu10, 0, 0, 0, 0, 0, -ctz43, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kh34, 0, 0, 0, -z34 kh34, 0, kh43, 0, 0, 0, {z43}.{kh43}, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kh34, 0, z34 kh34, 0, 0, 0, kh43, 0, -{z43}.{kh43}, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kv34, 0, 0, 0, 0, 0, kv43, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z43 kh34, 0, -ctx34, 0, 0, 0, -{z43}.{kh43}, 0, tx43, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -z43 kh34, 0, 0, 0, -cty34, 0, {z43}.{kh43}, 0, 0, 0, ty43, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz34, 0, 0, 0, 0, 0, tz43, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd20}.{khd20}, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd20}.{khd20}, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd20}.{khd20}, 0, txd20, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd20}.{khd20}, 0, 0, 0, tyd20, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, tzd20}}))+I 2 Pi f(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, ix2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ix2 d2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iy2 d2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iz2 d2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, -ixd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixd2 d2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iyd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyd2 d2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -izd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izd2 d2}}))

(({{kh10+kh12, 0, 0, 0, {z10,z12}.{kh10,kh12}, 0, -kh21, 0, 0, 0, -z21 kh21, 0}, {0, kh10+kh12, 0, -{z10,z12}.{kh10,kh12}, 0, 0, 0, -kh21, 0, z21 kh21, 0, 0}, {0, 0, kv10+kv12, 0, 0, 0, 0, 0, -kv21, 0, 0, 0}, {0, -{z10,z12}.{kh10,kh12}, 0, tx10+tx12, 0, 0, 0, z12 kh21, 0, -ctx21, 0, 0}, {{z10,z12}.{kh10,kh12}, 0, 0, 0, ty10+ty12, 0, -z12 kh21, 0, 0, 0, -cty21, 0}, {0, 0, 0, 0, 0, tz10+tz12, 0, 0, 0, 0, 0, -ctz21}, {-kh12, 0, 0, 0, -z12 kh12, 0, kh21+kh23, 0, 0, 0, {z21,z23}.{kh21,kh23}, 0}, {0, -kh12, 0, z12 kh12, 0, 0, 0, kh21+kh23, 0, -{z21,z23}.{kh21,kh23}, 0, 0}, {0, 0, -kv12, 0, 0, 0, 0, 0, kv21+kv23, 0, 0, 0}, {0, z21 kh12, 0, -ctx12, 0, 0, 0, -{z21,z23}.{kh21,kh23}, 0, tx21+tx23, 0, 0}, {-z21 kh12, 0, 0, 0, -cty12, 0, {z21,z23}.{kh21,kh23}, 0, 0, 0, ty21+ty23, 0}, {0, 0, 0, 0, 0, -ctz12, 0, 0, 0, 0, 0, tz21+tz23}, {0, 0, 0, 0, 0, 0, -kh23, 0, 0, 0, -z23 kh23, 0}, {0, 0, 0, 0, 0, 0, 0, -kh23, 0, z23 kh23, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -kv23, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, z32 kh23, 0, -ctx23, 0, 0}, {0, 0, 0, 0, 0, 0, -z32 kh23, 0, 0, 0, -cty23, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz23}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}));

(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-kh32, 0, 0, 0, -z32 kh32, 0, 0, 0, 0, 0, 0, 0}, {0, -kh32, 0, z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -kv32, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, z23 kh32, 0, -ctx32, 0, 0, 0, 0, 0, 0, 0, 0}, {-z23 kh32, 0, 0, 0, -cty32, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -ctz32, 0, 0, 0, 0, 0, 0}, {kh32+kh34+kxu10, 0, 0, 0, {z32,z34,zu10}.{kh32,kh34,kxu10}, -yu10 kxu10, -kh43, 0, 0, 0, -z43 kh43, 0}, {0, kh32+kh34+kyu10, 0, -{z32,z34,zu10}.{kh32,kh34,kyu10}, 0, -xu10 kyu10, 0, -kh43, 0, z43 kh43, 0, 0}, {0, 0, kv32+kv34+kzu10, -yu10 kzu10, -xu10 kzu10 , 0, 0, 0, -kv43, 0, 0, 0}, {0, -{z32,z34,zu10}.{kh32,kh34,kxu10}, 0, tx32+tx34+txu10, -yu10 xu10 kzu10 , -zu10 xu10 kyu10, 0, z34 kh43, 0, -ctx43, 0, 0}, {{z32,z34,zu10}.{kh32,kh34,kyu10}, 0, yu10 kzu10, -xu10 yu10 kzu10, ty32+ty34+tyu10, -zu10 yu10 kxu10, -z34 kh43, 0, 0, 0, -cty43, 0}, {-yu10 kxu10, xu10 kyu10, -xu10 kzu10, -xu10 zu10 kyu10, -yu10 zu10 kxu10, tz32+tz34+tzu10, 0, 0, 0, 0, 0, -ctz43}, {-kh34, 0, 0, 0, -z34 kh34, 0, kh43, 0, 0, 0, {z43}.{kh43}, 0}, {0, -kh34, 0, z34 kh34, 0, 0, 0, kh43, 0, -{z43}.{kh43}, 0, 0}, {0, 0, -kv34, 0, 0, 0, 0, 0, kv43, 0, 0, 0}, {0, z43 kh34, 0, -ctx34, 0, 0, 0, -{z43}.{kh43}, 0, tx43, 0, 0}, {-z43 kh34, 0, 0, 0, -cty34, 0, {z43}.{kh43}, 0, 0, 0, ty43, 0}, {0, 0, 0, 0, 0, -ctz34, 0, 0, 0, 0, 0, tz43}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}));

(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd20}.{khd20}, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd20}.{khd20}, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd20}.{khd20}, 0, txd20, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd20}.{khd20}, 0, 0, 0, tyd20, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, tzd20}}));

parameter set

{f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,
kxu10_,kyu10_,kzu10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
txu10_,tyu10_,tzu10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,
ctxd20_,ctyd20_,ctzd20_,ctxu10_,ctyu10_,ctzu10_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,
d2_}

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2}

TRF, seismoc noise & thermal noise

matForceRoomQuadSa[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,
kxu10_,kyu10_,kzu10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
txu10_,tyu10_,tzu10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,
ctxd20_,ctyd20_,ctzd20_,ctxu10_,ctyu10_,ctzu10_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,
d2_]:=(({{kh10, 0, 0, 0, z01 kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd02}.{khd20}, 0}, {0, kh10, 0, -z01 kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd02}.{khd20}, 0, 0}, {0, 0, kv10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, 0, 0, 0}, {0, -z10 kh10, 0, ctx10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd20}.{khd20}, 0, txd20, 0, 0}, {z10 kh10, 0, 0, 0, cty10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd20}.{khd20}, 0, 0, 0, tyd20, 0}, {0, 0, 0, 0, 0, ctz10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, tzd20}}))

matForceCryoQuadSa[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,
kxu10_,kyu10_,kzu10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
txu10_,tyu10_,tzu10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,
ctxd20_,ctyd20_,ctzd20_,ctxu10_,ctyu10_,ctzu10_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,
d2_
]:=(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kxu10, 0, 0, 0, -zu10 kxu10, -yu10 kxu10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kyu10, 0, zu10 kyu10, 0, -xu10 kyu10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kzu10, -yu01 kzu10, -xu01 kzu10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -zu10 kyu10, yu10 kzu10, ctxu10, -yu10 xu01 kzu10, -zu10 xu01 kyu10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, zu10 kxu10, 0, -xu10 kzu10, -xu10 yu01 kzu10, ctyu10, -zu10 yu01 kxu10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -yu10 kxu10, xu10 kyu10, 0, -xu10 zu01 kyu10, -yu10 zu01 kxu10, ctzu10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}))

matSeisRoomQuadSa[f_]:=(({{seisK[f]}, {seisK[f]}, {seisK[f]}, {seisKRot[f]}, {seisKRot[f]}, {seisKRot[f]}}))

matSeisCryoQuadSa[a_,f_]:=a*(({{seisK[f]}, {seisK[f]}, {seisK[f]}, {seisKRot[f]}, {seisKRot[f]}, {seisKRot[f]}})) (*vibration in a cryostat. a: amplifivation factor*)

trfAmpQuadSa[a_,b_,c_,d_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,
kxu10_,kyu10_,kzu10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
txu10_,tyu10_,tzu10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,
ctxd20_,ctyd20_,ctzd20_,ctxu10_,ctyu10_,ctzu10_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,
d2_
] :=Abs[Part[Inverse[matQuadSa[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2

]],(6(d-1)+c),(6(b-1)+a)]]/Abs[Part[Inverse[matQuadSa[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2

]],(6(b-1)+a),(6(b-1)+a)]]

(*amplitude to amplitude trf from direction "a" of mass "b" to direction "c" of mass "d".*)

trfSeisRoomQuadSa[a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,
kxu10_,kyu10_,kzu10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
txu10_,tyu10_,tzu10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,
ctxd20_,ctyd20_,ctzd20_,ctxu10_,ctyu10_,ctzu10_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,
d2_
] :=Abs[Part[Inverse[matQuadSa[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2
]].

Part[matForceRoomQuadSa[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2
],a],(6(c-1)+b)]]

(*transfer function a to b.
c: interesting item.
a, b= 1 -> X to X*)

trfSeisCryoQuadSa[a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,
kxu10_,kyu10_,kzu10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
txu10_,tyu10_,tzu10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,
ctxd20_,ctyd20_,ctzd20_,ctxu10_,ctyu10_,ctzu10_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,
d2_
] :=Abs[Part[Inverse[matQuadSa[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2
]].

Part[matForceCryoQuadSa[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2
],a],(6(c-1)+b)]]

(*transfer function a to b for seismic noise by heat link.
c: interesting item.
a, b= 1 -> X to X*)

seisRoomQuadSa[a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,
kxu10_,kyu10_,kzu10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
txu10_,tyu10_,tzu10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,
ctxd20_,ctyd20_,ctzd20_,ctxu10_,ctyu10_,ctzu10_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,
d2_
]:=trfSeisRoomQuadSa[a,b,c,
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2
] *Part[matSeisRoomQuadSa[f],a] 

(*seismicnoise: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

seisCryoQuadSa[d_,a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,
kxu10_,kyu10_,kzu10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
txu10_,tyu10_,tzu10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,
ctxd20_,ctyd20_,ctzd20_,ctxu10_,ctyu10_,ctzu10_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,
d2_
]:=trfSeisCryoQuadSa[a,b,c,
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2
] *Part[matSeisCryoQuadSa[d,f],a] 

(*seismicnoise by heat link: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item. d: amplification factor.
a, b= 1 -> X to X*)

seisQuadSa[d_,a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,
kxu10_,kyu10_,kzu10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
txu10_,tyu10_,tzu10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,
ctxd20_,ctyd20_,ctzd20_,ctxu10_,ctyu10_,ctzu10_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,
d2_
]:= seisRoomQuadSa[a,b,c,
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2
]+seisCryoQuadSa[d,a,b,c,
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2
](*total seismic noise at mirror*)

tNoiseQuadSa[a_,b_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,
kxu10_,kyu10_,kzu10_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,
txu10_,tyu10_,tzu10_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,
ctxd20_,ctyd20_,ctzd20_,ctxu10_,ctyu10_,ctzu10_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,
d2_
]:=Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matQuadSa[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2
]]],6(b-1)+a,6(b-1)+a]]

(*thermal noise: thermal noise in "b" direction caused by flctuation force in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

Quad pendulum simplified + heat link+heat link suspension 1(2004/01)

matrix

nTotalQuadSb = 6;

matQuadSb[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
mk1_,ixk1_,iyk1_,izk1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,khk10_,kvk10_,
kxu10_,kyu10_,kzu10_,kxu13_,kyu13_,kzu13_,kxu31_,kyu31_,kzu31_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,txk10_,tyk10_,tzk10_,
txu10_,tyu10_,tzu10_,txu13_,tyu13_,tzu13_,txu31_,tyu31_,tzu31_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,ctxk10_,ctyk10_,ctzk10_,
ctxu10_,ctyu10_,ctzu10_,ctxu13_,ctyu13_,ctzu13_,ctxu31_,ctyu31_,ctzu31_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,zk01_,zk10_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,xu13_,yu13_,zu13_,xu31_,yu31_,zu31_,
d2_,dk1_
]:= -(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, ix1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, iy1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, iz1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, ix2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ix3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ix4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixd2, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyd2, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izd2, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, mk1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, mk1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, mk1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixk1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyk1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izk1}}))+(({{kh10+kh12, 0, 0, 0, {z10,z12}.{kh10,kh12}, 0, -kh21, 0, 0, 0, -z21 kh21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, kh10+kh12, 0, -{z10,z12}.{kh10,kh12}, 0, 0, 0, -kh21, 0, z21 kh21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, kv10+kv12, 0, 0, 0, 0, 0, -kv21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -{z10,z12}.{kh10,kh12}, 0, tx10+tx12, 0, 0, 0, z12 kh21, 0, -ctx21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {{z10,z12}.{kh10,kh12}, 0, 0, 0, ty10+ty12, 0, -z12 kh21, 0, 0, 0, -cty21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, tz10+tz12, 0, 0, 0, 0, 0, -ctz21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-kh12, 0, 0, 0, -z12 kh12, 0, kh21+kh23, 0, 0, 0, {z21,z23}.{kh21,kh23}, 0, -kh32, 0, 0, 0, -z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -kh12, 0, z12 kh12, 0, 0, 0, kh21+kh23, 0, -{z21,z23}.{kh21,kh23}, 0, 0, 0, -kh32, 0, z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -kv12, 0, 0, 0, 0, 0, kv21+kv23, 0, 0, 0, 0, 0, -kv32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, z21 kh12, 0, -ctx12, 0, 0, 0, -{z21,z23}.{kh21,kh23}, 0, tx21+tx23, 0, 0, 0, z23 kh32, 0, -ctx32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-z21 kh12, 0, 0, 0, -cty12, 0, {z21,z23}.{kh21,kh23}, 0, 0, 0, ty21+ty23, 0, -z23 kh32, 0, 0, 0, -cty32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -ctz12, 0, 0, 0, 0, 0, tz21+tz23, 0, 0, 0, 0, 0, -ctz32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -kh23, 0, 0, 0, -z23 kh23, 0, kh32+kh34+kxu31, 0, 0, 0, {z32,z34,zu31}.{kh32,kh34,kxu31}, -yu31 kxu31, -kh43, 0, 0, 0, -z43 kh43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, -kh23, 0, z23 kh23, 0, 0, 0, kh32+kh34+kyu31, 0, -{z32,z34,zu31}.{kh32,kh34,kyu31}, 0, xu31 kyu31, 0, -kh43, 0, z43 kh43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -kv23, 0, 0, 0, 0, 0, kv32+kv34+kzu31, yu31 kzu31, -xu31 kzu31, 0, 0, 0, -kv43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, z32 kh23, 0, -ctx23, 0, 0, 0, -{z32,z34,zu31}.{kh32,kh34,kyu31}, yu31 kzu31, tx32+tx34+txu31, -yu31 xu31 kzu31, -zu31 xu31 kyu31, 0, z34 kh43, 0, -tx43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -z32 kh23, 0, 0, 0, -cty23, 0, {z32,z34,zu31}.{kh32,kh34,kxu31}, 0, -xu31 kzu31, -xu31 yu31 kzu31, ty32+ty34+tyu31, -zu31 yu31 kxu31, -z34 kh43, 0, 0, 0, -ty43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz23, -yu31 kxu31, xu31 kyu31, 0, -xu31 zu31 kyu31, -yu31 zu31 kxu31, tz32+tz34+tzu31, 0, 0, 0, 0, 0, -tz43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kh34, 0, 0, 0, -z34 kh34, 0, kh43, 0, 0, 0, {z43}.{kh43}, 0, 0, 0, 0, 0, 0, 0, -kxu13, 0, 0, 0, -zu13 kxu13, yu13 kxu13}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kh34, 0, z34 kh34, 0, 0, 0, kh43, 0, -{z43}.{kh43}, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kyu13, 0, zu13 kyu13, 0, -xu13 kyu13}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kv34, 0, 0, 0, 0, 0, kv43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kzu13, -yu13 kzu13, xu13 kzu13, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z43 kh34, 0, -ctx34, 0, 0, 0, -{z43}.{kh43}, 0, tx43, 0, 0, 0, 0, 0, 0, 0, 0, 0, zu31 kyu13, -yu31 kzu13, -txu13, yu31 xu13 kzu13, zu31 xu13 kyu13}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -z43 kh34, 0, 0, 0, -cty34, 0, {z43}.{kh43}, 0, 0, 0, ty43, 0, 0, 0, 0, 0, 0, 0, -zu31 kxu13, 0, xu31 kzu13, xu31 yu13 kzu13, -tyu13, zu31 yu13 kxu13}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz34, 0, 0, 0, 0, 0, tz43, 0, 0, 0, 0, 0, 0, yu31 kxu13, -xu31 kyu13, 0, xu31 zu13 kyu13 , yu31 zu13 kxu13, -tzu13}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd20}.{khd20}, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd20}.{khd20}, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd20}.{khd20}, 0, txd20, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd20}.{khd20}, 0, 0, 0, tyd20, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, tzd20, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kxu31, 0, 0, 0, -zu31 kxu31, yu31 kxu31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khk10+kxu10+kxu13, 0, 0, 0, -{zk10,zu10,zu13}.{khk10,kxu10,kxu13}, -{yu10,yu13}.{kxu10,kxu13}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kyu31, 0, zu31 kyu31, 0, -xu31 kyu31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khk10+kyu10+kyu13, 0, -{zk10,zu10,zu13}.{khk10,kyu10,kyu13}, 0, {xu10,xu13}.{kyu10,kyu13}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kzu31, -yu31 kzu31, xu31 kzu31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvk10+kzu10+kzu13, {yu10,yu13}.{kzu10,kzu13}, -{xu10,xu13}.{kzu10,kzu13}, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, zu13 kyu31, -yu13 kzu31, -ctxu31, yu13 xu31 kzu31, zu13 xu31 kyu31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zk10,zu10,zu13}.{khk10,kyu10,kyu13}, {yu10,yu13}.{kzu10,kzu13}, txk10+txu10+txu13, -{yu10 xu10,yu13 xu13}.{kzu10,kzu13}, -{zu10 xu10,zu13 xu13}.{kyu10,kyu13}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -zu13 kxu31, 0, xu13 kzu31, xu13 yu31 kzu31, -ctyu31, zu13 yu31 kxu31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zk10,zu10,zu13}.{khk10,kxu10,kxu13}, 0, -{xu10,xu13}.{kzu10,kzu13}, -{xu10 yu10,xu13 yu13}.{kzu10,kzu13}, tyk10+tyu10+tyu13, -{zu10 yu10,zu13 yu13}.{kxu10,kxu13}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, yu13 kxu31, -xu13 kyu31, 0, xu13 zu31 kyu31, yu13 zu31 kxu31, -ctzu31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{yu10,yu13}.{kxu10,kxu13}, {xu10,xu13}.{kyu10,kyu13}, 0, -{xu10 zu10,xu13 zu13}.{kyu10,kyu13}, -{yu10 zu10,yu13 zu13}.{kxu10,kxu13}, tzk10+tzu10+tzu13}}))+I 2 Pi f(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, ix2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ix2 d2, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iy2 d2, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iz2 d2, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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(({{kh10+kh12, 0, 0, 0, {z10,z12}.{kh10,kh12}, 0, -kh21, 0, 0, 0, -z21 kh21, 0}, {0, kh10+kh12, 0, -{z10,z12}.{kh10,kh12}, 0, 0, 0, -kh21, 0, z21 kh21, 0, 0}, {0, 0, kv10+kv12, 0, 0, 0, 0, 0, -kv21, 0, 0, 0}, {0, -{z10,z12}.{kh10,kh12}, 0, tx10+tx12, 0, 0, 0, z12 kh21, 0, -ctx21, 0, 0}, {{z10,z12}.{kh10,kh12}, 0, 0, 0, ty10+ty12, 0, -z12 kh21, 0, 0, 0, -cty21, 0}, {0, 0, 0, 0, 0, tz10+tz12, 0, 0, 0, 0, 0, -ctz21}, {-kh12, 0, 0, 0, -z12 kh12, 0, kh21+kh23, 0, 0, 0, {z21,z23}.{kh21,kh23}, 0}, {0, -kh12, 0, z12 kh12, 0, 0, 0, kh21+kh23, 0, -{z21,z23}.{kh21,kh23}, 0, 0}, {0, 0, -kv12, 0, 0, 0, 0, 0, kv21+kv23, 0, 0, 0}, {0, z21 kh12, 0, -ctx12, 0, 0, 0, -{z21,z23}.{kh21,kh23}, 0, tx21+tx23, 0, 0}, {-z21 kh12, 0, 0, 0, -cty12, 0, {z21,z23}.{kh21,kh23}, 0, 0, 0, ty21+ty23, 0}, {0, 0, 0, 0, 0, -ctz12, 0, 0, 0, 0, 0, tz21+tz23}, {0, 0, 0, 0, 0, 0, -kh23, 0, 0, 0, -z23 kh23, 0}, {0, 0, 0, 0, 0, 0, 0, -kh23, 0, z23 kh23, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -kv23, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, z32 kh23, 0, -ctx23, 0, 0}, {0, 0, 0, 0, 0, 0, -z32 kh23, 0, 0, 0, -cty23, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz23}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}));

(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-kh32, 0, 0, 0, -z32 kh32, 0, 0, 0, 0, 0, 0, 0}, {0, -kh32, 0, z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -kv32, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, z23 kh32, 0, -ctx32, 0, 0, 0, 0, 0, 0, 0, 0}, {-z23 kh32, 0, 0, 0, -cty32, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -ctz32, 0, 0, 0, 0, 0, 0}, {kh32+kh34+kxu31, 0, 0, 0, {z32,z34,zu31}.{kh32,kh34,kxu31}, -yu31 kxu31, -kh43, 0, 0, 0, -z43 kh43, 0}, {0, kh32+kh34+kyu31, 0, -{z32,z34,zu31}.{kh32,kh34,kyu31}, 0, xu31 kyu31, 0, -kh43, 0, z43 kh43, 0, 0}, {0, 0, kv32+kv34+kzu31, yu31 kzu31, -xu31 kzu31, 0, 0, 0, -kv43, 0, 0, 0}, {0, -{z32,z34,zu31}.{kh32,kh34,kyu31}, yu31 kzu31, tx32+tx34+txu31, -yu31 xu31 kzu31, -zu31 xu31 kyu31, 0, z34 kh43, 0, -tx43, 0, 0}, {{z32,z34,zu31}.{kh32,kh34,kxu31}, 0, -xu31 kzu31, -xu31 yu31 kzu31, ty32+ty34+tyu31, -zu31 yu31 kxu31, -z34 kh43, 0, 0, 0, -ty43, 0}, {-yu31 kxu31, xu31 kyu31, 0, -xu31 zu31 kyu31, -yu31 zu31 kxu31, tz32+tz34+tzu31, 0, 0, 0, 0, 0, -tz43}, {-kh34, 0, 0, 0, -z34 kh34, 0, kh43, 0, 0, 0, {z43}.{kh43}, 0}, {0, -kh34, 0, z34 kh34, 0, 0, 0, kh43, 0, -{z43}.{kh43}, 0, 0}, {0, 0, -kv34, 0, 0, 0, 0, 0, kv43, 0, 0, 0}, {0, z43 kh34, 0, -ctx34, 0, 0, 0, -{z43}.{kh43}, 0, tx43, 0, 0}, {-z43 kh34, 0, 0, 0, -cty34, 0, {z43}.{kh43}, 0, 0, 0, ty43, 0}, {0, 0, 0, 0, 0, -ctz34, 0, 0, 0, 0, 0, tz43}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-kxu31, 0, 0, 0, -zu31 kxu31, yu31 kxu31, 0, 0, 0, 0, 0, 0}, {0, -kyu31, 0, zu31 kyu31, 0, -xu31 kyu31, 0, 0, 0, 0, 0, 0}, {0, 0, -kzu31, -yu31 kzu31, xu31 kzu31, 0, 0, 0, 0, 0, 0, 0}, {0, zu13 kyu31, -yu13 kzu31, -ctxu31, yu13 xu31 kzu31, zu13 xu31 kyu31, 0, 0, 0, 0, 0, 0}, {-zu13 kxu31, 0, xu13 kzu31, xu13 yu31 kzu31, -ctyu31, zu13 yu31 kxu31, 0, 0, 0, 0, 0, 0}, {yu13 kxu31, -xu13 kyu31, 0, xu13 zu31 kyu31, yu13 zu31 kxu31, -ctzu31, 0, 0, 0, 0, 0, 0}}));

(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kxu13, 0, 0, 0, -zu13 kxu13, yu13 kxu13}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kyu13, 0, zu13 kyu13, 0, -xu13 kyu13}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kzu13, -yu13 kzu13, xu13 kzu13, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, zu31 kyu13, -yu31 kzu13, -txu13, yu31 xu13 kzu13, zu31 xu13 kyu13}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -zu31 kxu13, 0, xu31 kzu13, xu31 yu13 kzu13, -tyu13, zu31 yu13 kxu13}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, yu31 kxu13, -xu31 kyu13, 0, xu31 zu13 kyu13 , yu31 zu13 kxu13, -tzu13}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd20}.{khd20}, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd20}.{khd20}, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd20}.{khd20}, 0, txd20, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd20}.{khd20}, 0, 0, 0, tyd20, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, tzd20, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khk10+kxu10+kxu13, 0, 0, 0, -{zk10,zu10,zu13}.{khk10,kxu10,kxu13}, -{yu10,yu13}.{kxu10,kxu13}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khk10+kyu10+kyu13, 0, -{zk10,zu10,zu13}.{khk10,kyu10,kyu13}, 0, {xu10,xu13}.{kyu10,kyu13}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvk10+kzu10+kzu13, {yu10,yu13}.{kzu10,kzu13}, -{xu10,xu13}.{kzu10,kzu13}, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zk10,zu10,zu13}.{khk10,kyu10,kyu13}, {yu10,yu13}.{kzu10,kzu13}, txk10+txu10+txu13, -{yu10 xu10,yu13 xu13}.{kzu10,kzu13}, -{zu10 xu10,zu13 xu13}.{kyu10,kyu13}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zk10,zu10,zu13}.{khk10,kxu10,kxu13}, 0, -{xu10,xu13}.{kzu10,kzu13}, -{xu10 yu10,xu13 yu13}.{kzu10,kzu13}, tyk10+tyu10+tyu13, -{zu10 yu10,zu13 yu13}.{kxu10,kxu13}}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{yu10,yu13}.{kxu10,kxu13}, {xu10,xu13}.{kyu10,kyu13}, 0, -{xu10 zu10,xu13 zu13}.{kyu10,kyu13}, -{yu10 zu10,yu13 zu13}.{kxu10,kxu13}, tzk10+tzu10+tzu13}}));

parameter set

{f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
mk1_,ixk1_,iyk1_,izk1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,khk10_,kvk10_,
kxu10_,kyu10_,kzu10_,kxu13_,kyu13_,kzu13_,kxu31_,kyu31_,kzu31_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,txk10_,tyk10_,tzk10_,
txu10_,tyu10_,tzu10_,txu13_,tyu13_,tzu13_,txu31_,tyu31_,tzu31_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,ctxk10_,ctyk10_,ctzk10_,
ctxu10_,ctyu10_,ctzu10_,ctxu13_,ctyu13_,ctzu13_,ctxu31_,ctyu31_,ctzu31_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,zk01_,zk10_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,xu13_,yu13_,zu13_,xu31_,yu31_,zu31_,
d2_,dk1_}

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1}

TRF, seismoc noise & thermal noise

matForceRoomQuadSb[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
mk1_,ixk1_,iyk1_,izk1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,khk10_,kvk10_,
kxu10_,kyu10_,kzu10_,kxu13_,kyu13_,kzu13_,kxu31_,kyu31_,kzu31_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,txk10_,tyk10_,tzk10_,
txu10_,tyu10_,tzu10_,txu13_,tyu13_,tzu13_,txu31_,tyu31_,tzu31_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,ctxk10_,ctyk10_,ctzk10_,
ctxu10_,ctyu10_,ctzu10_,ctxu13_,ctyu13_,ctzu13_,ctxu31_,ctyu31_,ctzu31_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,zk01_,zk10_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,xu13_,yu13_,zu13_,xu31_,yu31_,zu31_,
d2_,dk1_]:=(({{kh10, 0, 0, 0, z01 kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, 0, 0, {zd02}.{khd20}, 0, khk10, 0, 0, 0, {zk01}.{khk10}, 0}, {0, kh10, 0, -z01 kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd20, 0, -{zd02}.{khd20}, 0, 0, 0, khk10, 0, -{zk01}.{khk10}, 0, 0}, {0, 0, kv10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd20, 0, 0, 0, 0, 0, kvk10, 0, 0, 0}, {0, -z10 kh10, 0, tx10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd20}.{khd20}, 0, txd20, 0, 0, 0, -{zk10}.{khk10}, 0, txk10, 0, 0}, {z10 kh10, 0, 0, 0, ty10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd20}.{khd20}, 0, 0, 0, tyd20, 0, {zk10}.{khk10}, 0, 0, 0, tyk10, 0}, {0, 0, 0, 0, 0, tz10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, tzd20, 0, 0, 0, 0, 0, tzk10}}))

matForceCryoQuadSb[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
mk1_,ixk1_,iyk1_,izk1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,khk10_,kvk10_,
kxu10_,kyu10_,kzu10_,kxu13_,kyu13_,kzu13_,kxu31_,kyu31_,kzu31_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,txk10_,tyk10_,tzk10_,
txu10_,tyu10_,tzu10_,txu13_,tyu13_,tzu13_,txu31_,tyu31_,tzu31_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,ctxk10_,ctyk10_,ctzk10_,
ctxu10_,ctyu10_,ctzu10_,ctxu13_,ctyu13_,ctzu13_,ctxu31_,ctyu31_,ctzu31_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,zk01_,zk10_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,xu13_,yu13_,zu13_,xu31_,yu31_,zu31_,
d2_,dk1_
]:=(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kxu10, 0, 0, 0, zu01 kxu10, -yu01 kxu10}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kyu10, 0, -zu01 kyu10, 0, xu01 kyu10}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kzu10, yu01 kzu10, -xu01 kzu10, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -zu10 kyu10, yu10 kyu10, txu10, -yu10 xu01 kzu10, -zu10 xu01 kyu10}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, zu10 kxu10, 0, -xu10 kyu10, -xu10 yu01 kzu10, tyu10, -zu10 yu01 kxu10}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -yu10 kxu10, xu10 kyu10, 0, -xu10 zu01 kyu10, -yu10 zu01 kxu10, tzu10}}))

matSeisRoomQuadSb[f_]:=(({{seisK[f]}, {seisK[f]}, {seisK[f]}, {seisKRot[f]}, {seisKRot[f]}, {seisKRot[f]}}))

matSeisCryoQuadSb[a_,f_]:=a*(({{seisK[f]}, {seisK[f]}, {seisK[f]}, {seisKRot[f]}, {seisKRot[f]}, {seisKRot[f]}})) (*vibration in a cryostat. a: amplifivation factor*)

trfAmpQuadSb[a_,b_,c_,d_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
mk1_,ixk1_,iyk1_,izk1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,khk10_,kvk10_,
kxu10_,kyu10_,kzu10_,kxu13_,kyu13_,kzu13_,kxu31_,kyu31_,kzu31_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,txk10_,tyk10_,tzk10_,
txu10_,tyu10_,tzu10_,txu13_,tyu13_,tzu13_,txu31_,tyu31_,tzu31_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,ctxk10_,ctyk10_,ctzk10_,
ctxu10_,ctyu10_,ctzu10_,ctxu13_,ctyu13_,ctzu13_,ctxu31_,ctyu31_,ctzu31_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,zk01_,zk10_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,xu13_,yu13_,zu13_,xu31_,yu31_,zu31_,
d2_,dk1_
] :=Abs[Part[Inverse[matQuadSb[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1

]],(6(d-1)+c),(6(b-1)+a)]]/Abs[Part[Inverse[matQuadSb[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1

]],(6(b-1)+a),(6(b-1)+a)]]

(*amplitude to amplitude trf from direction "a" of mass "b" to direction "c" of mass "d".*)

trfSeisRoomQuadSb[a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
mk1_,ixk1_,iyk1_,izk1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,khk10_,kvk10_,
kxu10_,kyu10_,kzu10_,kxu13_,kyu13_,kzu13_,kxu31_,kyu31_,kzu31_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,txk10_,tyk10_,tzk10_,
txu10_,tyu10_,tzu10_,txu13_,tyu13_,tzu13_,txu31_,tyu31_,tzu31_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,ctxk10_,ctyk10_,ctzk10_,
ctxu10_,ctyu10_,ctzu10_,ctxu13_,ctyu13_,ctzu13_,ctxu31_,ctyu31_,ctzu31_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,zk01_,zk10_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,xu13_,yu13_,zu13_,xu31_,yu31_,zu31_,
d2_,dk1_

] :=Abs[Part[Inverse[matQuadSb[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1
]].

Part[matForceRoomQuadSb[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1
],a],(6(c-1)+b)]]

(*transfer function a to b.
c: interesting item.
a, b= 1 -> X to X*)

trfSeisCryoQuadSb[a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
mk1_,ixk1_,iyk1_,izk1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,khk10_,kvk10_,
kxu10_,kyu10_,kzu10_,kxu13_,kyu13_,kzu13_,kxu31_,kyu31_,kzu31_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,txk10_,tyk10_,tzk10_,
txu10_,tyu10_,tzu10_,txu13_,tyu13_,tzu13_,txu31_,tyu31_,tzu31_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,ctxk10_,ctyk10_,ctzk10_,
ctxu10_,ctyu10_,ctzu10_,ctxu13_,ctyu13_,ctzu13_,ctxu31_,ctyu31_,ctzu31_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,zk01_,zk10_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,xu13_,yu13_,zu13_,xu31_,yu31_,zu31_,
d2_,dk1_
] :=Abs[Part[Inverse[matQuadSb[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1
]].

Part[matForceCryoQuadSb[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1
],a],(6(c-1)+b)]]

(*transfer function a to b for seismic noise by heat link.
c: interesting item.
a, b= 1 -> X to X*)

seisRoomQuadSb[a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
mk1_,ixk1_,iyk1_,izk1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,khk10_,kvk10_,
kxu10_,kyu10_,kzu10_,kxu13_,kyu13_,kzu13_,kxu31_,kyu31_,kzu31_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,txk10_,tyk10_,tzk10_,
txu10_,tyu10_,tzu10_,txu13_,tyu13_,tzu13_,txu31_,tyu31_,tzu31_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,ctxk10_,ctyk10_,ctzk10_,
ctxu10_,ctyu10_,ctzu10_,ctxu13_,ctyu13_,ctzu13_,ctxu31_,ctyu31_,ctzu31_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,zk01_,zk10_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,xu13_,yu13_,zu13_,xu31_,yu31_,zu31_,
d2_,dk1_
]:=trfSeisRoomQuadSb[a,b,c,
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1
] *Part[matSeisRoomQuadSb[f],a] 

(*seismicnoise: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

seisCryoQuadSb[d_,a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
mk1_,ixk1_,iyk1_,izk1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,khk10_,kvk10_,
kxu10_,kyu10_,kzu10_,kxu13_,kyu13_,kzu13_,kxu31_,kyu31_,kzu31_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,txk10_,tyk10_,tzk10_,
txu10_,tyu10_,tzu10_,txu13_,tyu13_,tzu13_,txu31_,tyu31_,tzu31_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,ctxk10_,ctyk10_,ctzk10_,
ctxu10_,ctyu10_,ctzu10_,ctxu13_,ctyu13_,ctzu13_,ctxu31_,ctyu31_,ctzu31_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,zk01_,zk10_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,xu13_,yu13_,zu13_,xu31_,yu31_,zu31_,
d2_,dk1_
]:=trfSeisCryoQuadSb[a,b,c,
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1
] *Part[matSeisCryoQuadSb[d,f],a] 

(*seismicnoise by heat link: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item. d: amplification factor.
a, b= 1 -> X to X*)

seisQuadSb[d_,a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
mk1_,ixk1_,iyk1_,izk1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,khk10_,kvk10_,
kxu10_,kyu10_,kzu10_,kxu13_,kyu13_,kzu13_,kxu31_,kyu31_,kzu31_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,txk10_,tyk10_,tzk10_,
txu10_,tyu10_,tzu10_,txu13_,tyu13_,tzu13_,txu31_,tyu31_,tzu31_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,ctxk10_,ctyk10_,ctzk10_,
ctxu10_,ctyu10_,ctzu10_,ctxu13_,ctyu13_,ctzu13_,ctxu31_,ctyu31_,ctzu31_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,zk01_,zk10_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,xu13_,yu13_,zu13_,xu31_,yu31_,zu31_,
d2_,dk1_
]:= seisRoomQuadSb[a,b,c,
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1
]+seisCryoQuadSb[d,a,b,c,
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1
](*total seismic noise at mirror*)

tNoiseQuadSb[a_,b_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
mk1_,ixk1_,iyk1_,izk1_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,
khd20_,kvd20_,khk10_,kvk10_,
kxu10_,kyu10_,kzu10_,kxu13_,kyu13_,kzu13_,kxu31_,kyu31_,kzu31_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd20_,tyd20_,tzd20_,txk10_,tyk10_,tzk10_,
txu10_,tyu10_,tzu10_,txu13_,tyu13_,tzu13_,txu31_,tyu31_,tzu31_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd20_,ctyd20_,ctzd20_,ctxk10_,ctyk10_,ctzk10_,
ctxu10_,ctyu10_,ctzu10_,ctxu13_,ctyu13_,ctzu13_,ctxu31_,ctyu31_,ctzu31_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd02_,zd20_,zk01_,zk10_,
xu01_,yu01_,zu01_,xu10_,yu10_,zu10_,xu13_,yu13_,zu13_,xu31_,yu31_,zu31_,
d2_,dk1_
]:=Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matQuadSb[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1
]]],6(b-1)+a,6(b-1)+a]]

(*thermal noise: thermal noise in "b" direction caused by flctuation force in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

New Quad pendulum simplified (2004/02)

matrix

nTotalQuadN = 5;

matQuadN[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd12_,kvd12_,khd21_,kvd21_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd12_,tyd12_,tzd12_,txd21_,tyd21_,tzd21_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd12_,ctyd12_,ctzd12_,ctxd21_,ctyd21_,ctzd21_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd12_,zd21_,
d2_
]:= -(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, ix1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, iy1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, iz1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, ix2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ix3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ix4, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy4, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz4, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixd2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyd2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izd2}}))+(({{kh10+kh12+khd12, 0, 0, 0, {z10,z12,zd12}.{kh10,kh12,khd12}, 0, -kh21, 0, 0, 0, -z21 kh21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -khd21, 0, 0, 0, -{zd21}.{khd21}, 0}, {0, kh10+kh12+khd12, 0, -{z10,z12,zd12}.{kh10,kh12,khd12}, 0, 0, 0, -kh21, 0, z21 kh21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -khd21, 0, {zd21}.{khd21}, 0, 0}, {0, 0, kv10+kv12+kvd12, 0, 0, 0, 0, 0, -kv21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kvd21, 0, 0, 0}, {0, -{z10,z12,zd12}.{kh10,kh12,khd12}, 0, tx10+tx12+txd12, 0, 0, 0, z12 kh21, 0, -ctx21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd12}.{khd21}, 0, -ctxd21, 0, 0}, {{z10,z12,zd12}.{kh10,kh12,khd12}, 0, 0, 0, ty10+ty12+tyd12, 0, -z12 kh21, 0, 0, 0, -cty21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd12}.{khd21}, 0, 0, 0, -ctyd21, 0}, {0, 0, 0, 0, 0, tz10+tz12+tzd12, 0, 0, 0, 0, 0, -ctz21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctzd21}, {-kh12, 0, 0, 0, -z12 kh12, 0, kh21+kh23, 0, 0, 0, {z21,z23}.{kh21,kh23}, 0, -kh32, 0, 0, 0, -z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -kh21, 0, z12 kh12, 0, 0, 0, kh21+kh23, 0, -{z21,z23}.{kh21,kh23}, 0, 0, 0, -kh32, 0, z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -kv12, 0, 0, 0, 0, 0, kv21+kv23, 0, 0, 0, 0, 0, -kv32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, z21 kh12, 0, -ctx12, 0, 0, 0, -{z21,z23}.{kh21,kh23}, 0, tx21+tx23, 0, 0, 0, z23 kh32, 0, -ctx32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-z21 kh12, 0, 0, 0, -cty12, 0, {z21,z23}.{kh21,kh23}, 0, 0, 0, ty21+ty23, 0, -z23 kh32, 0, 0, 0, -cty32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -ctz12, 0, 0, 0, 0, 0, tz21+tz23, 0, 0, 0, 0, 0, -ctz32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -kh23, 0, 0, 0, -z23 kh23, 0, kh32+kh34, 0, 0, 0, {z32,z34}.{kh32,kh34}, 0, -kh43, 0, 0, 0, -z34 kh43, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, -kh23, 0, z23 kh23, 0, 0, 0, kh32+kh34, 0, -{z32,z34}.{kh32,kh34}, 0, 0, 0, -kh43, 0, z43 kh43, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -kv23, 0, 0, 0, 0, 0, kv32+kv34, 0, 0, 0, 0, 0, -kv43, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, z32 kh23, 0, -ctx23, 0, 0, 0, -{z32,z34}.{kh32,kh34}, 0, tx32+tx34, 0, 0, 0, z34 kh43, 0, -ctx43, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -z32 kh23, 0, 0, 0, -cty23, 0, {z32,z34}.{kh32,kh34}, 0, 0, 0, ty32+ty34, 0, -z34 kh43, 0, 0, 0, -cty43, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz23, 0, 0, 0, 0, 0, tz32+tz34, 0, 0, 0, 0, 0, -ctz43, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kh34, 0, 0, 0, -z34 kh34, 0, kh43, 0, 0, 0, {z43}.{kh43}, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kh34, 0, z34 kh34, 0, 0, 0, kh43, 0, -{z43}.{kh43}, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kv34, 0, 0, 0, 0, 0, kv43, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z43 kh34, 0, -ctx34, 0, 0, 0, -{z43}.{kh43}, 0, tx43, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -z43 kh34, 0, 0, 0, -cty34, 0, {z43}.{kh43}, 0, 0, 0, ty43, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz34, 0, 0, 0, 0, 0, tz43, 0, 0, 0, 0, 0, 0}, {-khd12, 0, 0, 0, -{zd12}.{khd12}, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd21, 0, 0, 0, {zd21}.{khd21}, 0}, {0, -khd12, 0, {zd12}.{khd12}, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd21, 0, -{zd21}.{khd21}, 0, 0}, {0, 0, -kvd12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd21, 0, 0, 0}, {0, {zd21}.{khd21}, 0, -ctxd12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd21}.{khd21}, 0, txd21, 0, 0}, {-{zd21}.{khd12}, 0, 0, 0, -ctyd12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd21}.{khd21}, 0, 0, 0, tyd21, 0}, {0, 0, 0, 0, 0, -ctzd12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, tzd21}}))+I 2 Pi f(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -m2 d2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, ix2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ix2 d2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iy2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iy2 d2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iz2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iz2 d2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -md2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, md2 d2, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, -ixd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ixd2 d2, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -iyd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, iyd2 d2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -izd2 d2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, izd2 d2}}))

(({{kh10+kh12+khd12, 0, 0, 0, {z10,z12,zd12}.{kh10,kh12,khd12}, 0, -kh21, 0, 0, 0, -z21 kh21, 0}, {0, kh10+kh12+khd12, 0, -{z10,z12,zd12}.{kh10,kh12,khd12}, 0, 0, 0, -kh21, 0, z21 kh21, 0, 0}, {0, 0, kv10+kv12+kvd12, 0, 0, 0, 0, 0, -kv21, 0, 0, 0}, {0, -{z10,z12,zd12}.{kh10,kh12,khd12}, 0, tx10+tx12+txd12, 0, 0, 0, z12 kh21, 0, -ctx21, 0, 0}, {{z10,z12,zd12}.{kh10,kh12,khd12}, 0, 0, 0, ty10+ty12+tyd12, 0, -z12 kh21, 0, 0, 0, -cty21, 0}, {0, 0, 0, 0, 0, tz10+tz12+tzd12, 0, 0, 0, 0, 0, -ctz21}, {-kh12, 0, 0, 0, -z12 kh12, 0, kh21+kh23, 0, 0, 0, {z21,z23}.{kh21,kh23}, 0}, {0, -kh21, 0, z12 kh12, 0, 0, 0, kh21+kh23, 0, -{z21,z23}.{kh21,kh23}, 0, 0}, {0, 0, -kv12, 0, 0, 0, 0, 0, kv21+kv23, 0, 0, 0}, {0, z21 kh12, 0, -ctx12, 0, 0, 0, -{z21,z23}.{kh21,kh23}, 0, tx21+tx23, 0, 0}, {-z21 kh12, 0, 0, 0, -cty12, 0, {z21,z23}.{kh21,kh23}, 0, 0, 0, ty21+ty23, 0}, {0, 0, 0, 0, 0, -ctz12, 0, 0, 0, 0, 0, tz21+tz23}, {0, 0, 0, 0, 0, 0, -kh23, 0, 0, 0, -z23 kh23, 0}, {0, 0, 0, 0, 0, 0, 0, -kh23, 0, z23 kh23, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, -kv23, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, z32 kh23, 0, -ctx23, 0, 0}, {0, 0, 0, 0, 0, 0, -z32 kh23, 0, 0, 0, -cty23, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctz23}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-khd12, 0, 0, 0, -{zd12}.{khd12}, 0, 0, 0, 0, 0, 0, 0}, {0, -khd12, 0, {zd12}.{khd12}, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -kvd12, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, {zd21}.{khd21}, 0, -ctxd12, 0, 0, 0, 0, 0, 0, 0, 0}, {-{zd21}.{khd12}, 0, 0, 0, -ctyd12, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -ctzd12, 0, 0, 0, 0, 0, 0}}));

(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-kh32, 0, 0, 0, -z32 kh32, 0, 0, 0, 0, 0, 0, 0}, {0, -kh32, 0, z32 kh32, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -kv32, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, z23 kh32, 0, -ctx32, 0, 0, 0, 0, 0, 0, 0, 0}, {-z23 kh32, 0, 0, 0, -cty32, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -ctz32, 0, 0, 0, 0, 0, 0}, {kh32+kh34, 0, 0, 0, {z32,z34}.{kh32,kh34}, 0, -kh43, 0, 0, 0, -z34 kh43, 0}, {0, kh32+kh34, 0, -{z32,z34}.{kh32,kh34}, 0, 0, 0, -kh43, 0, z43 kh43, 0, 0}, {0, 0, kv32+kv34, 0, 0, 0, 0, 0, -kv43, 0, 0, 0}, {0, -{z32,z34}.{kh32,kh34}, 0, tx32+tx34, 0, 0, 0, z34 kh43, 0, -ctx43, 0, 0}, {{z32,z34}.{kh32,kh34}, 0, 0, 0, ty32+ty34, 0, -z34 kh43, 0, 0, 0, -cty43, 0}, {0, 0, 0, 0, 0, tz32+tz34, 0, 0, 0, 0, 0, -ctz43}, {-kh34, 0, 0, 0, -z34 kh34, 0, kh43, 0, 0, 0, {z43}.{kh43}, 0}, {0, -kh34, 0, z34 kh34, 0, 0, 0, kh43, 0, -{z43}.{kh43}, 0, 0}, {0, 0, -kv34, 0, 0, 0, 0, 0, kv43, 0, 0, 0}, {0, z43 kh34, 0, -ctx34, 0, 0, 0, -{z43}.{kh43}, 0, tx43, 0, 0}, {-z43 kh34, 0, 0, 0, -cty34, 0, {z43}.{kh43}, 0, 0, 0, ty43, 0}, {0, 0, 0, 0, 0, -ctz34, 0, 0, 0, 0, 0, tz43}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}));

(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -khd21, 0, 0, 0, -{zd21}.{khd21}, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -khd21, 0, {zd21}.{khd21}, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -kvd21, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd12}.{khd21}, 0, -ctxd21, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd12}.{khd21}, 0, 0, 0, -ctyd21, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -ctzd21}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd21, 0, 0, 0, {zd21}.{khd21}, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, khd21, 0, -{zd21}.{khd21}, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, kvd21, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -{zd21}.{khd21}, 0, txd21, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {zd21}.{khd21}, 0, 0, 0, tyd21, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, tzd21}}));

parameter set

{f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd12_,kvd12_,khd21_,kvd21_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd12_,tyd12_,tzd12_,txd21_,tyd21_,tzd21_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd12_,ctyd12_,ctzd12_,ctxd21_,ctyd21_,ctzd21_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd12_,zd21_,
d2_}

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd12,kvd12,khd21,kvd21,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd12,tyd12,tzd12,txd21,tyd21,tzd21,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd12,ctyd12,ctzd12,ctxd21,ctyd21,ctzd21,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd12,zd21,
d2}

TRF, seismoc noise & thermal noise

matForceQuadN[f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd12_,kvd12_,khd21_,kvd21_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd12_,tyd12_,tzd12_,txd21_,tyd21_,tzd21_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd12_,ctyd12_,ctzd12_,ctxd21_,ctyd21_,ctzd21_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd12_,zd21_,
d2_]:=(({{kh10, 0, 0, 0, z10 kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, kh10, 0, -z10 kh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, kv10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -z10 kh10, 0, ctx10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {z10 kh10, 0, 0, 0, cty10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, ctz10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}))

matSeisQuadN[f_]:=(({{seisK[f]}, {seisK[f]}, {seisK[f]}, {seisKRot[f]}, {seisKRot[f]}, {seisKRot[f]}}))

trfAmpQuadN[a_,b_,c_,d_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd12_,kvd12_,khd21_,kvd21_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd12_,tyd12_,tzd12_,txd21_,tyd21_,tzd21_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd12_,ctyd12_,ctzd12_,ctxd21_,ctyd21_,ctzd21_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd12_,zd21_,
d2_
] :=Abs[Part[Inverse[matQuadN[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd12,kvd12,khd21,kvd21,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd12,tyd12,tzd12,txd21,tyd21,tzd21,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd12,ctyd12,ctzd12,ctxd21,ctyd21,ctzd21,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd12,zd21,
d2

]],(6(d-1)+c),(6(b-1)+a)]]/Abs[Part[Inverse[matQuadN[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd12,kvd12,khd21,kvd21,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd12,tyd12,tzd12,txd21,tyd21,tzd21,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd12,ctyd12,ctzd12,ctxd21,ctyd21,ctzd21,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd12,zd21,
d2

]],(6(b-1)+a),(6(b-1)+a)]]

(*amplitude to amplitude trf from direction "a" of mass "b" to direction "c" of mass "d".*)

trfSeisQuadN[a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd12_,kvd12_,khd21_,kvd21_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd12_,tyd12_,tzd12_,txd21_,tyd21_,tzd21_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd12_,ctyd12_,ctzd12_,ctxd21_,ctyd21_,ctzd21_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd12_,zd21_,
d2_
] :=Abs[Part[Inverse[matQuadN[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd12,kvd12,khd21,kvd21,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd12,tyd12,tzd12,txd21,tyd21,tzd21,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd12,ctyd12,ctzd12,ctxd21,ctyd21,ctzd21,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd12,zd21,
d2
]].

Part[matForceQuadN[f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd12,kvd12,khd21,kvd21,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd12,tyd12,tzd12,txd21,tyd21,tzd21,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd12,ctyd12,ctzd12,ctxd21,ctyd21,ctzd21,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd12,zd21,
d2
],a],(6(c-1)+b)]]

(*transfer function a to b.
c: interesting item.
a, b= 1 -> X to X*)

seisQuadN[a_,b_,c_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd12_,kvd12_,khd21_,kvd21_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd12_,tyd12_,tzd12_,txd21_,tyd21_,tzd21_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd12_,ctyd12_,ctzd12_,ctxd21_,ctyd21_,ctzd21_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd12_,zd21_,
d2_
]:=trfSeisQuadN[a,b,c,
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd12,kvd12,khd21,kvd21,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd12,tyd12,tzd12,txd21,tyd21,tzd21,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd12,ctyd12,ctzd12,ctxd21,ctyd21,ctzd21,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd12,zd21,
d2
] *Part[matSeisQuadN[f],a] 

(*seismicnoise: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

tNoiseQuadN[a_,b_,
f_,
m1_,ix1_,iy1_,iz1_,
m2_,ix2_,iy2_,iz2_,
m3_,ix3_,iy3_,iz3_,
m4_,ix4_,iy4_,iz4_,
md2_,ixd2_,iyd2_,izd2_,
kh10_,kv10_,kh12_,kv12_,kh21_,kv21_,kh23_,kv23_,kh32_,kv32_,kh34_,kv34_,kh43_,kv43_,khd12_,kvd12_,khd21_,kvd21_,
tx10_,ty10_,tz10_,tx12_,ty12_,tz12_,tx21_,ty21_,tz21_,tx23_,ty23_,tz23_,tx32_,ty32_,tz32_,tx34_,ty34_,tz34_,tx43_,ty43_,tz43_,txd12_,tyd12_,tzd12_,txd21_,tyd21_,tzd21_,
ctx10_,cty10_,ctz10_,ctx12_,cty12_,ctz12_,ctx21_,cty21_,ctz21_,ctx23_,cty23_,ctz23_,ctx32_,cty32_,ctz32_,ctx34_,cty34_,ctz34_,ctx43_,cty43_,ctz43_,ctxd12_,ctyd12_,ctzd12_,ctxd21_,ctyd21_,ctzd21_,
z01_,
z10_,z12_,z21_,z23_,z32_,z34_,z43_,
zd12_,zd21_,
d2_
]:=Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matQuadN[
f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd12,kvd12,khd21,kvd21,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd12,tyd12,tzd12,txd21,tyd21,tzd21,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd12,ctyd12,ctzd12,ctxd21,ctyd21,ctzd21,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd12,zd21,
d2
]]],6(b-1)+a,6(b-1)+a]]

(*thermal noise: thermal noise in "b" direction caused by flctuation force in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

LCGT cryogenic suspension (2004/04)

matrix

nTotalLCGT = 5;

matLCGT[f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
]:= -(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m5, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m5, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m5}}))+(({{gh10+gh12+gh14+hx10+hx12+hx14, 0, 0, -gh12-hx12, 0, 0, 0, 0, 0, -gh14-hx14, 0, 0, 0, 0, 0}, {0, gh10+gh12+gh14+hy10+hy12+hy14, 0, 0, -gh12-hy12, 0, 0, 0, 0, 0, -gh14-hy14, 0, 0, 0, 0}, {0, 0, gv10+gv12+gv14+hz10+hz12+hz14, 0, 0, -gv12-hz12, 0, 0, 0, 0, 0, -gv14-hz14, 0, 0, 0}, {-gh21-hx21, 0, 0, gh21+gh23+hx21, 0, 0, -gh23, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -gh21-hy21, 0, 0, gh21+gh23+hy21, 0, 0, -gh23, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -gv21-hz21, 0, 0, gv21+gv23+hz21, 0, 0, -gv23, 0, 0, 0, 0, 0, 0}, {-gh41-hx41, 0, 0, -gh32, 0, 0, gh32, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -gh41-hy41, 0, 0, -gh32, 0, 0, gh32, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -gh41-hz41, 0, 0, -gv32, 0, 0, gv32, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, gh41+gh45+hx41, 0, 0, -gh45, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, gh41+gh45+hy41, 0, 0, -gh45, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, gv41+gv45+hz41, 0, 0, -gv45}, {0, 0, 0, 0, 0, 0, 0, 0, 0, -gh54, 0, 0, gh54, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -gh54, 0, 0, gh54, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -gv45, 0, 0, gv54}}))

parameter set

{f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_}

{f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41}

TRF, seismoc noise & thermal noise

matForceRoomLCGT[f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
]:=(({{gh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, gh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, gv10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}))

matForceCryoLCGT[f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
]:=(({{hx10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, hy10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, hz10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}))

matSeisRoomLCGT[f_]:=(({{trfHSAS[f] seisK[f]}, {trfHSAS[f] seisK[f]}, {trfVSAS[f] seisK[f]}}))

matSeisCryoLCGT[a_,f_]:=a*(({{seisK[f]}, {seisK[f]}, {seisK[f]}}))

trfAmpLCGT[a_,b_,c_,d_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
] :=Abs[Part[Inverse[matLCGT[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41

]],(3(d-1)+c),(3(b-1)+a)]]/Abs[Part[Inverse[matLCGT[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41

]],(3(b-1)+a),(3(b-1)+a)]]

(*amplitude to amplitude trf from direction "a" of mass "b" to direction "c" of mass "d".*)

trfSeisRoomLCGT[a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
] :=Abs[Part[Inverse[matLCGT[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
]].

Part[matForceRoomLCGT[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
],a],(3(c-1)+b)]]

(*transfer function a to b.
c: interesting item.
a, b= 1 -> X to X*)

trfSeisCryoLCGT[a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_

] :=Abs[Part[Inverse[matLCGT[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
]].

Part[matForceCryoLCGT[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
],a],(3(c-1)+b)]]

(*transfer function a to b for seismic noise by heat link.
c: interesting item.
a, b= 1 -> X to X*)

seisRoomLCGT[a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
]:=trfSeisRoomLCGT[a,b,c,
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
] *Part[matSeisRoomLCGT[f],a] 

(*seismicnoise: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

seisCryoLCGT[d_,a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_

]:=trfSeisCryoLCGT[a,b,c,
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41

] *Part[matSeisCryoLCGT[d,f],a] 

(*seismicnoise by heat link: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item. d: amplification factor.
a, b= 1 -> X to X*)

seisLCGT[d_,a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
]:= seisRoomLCGT[a,b,c,
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41

]+seisCryoLCGT[d,a,b,c,
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41

](*total seismic noise at mirror*)

tNoiseLCGT[a_,b_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_

]:=Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matLCGT[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh45,gv45,gh54,gv54,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
]]],3(b-1)+a,3(b-1)+a]]

(*thermal noise: thermal noise of mass "a" in "b" direction*)

LCGT cryogenic suspension no vspi (2004/04/26)

matrix

nTotalLCGTb = 5;

matLCGTb[f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
]:= -(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m5, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m5, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m5}}))+(({{gh10+gh12+gh14+hx10+hx12+hx14, 0, 0, -gh12-hx12, 0, 0, 0, 0, 0, -gh14-hx14, 0, 0, 0, 0, 0}, {0, gh10+gh12+gh14+hy10+hy12+hy14, 0, 0, -gh12-hy12, 0, 0, 0, 0, 0, -gh14-hy14, 0, 0, 0, 0}, {0, 0, gv10+gv12+gv14+hz10+hz12+hz14, 0, 0, -gv12-hz12, 0, 0, 0, 0, 0, -gv14-hz14, 0, 0, 0}, {-gh21-hx21, 0, 0, gh21+gh23+gh25+hx21, 0, 0, -gh23, 0, 0, 0, 0, 0, -gh25, 0, 0}, {0, -gh21-hy21, 0, 0, gh21+gh23+gh25+hy21, 0, 0, -gh23, 0, 0, 0, 0, 0, -gh25, 0}, {0, 0, -gv21-hz21, 0, 0, gv21+gv23+gv25+hz21, 0, 0, -gv23, 0, 0, 0, 0, 0, -gv25}, {-gh41-hx41, 0, 0, -gh32, 0, 0, gh32, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -gh41-hy41, 0, 0, -gh32, 0, 0, gh32, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -gh41-hz41, 0, 0, -gv32, 0, 0, gv32, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, gh41+hx41, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, gh41+hy41, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, gv41+hz41, 0, 0, 0}, {0, 0, 0, -gh52, 0, 0, 0, 0, 0, 0, 0, 0, gh52, 0, 0}, {0, 0, 0, 0, -gh52, 0, 0, 0, 0, 0, 0, 0, 0, gh52, 0}, {0, 0, 0, 0, 0, -gv52, 0, 0, 0, 0, 0, 0, 0, 0, gv52}}))

parameter set

{f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_}

{f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41}

TRF, seismoc noise & thermal noise

matForceRoomLCGTb[f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
]:=(({{gh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, gh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, gv10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}))

matForceCryoLCGTb[f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
]:=(({{hx10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, hy10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, hz10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}))

matSeisRoomLCGTb[f_]:=(({{trfHSAS[f] seisK[f]}, {trfHSAS[f] seisK[f]}, {trfVSAS[f] seisK[f]}}))

matSeisCryoLCGTb[a_,f_]:=a*(({{seisK[f]}, {seisK[f]}, {seisK[f]}}))

trfAmpLCGTb[a_,b_,c_,d_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
] :=Abs[Part[Inverse[matLCGTb[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41

]],(3(d-1)+c),(3(b-1)+a)]]/Abs[Part[Inverse[matLCGTb[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41

]],(3(b-1)+a),(3(b-1)+a)]]

(*amplitude to amplitude trf from direction "a" of mass "b" to direction "c" of mass "d".*)

trfSeisRoomLCGTb[a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
] :=Abs[Part[Inverse[matLCGTb[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
]].

Part[matForceRoomLCGTb[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
],a],(3(c-1)+b)]]

(*transfer function a to b.
c: interesting item.
a, b= 1 -> X to X*)

trfSeisCryoLCGTb[a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_

] :=Abs[Part[Inverse[matLCGTb[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
]].

Part[matForceCryoLCGTb[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
],a],(3(c-1)+b)]]

(*transfer function a to b for seismic noise by heat link.
c: interesting item.
a, b= 1 -> X to X*)

seisRoomLCGTb[a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
]:=trfSeisRoomLCGTb[a,b,c,
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
] *Part[matSeisRoomLCGTb[f],a] 

(*seismicnoise: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

seisCryoLCGTb[d_,a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_

]:=trfSeisCryoLCGTb[a,b,c,
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41

] *Part[matSeisCryoLCGTb[d,f],a] 

(*seismicnoise by heat link: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item. d: amplification factor.
a, b= 1 -> X to X*)

seisLCGTb[d_,a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_
]:= seisRoomLCGTb[a,b,c,
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
]+seisCryoLCGTb[d,a,b,c,
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41

](*total seismic noise at mirror*)

tNoiseLCGTb[a_,b_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_

]:=Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matLCGTb[
f,
m1,m2,m3,m4,m5,
gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,
hx10,hy10,hz10,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41
]]],3(b-1)+a,3(b-1)+a]]

(*thermal noise: thermal noise of mass "b" in "a" direction*)

LCGT cryogenic suspension no spi (2008/07/07)

matrix

nTotalLCGTc = 5;

matLCGTc[f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_
]:= -(2 Pi f)^2*(({{m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, m1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, m2, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, m3, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m4, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m5, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m5, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, m5}}))+(({{gh10+gh12+gh14+hx12+hx14, 0, 0, -gh12-hx12, 0, 0, 0, 0, 0, -gh14-hx14, 0, 0, 0, 0, 0}, {0, gh10+gh12+gh14+hy12+hy14, 0, 0, -gh12-hy12, 0, 0, 0, 0, 0, -gh14-hy14, 0, 0, 0, 0}, {0, 0, gv10+gv12+gv14+hz12+hz14, 0, 0, -gv12-hz12, 0, 0, 0, 0, 0, -gv14-hz14, 0, 0, 0}, {-gh21-hx21, 0, 0, gh21+gh23+gh25+hx21, 0, 0, -gh23, 0, 0, 0, 0, 0, -gh25, 0, 0}, {0, -gh21-hy21, 0, 0, gh21+gh23+gh25+hy21, 0, 0, -gh23, 0, 0, 0, 0, 0, -gh25, 0}, {0, 0, -gv21-hz21, 0, 0, gv21+gv23+gv25+hz21, 0, 0, -gv23, 0, 0, 0, 0, 0, -gv25}, {-gh41-hx41, 0, 0, -gh32, 0, 0, gh32, 0, 0, 0, 0, 0, 0, 0, 0}, {0, -gh41-hy41, 0, 0, -gh32, 0, 0, gh32, 0, 0, 0, 0, 0, 0, 0}, {0, 0, -gh41-hz41, 0, 0, -gv32, 0, 0, gv32, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, gh41+hx41+hx40, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, gh41+hy41+hy40, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, gv41+hz41+hz40, 0, 0, 0}, {0, 0, 0, -gh52, 0, 0, 0, 0, 0, 0, 0, 0, gh52, 0, 0}, {0, 0, 0, 0, -gh52, 0, 0, 0, 0, 0, 0, 0, 0, gh52, 0}, {0, 0, 0, 0, 0, -gv52, 0, 0, 0, 0, 0, 0, 0, 0, gv52}}))

parameter set

{f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_}

{f,m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40}

TRF, seismoc noise & thermal noise

matForceRoomLCGTc[f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_
]:=(({{gh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, gh10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, gv10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}))

matForceCryoLCGTc[f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_
]:=(({{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, hx40, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, hy40, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, hz40, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}))

matSeisRoomLCGTc[f_]:=(({{trfHSAS[f] seisK[f]}, {trfHSAS[f] seisK[f]}, {trfVSAS[f] seisK[f]}}))

matSeisCryoLCGTc[a_,f_]:=a*(({{seisK[f]}, {seisK[f]}, {seisK[f]}}))

trfAmpLCGTc[a_,b_,c_,d_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_
] :=Abs[Part[Inverse[matLCGTc[
f,
m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40

]],(3(d-1)+c),(3(b-1)+a)]]/Abs[Part[Inverse[matLCGTc[
f,
m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40

]],(3(b-1)+a),(3(b-1)+a)]]

(*amplitude to amplitude trf from direction "a" of mass "b" to direction "c" of mass "d".*)

trfSeisRoomLCGTc[a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_
] :=Abs[Part[Inverse[matLCGTc[
f,m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40
]].

Part[matForceRoomLCGTc[
f,
m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40
],a],(3(c-1)+b)]]

(*transfer function a to b.
c: interesting item.
a, b= 1 -> X to X*)

trfSeisCryoLCGTc[a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_

] :=Abs[Part[Inverse[matLCGTc[
f,
m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40
]].

Part[matForceCryoLCGTc[
f,
m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40
],3 (4-1)+a],(3(c-1)+b)]]

(*transfer function a to b for seismic noise by heat link.
c: interesting item.
a, b= 1 -> X to X*)

seisRoomLCGTc[a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_
]:=trfSeisRoomLCGTc[a,b,c,
f,
m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40
] *Part[matSeisRoomLCGTc[f],a] 

(*seismicnoise: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item.
a, b= 1 -> X to X*)

seisCryoLCGTc[d_,a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_

]:=trfSeisCryoLCGTc[a,b,c,
f,
m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40

] *Part[matSeisCryoLCGTc[d,f],a] 

(*seismicnoise by heat link: seismic noise in "b" direction caused by seismic motion in "a" direction.
c: interesting item. d: amplification factor.
a, b= 1 -> X to X*)

seisLCGTc[d_,a_,b_,c_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_
]:= seisRoomLCGTc[a,b,c,
f,
m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40
]+seisCryoLCGTc[d,a,b,c,
f,
m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40

](*total seismic noise at mirror*)

tNoiseLCGTc[a_,b_,
f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh25_,gv25_,gh52_,gv52_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_

]:=Sqrt[4*kb/(2*Pi*f)*(-1)*Part[Im[Inverse[matLCGTc[
f,
m1,m2,m3,m4,m5,gh10,gv10,gh12,gv12,gh21,gv21,gh23,gv23,gh32,gv32,gh14,gv14,gh41,gv41,gh25,gv25,gh52,gv52,hx12,hy12,hz12,hx21,hy21,hz21,hx14,hy14,hz14,hx41,hy41,hz41,hx40,hy40,hz40
]]],3(b-1)+a,3(b-1)+a]]

(*thermal noise: thermal noise of mass "b" in "a" direction*)

Common parameters

Characteristics of materials

sus301

susYoung = 208.54*10^(9); (*Young,s modulus [Pa]*)

susShear = 8.2*10^(10); (*Shear modulus [Pa]*)

susTensile = 13.3*10^(8); (*Tensile strength [Pa]. 11-15.5 in the book*)

susDens = 7.86*10^3 kg/m^3; (*Density [kg/m^3]*)

susPoisson = 0.3; (*Poisson's ratio*)

CuBe

cbYoung = 130*10^(9); (*Young,s modulus [Pa]*)

cbShear = 4.8*10^(10); (*Shear modulus [Pa]*)

cbTensile = 12*10^(8); (*Tensile strength [Pa].*)

cbDens = 8.23*10^3 kg/m^3; (*Density [kg/m^3]*)

cbPoisson = 0.3; (*Poisson's ratio????unknown*)

scBV[cbYoung,cbPoisson,cbDens,1.8cm,10 cm,1 mm,9.8]

fiBV[cbYoung,cbPoisson,cbDens,1.8cm,10 cm,1 mm,9.8]

stMaxBV[cbYoung,cbPoisson,cbDens,1.8cm,10 cm,1 mm,9.8]

bBV[cbYoung,cbPoisson,cbDens,1.8cm,10 cm,1 mm,9.8]

tungsten

tunYoung = 40.7*10^(10); (*Young,s modulus [Pa]*)

tunShear = 17.3*10^(10); (*Shear modulus [Pa]*)

tunTensile = 25*10^(8); (*Tensile strength [Pa]. 15-35 in the book*)

tunDens = 19.1*10^3 kg/m^3; (*Density [kg/m^3]*)

tunPoisson = 0.22; (*Poisson's ratio*)

piano wire

pwYoung = 20*10^(10); (*Young,s modulus [Pa]*)

pwShear = 8.1*10^(10); (*Shear modulus [Pa]*)

pwTensile = 21*10^(8); (*Tensile strength [Pa]. 15-35 in the book*)

pwDens = 7.86*10^3 kg/m^3; (*Density [kg/m^3]*)

pwPoisson = 0.29; (*Poisson's ratio*)

phosphorus bronze

phbYoung = 120*10^(9); (*Young,s modulus [Pa]*)

phbShear = 4.36*10^(10); (*Shear modulus [Pa]*)

phbTensile = 8.9*10^(8); (*Tensile strength [Pa]. 6.9-10.8 in the book*)

phbDens = 8.93*10^3 kg/m^3; (*Density [kg/m^3]*)

phbPoisson = 0.38; (*Poisson's ratio*)

aluminum

alYoung = 7.03*10^(10); (*Young,s modulus [Pa]*)

alShear = 4.34*10^(10); (*Shear modulus [Pa]*)

alTensile = 3.3*10^(8); (*Tensile strength [Pa]. 2.5-4.5 in the book*)

alDens = 2.69*10^3 kg/m^3; (*Density [kg/m^3]*)

alPoisson = 0.345; (*Poisson's ratio*)

alEmis = 0.1; (*Emissivity of aluminum*)

copper

cuYoung = 12.98*10^(10); (*Young,s modulus [Pa]*)

cuShear = 4.83*10^(10); (*Shear modulus [Pa]*)

cuTensile = 2.9*10^(8); (*Tensile strength [Pa]. 2.5-4.5 in the book*)

cuDens = 8.93*10^3 kg/m^3; (*Density [kg/m^3]*)

cuPoisson = 0.343; (*Poisson's ratio*)

cuEmis = 0.1; (*Emissivity of aluminum*)

fused silica

fsYoung = 7.31*10^(10); (*Young,s modulus [Pa]*)

fsShear = 3.12*10^(10); (*Shear modulus [Pa]*)

fsTensile = 10*10^(8); (*Tensile strength [Pa]*)

fsDens = 2.22*10^3 kg/m^3; (*Density [kg/m^3]*)

fsPoisson = 0.17; (*Poisson's ratio*)

sapphire

saYoung = 40*10^(10); (*Young,s modulus [Pa]*)

(*saShear = 2.61*10^(10); (*Shear modulus [Pa]*)*)

saTensile = 2.25*10^(9); (*Tensile strength [Pa].*)

saDens = 3.99*10^3 kg/m^3; (*Density [kg/m^3]*)

saPoisson = 0.27; (*Poisson's ratio*)

(*saabs = 30 ppm/cm ;(*laser absorption ratio*)*)

saEmis = 0.1*10; (*Emissivity*)

saQfiber = 5*10^6; (*quality factor of fiber at 10K*)

saQMass20 = 10^8;(*quality factor of mirror at 20K*)
saQMass25 = 6*10^7;(*quality factor of mirror at 25K*)
saQMass300 = 10^7;(*quality factor of mirror at 300K*)

saKappa300 = 46; (*thermal conductivuty at 300K [W/m/K]*)
saKappa25 = 2.02*10^4; (*thermal conductivuty at 25K [W/m/K]*)
saKappa20 = 1.57*10^4; (*thermal conductivuty at 20K [W/m/K]*)

saSpHeat300 = 3.09*10^6; (*specific heat at 300K [J/K/m^3]*) 
saSpHeat25 = 5.52*10^3; (*specific heat at 25K [J/K/m^3]*) 
saSpHeat20 = 2.76*10^3; (*specific heat at 20K [J/K/m^3]*)

saAlpha300 = 5.40*10^-6 ;(*linear expansion ratio at 300K*)
saAlpha25 = 1.09*10^-8; (*linear expansion ratio at 25K*)
saAlpha20 = 5.6*10^-9; (*linear expansion ratio at 20K*)

Final mass & final suspension

Final mass

rMass= 12.5 cm;

lMass = 15 cm;

sMass = sACyl[rMass,lMass]; (*surface aria m^2*)

vMass=  vCyl[rMass,lMass] ;(*volume m^3*)

mMass= vMass saDens (*mass kg*)

pZMass = 800 mm;(*position in Z direction from ground*)

Recoil mass for final mass

rRMass= 12.5 cm;

lRMass = 15 cm;

sRMass = sACyl[rRMass,lRMass]; (*surface aria m^2*)

vRMass=  vCyl[rRMass,lRMass] ;(*volume m^3*)

mRMass= vRMass saDens (*mass kg*)

pZRMass = 800 mm;(*position in Z direction from ground*)

Upper mass

UMassDens = saDens;
rUMass = 12.5 cm;
lUMass =  15 cm;

sUMass = sACyl[rUMass,lUMass];
vUMass = vCyl[rUMass,lUMass];
mUMass = UMassDens vUMass

Recoil mass for upper mass

RUMassDens = saDens;
rRUMass = 12.5 cm;
lRUMass =  15 cm;

sRUMass = sACyl[rRUMass,lUMass];
vRUMass = vCyl[rRUMass,lRUMass];
mRUMass = RUMassDens vRUMass

Suspension platform

SpMassDens = cuDens;
SpMassX = 25 cm;
SpMassY = 25 cm;
SpMassZ = 11 cm;

sSpMass = sACube[SpMassX,SpMassY,SpMassZ];
vSpMass = vCube[SpMassX,SpMassY,SpMassZ];
mSpMass = SpMassDens vSpMass

Coating

dcoa=7.5*10^(-6);(* thickness of coating (m) *)

phicoa=4*10^(-4);(* loss angle of coating*)

Final suspension

lSaPend = 0.4m;(*length of final pendulum*)

numSaPend = 4;(*number of sapphire fiber*)

diaSaPend = 1.8mm; (*diamete of sapphire fiber*)

Upper mass suspension

lUMassPend = 0.4 m;

numUMassPend = 4;(*number of sapphire fiber*)

Suspension platform suspension

lSpMassPend = 1.0 m;

numSpMassPend = 4;(*number of sapphire fiber*)

Dimensions of cryostat

thickness of radiation shield

tPlate = 5mm; (*thickness of aluminum plate*)

number of super insulator

numSI = 60;

Cryostat

bottom part(BPart)

xBPart = 1.3m;(*longer side of bottom part. X direction. Without flange*)

yBPart = 0.9 m; (*shorter side of bottom part. Y direction.Without flange*)

zBPart = 0.35m ;(*height of bottom part. Z direction.*)

rTABPart = 300mm/2;(*radius of thermal anchor*)

lTABPart = 300mm;(*length of thermal anchor*)

pXTABPart = 300mm ;(*X position from center*)

rSBPart = 250mm;(*radius of stage support pipe*)

lSBPart = 350mm;(*length of stage support pipe*)

numSBPart = 4;(*number of stage support pipe*)

pXSBPart = 500mm;(*Absolute X position of stage support pipe*)

pYSBPart = 325mm;(*Absolute Y position of stage support pipe*)

main body(MBody)

xMBody = 1.3m; (*longer side of main cryostat. X direction*)

yMBody= 0.9 m; (*shorter side of main cryostat*)

zMBody = 1.35m; (*height of main cryostat body*)

pZMBody = zBPart;(*Z position of bottom flange from ground*)

rLSMBody = 400 mm/2;(*radius of longer side beam pipe*)

lLSMBody = 1.2m;(*length of longer side beam pipe*)

rSSMBody = 400 mm/2;(*radius of shorter side beam pipe*)

lSSMBody = 0.3m;(*length of shorter side beam pipe*)

outer shield in main body(OSMBody)

rOSMBody = 0.85m/2; (*radius of 80K rad-shield *)

lOSMBody = 0.9m; (*length of 80K rad-shield*)

pZOSMBody = 0.55 m;(*Z position of bottom from ground*)

rSSOSMBody = 300 mm/2; (*radius of shorter side outer shield*)

lSSOSMBody = 0.3m;(*length of shorter side outer shield*)

rLSOSMBody = 300 mm/2; (*radius of longer side outer shield*)

lLSOSMBody = 1.2m;(*length of longer side outer shield*)

rCWOSMBody = 200 mm/2;(*radius of center wire outer shield*)

lCWOSMBody = 450 mm;(*length of center wire outer shield*)

numCWOSMBody = 1;(*number of center wire outer shield*)

rOWOSMBody = 150 mm/2;(*radius of outer wire outer shield*)

lOWOSMBody = 450 mm;(*length of outer wire outer shield*)

numOWOSMBody = 4;(*number of outer wire outer shield*)

pROWOSMBody = 300 mm;(*position of outer wire outer shield from center*)

rTAOSMBody = 200 mm/2;(*radius of thermal anchor outer shield*)

lTAOSMBody = 450 mm;(*length of outer wire outer shield*)

G10 support of outer shield in main body

rG10OSMBody = 20 mm/2;(*radius of support G10rod*)

lG10OSMBody = 150 mm;(*radius of support G10rod*)

numG10OSMBody = 8;(*radius of support G10rod*)

hole on outer shield in main body

rHSSOSMBody = 300mm /2;(*radius of hole of shorter side outer shield*)

rHLSOSMBody = 20mm /2;(*radius of hole of longer side outer shield*)

rHCWOSMBody = 20mm/2;(*radius of hole of center wire outer shield*)

numHCWOSMBody=4;(*number of hole of center wire outer shield*)

rHOWOSMBody = 20mm/2;(*radius of hole of outer wire outer shield*)

numHOWOSMBody=4;(*number of hole of center wire outer shield*)

inner shield in main body(ISMBody)

rISMBody = 0.8m/2; (*radius of 80K rad-shield *)

lISMBody = 0.8m; (*length of 80K rad-shield*)

pZISMBody = 0.6 m;(*Z position of bottom from ground*)

G10 support of inner shield in main body

rG10ISMBody = 10 mm/2;(*radius of support G10rod*)

lG10ISMBody = 50 mm;(*length of support G10rod*)

numG10ISMBody = 8;(*number of support G10rod*)

hole on inner shield in main body

rHSSISMBody = rMass;(*radius of hole of shorter side inner shield*)

rHLSISMBody = rMass;(*radius of hole of longer side inner shield*)

rHCWISMBody = 20mm/2;(*radius of hole of center wire inner shield*)

numHCWISMBody=4;(*number of hole of center wire inner shield*)

rHOWISMBody = 20mm/2;(*radius of hole of outer wire inner shield*)

numHOWISMBody=4;(*number of hole of outer wire inner shield*)

signal lines in main body

lSigOSMBody = 1*2*Pi*rOSMBody(*length of signal cable between outer shield to 300K. 1 turn aroud outer shield[m].*)

numSigOSMBody = 4*5/2 ;(*number of coaxial signal lines at outer shield. 5thermometers*)

lSigISMBody = 1*2*Pi*rISMBody(*length of signal cable between inner shield to outer shield. 1 turn aroud inner shield[m].*)

numSigISMBody = 0+4*22/2+5*4/2 ;(*number of coaxial signal lines at inner shield. 0lemo+4*22pin+5thermometers*)

top roof

xTRoof = 1.3m; (*longer side of main cryostat. X direction*)

yTRoof= 0.9 m; (*shorter side of main cryostat*)

zTRoof = 0.7m; (*height of main cryostat body*)

pTRoof = zBPart+zMBody;(*Z position of bottom flange from ground*)

connection pipe for cryostat

rCPCryo = 150mm/2;(*radius of connection pipe for cryostat*)

lCPCryo = 1000mm ;(*length of connection pipe for cryostat*)

rOSCPCryo = 100mm/2;(*radius of outer shield in connection pipe for cryostat*)

lOSCPCryo = 1000mm;(*length of outer shield in connection pipe for cryostat*)

xTCCPCryo = 1000 mm;(*length of thermal conducter in connecte pipe of cryostat*)

yTCCPCryo = 50 mm;(*length of thermal conducter in connecte pipe of cryostat*)

zTCCPCryo = 10 mm;(*length of thermal conducter in connecte pipe of cryostat*)

refrigerator unit for cryostat

rRUCryo = 360mm/2;(*radius of refrigerator unit for cryostat *)

lRUCryo = 800 mm;(*radius of refrigerator unit for cryostat *)

rOSRUCryo = 240mm/2;(*radius of outer shield in refrigerator unit for cryostat *)

lOSRUCryo = 500mm;(*length of outer shield in refrigerator unit for cryostat *)

signal lines in refrigerator unit

lSigOSRUCryo = 1*2*Pi*rOSRUCryo(*length of signal cable between outer shield to 300K. 1 turn aroud outer shield.[m]*)

numSigOSRUCryo = 3*4/2 ;(*number of coaxial signal lines at outer shield. 3thermometers*)

lSigISRUCryo = 1*2*Pi*rOSRUCryo(*length of signal cable between inner shield to outer shield. 1 turn aroud inner shield.[m]*)

numSigISRUCryo = 0+0*22/2+5*4/2 ;(*number of coaxial signal lines at inner shield. 0lemo+0*22pin+3thermometers*)

Surface area of cryostat

chamber

sACryo=sACube[xMBody,yMBody,zMBody+zTRoof]+sACyl[rRUCryo,lRUCryo]+sAPipe[rCPCryo,lCPCryo]+sAPipe[rTABPart,lTABPart]+sAPipe[rSBPart,lSBPart]*numSBPart+sAPipe[rLSMBody,lLSMBody]+sAPipe[rSSMBody,lSSMBody]-2*aC[rCPCryo] (*surface area of chamber. [m^2]*)

outer shield

sAOSCryo = sACyl[rOSMBody,lOSMBody]+sACyl[rOSRUCryo,lOSRUCryo]+sAPipe[rOSCPCryo,lOSCPCryo]+sAPipe[rCWOSMBody,lCWOSMBody]+sAPipe[rOWOSMBody,lOWOSMBody]*numOWOSMBody+sAPipe[rTAOSMBody,lTAOSMBody]+sAPipe[rSSOSMBody,lSSOSMBody]+sAPipe[rLSOSMBody,lLSOSMBody]-2*aC[rOSCPCryo] (*surface area of outer shield in cryostat. [m^2]*)

inner shield

sAISCryo = sACyl[rISMBody,lISMBody]+sACube[xTCCPCryo,yTCCPCryo,zTCCPCryo](*surface area of inner shield & thermal conducter in cryostat. [m^2]*)

Vacuum pipe

pipe

rVPipe = 300 mm/2;(*radius of vacuum pipe*)

lVPipe =20 m;(*length of vacuum pipe*)

rTAVPipe = xx mm/2;(*radius of thermal anchor of vacuum pipe*)

lTAVPipe = xx mm/2;(*length of thermal anchor of vacuum pipe*)

shield

rSVPipe = 300mm/2; (*radius of shield in vacuum pipe*)

lSVPipe = 20m; (*length of shield in vacuum pipe*)

rTASVPipe = xx mm/2;(*radius of shield thermal anchor of vacuum pipe*)

lTASVPipe = xx mm/2;(*length of shield thermal anchor of vacuum pipe*)

G10 support for shield

rG10VPipe =xx mm;(*radius of G10 rod for shield in vacuum pipe*)

lG10VPipe=xx mm ;(*length of G10 rod for shield in vacuum pipe*)

numG10VPipe=xx mm;(*number of G10 rod for shield in vacuum pipe*)

Signal lines in vacuum pipe

lSigSVPipe = 1*2*Pi*rSVPipe;(*length of signal cable between outer shield to 300K. 1 turn aroud outer shield.[m]*)

numSigSVPipe = 6*4/2 ;(*number of coaxial signal lines at outer shield. 6thermometers*)

connection pipe for vacuum pipe

rCPVPipe = xx mm/2;(*radius of connection pipe for vacuum pipe*)

lCPVPipe = xx mm ;(*length of connection pipe for vacuum pipe*)

rSCPVPipe = xx mm/2;(*radius of outer shield in connection pipe for vacuum pipe*)

lSCPVPipe = xx mm;(*length of outer shield in connection pipe for vacuum pipe*)

refrigerator unit for vacuum pipe

rRUVPipe = xx mm/2;(*radius of refrigerator unit for vacuum pipe *)

lRUVPipe = xx mm;(*radius of refrigerator unit for vacuum pipe *)

Signal lines in refrigerator unit of  vacuum pipe

lSigRUVPipe = 1*2*Pi*rRUVPipe(*length of signal cable between outer shield to 300K. 1 turn aroud outer shield.[m]*)

numSigRUVPipe = 3*4/2 ;(*number of coaxial signal lines at outer shield. 3thermometers*)

Surface area of vacuum pipe

pipe

sAVPipe = sACyl[rRUVPipe,lRUVPipe]+sAPipe[rSVPipe,lSVPipe]+sAPipe[rTAVPipe,lTAVPipe]+sAPipe[rCPVPipe,lCPVPipe]-2*aC[rCPVPipe]

shield

sASVPipe = sAPipe[rSVPipe,lSVPipe]+sAPipe[rTASVPipe,lTASVPipe]+sAPipe[rSCPVPipe,lSCPVPipe]

Laser and cavity

Laser

lambda=1064*10^(-9);(* wavelength (m) *)

gRecycling = 11;(*recycling gain*)

p = 75 W ;(*effective laser power before recycling mirror [W]*)

cavity

l=3*10^3;(* length of cavity (m) *)
finesse=1550;(* finesse of cavity *)
gBand = 15(*signal band width gain by RSE*);
pCav = pcav[p,finesse,gRecycling](*power in cavity*);
tau=sTime[l,finesse];(* storage time of cavity (sec) *)
fcut=gBand fCut[l,finesse];(* cut-off frequency of cavity (Hz) *)
R2=250;(* curvature of end mirror (m) *)
g1=1;
g2=1-l/R2;
(*w1=Sqrt[l*lambda/Pi/Abs[g1]*Sqrt[g1*g2/(1-g1*g2)]];(* beam radius at front mirror (m) *)
w2=Sqrt[l*lambda/Pi/Abs[g2]*Sqrt[g1*g2/(1-g1*g2)]];(* beam radius at end mirror (m) *)
*)
w1= 3 cm;
w2 = 3 cm;

StringForm["beam radius at front mirror is `` mm",NumberForm[N[w1]*1000,3]]
StringForm["beam radius at end mirror is `` mm",NumberForm[N[w2]*1000,3]]
StringForm["storage time of cavity is `` msec",NumberForm[tau*1000,3]]
StringForm["cut-off frequency of cavity is `` Hz",NumberForm[fcut,3]]

Temeperature

tMass = 20 K; (*temperature of final mass [K]*)

tISCryo = 8 K;(*temperature of 4K rad-shield*)

tOSCryo = 100 K; (*temperature of 80K rad-shield*)

tRoom = 300 K; (*room temperature*)

real DATA

real data LISM 030214

dataLISM030214=ReadList["~/Study/CurrentProject/CLIO100/suspension/realdata/LISM030214.txt",{Number,Number}];

plotLISM030214=ListLogLogPlot[dataLISM030214,Joined->True]

real data LISM 030320

dataLISM030320=ReadList["~/Study/CurrentProject/CLIO100/suspension/realdata/LISM030320.txt",{Number,Number}];

plotLISM030320=ListLogLogPlot[dataLISM030320,Joined->True]

real data TAMA030712

dataTAMA030712=ReadList["~/Study/CurrentProject/CLIO100/suspension/realdata/tama030712.txt",{Number,Number}];

plotTAMA030712=ListLogLogPlot[dataTAMA030712,Joined->True,PlotStyle->RGBColor[1,0.5`,0.5`]]

Show[plotTAMA030712,plotLISM030320]

plotDummy=LogLogPlot[10^-10 (10/f)^14,{f,10,30},PlotStyle -> RGBColor[1,1,1]]

Show[plotDummy,plotTAMA030712,plotLISM030320]

Cooling

Heat in suspension

Parameters

absorption parameter

saAbs = 20 ppm/cm; (*Absorption of sapphire*)

coatAbs = 0.1  ppm; (*Absorption at coating*)

Safety margin

sMSus = 10; (*safety margin of upper mass suspension*)

sMHeat = 3; (*safety margin of heat*)

Calculation

Laser absorption

heatLAMass = hLAMass[p gRecycling,saAbs,lMass];

heatLACoat = hLACoat[p gRecycling,coatAbs,finesse];

heatLAbs = heatLAMass+heatLACoat;

Radiation into the final mass

solid angle of laser holes

sAngleHSSOSMBMass = sAngle[rHSSOSMBody,rOSMBody/2+lSSOSMBody];(*solid angle of hole of shoter side outer shield from mass. Vacuum pipe will attach this side. This solid angle is not important.from 300K*)

sAngleHLSOSMBMass = sAngle[rHLSOSMBody,rOSMBody/2+lLSOSMBody];(*solid angle of hole of longer side outer shield from mass.from 300K*)

sAngleSVPipeMass = sAngle[rSVPipe,rOSMBody/2+lSSOSMBody+lSVPipe];(*solid angle of hole of vacuum pipe from mass.from 300K*)

sAngleLHMassRoom = sAngleHLSOSMBMass+sAngleSVPipeMass; (*solid angle of laser hole from mass. 300K*)

sAngleHSSISMBMass = sAngle[rHSSISMBody,rISMBody/2];(*solid angle of hole of shorter side inner shield from mass.from 100K*)

sAngleHLSISMBMass = sAngle[rHLSISMBody,rISMBody/2];(*solid angle of hole of longer side inner shield from mass.from 100K*)

sAngleLHMassOS = sAngleHLSOSMBMass+sAngleSVPipeMass; (*solid angle of laser hole from mass. 100K*)

solid angle of suspension wire holes (not important for the final mass.)

sAngleHCWOSMBMass = numHCWOSMBody*sAngle[rHCWOSMBody,pZOSMBody+lOSMBody+lCWOSMBody-pZMass]; (*solid angle of wire hole from mass. from 300K*)

sAngleSHMassRoom = sAngleHCWOSMBMass;(*solid angle of wire hole from mass. from 300K*)

sAngleHCWISMBMass = numHCWISMBody*sAngle[rHCWISMBody,pZISMBody+lISMBody-pZMass];(*solid angle of wire hole from mass. from 100K*)

sAngleSHMassOS = sAngleHCWISMBMass;(*solid angle of wire hole from mass. from 100K*)

total solid angle

sAngleMassRoom = sAngleLHMassRoom;
sAngleMassOS = sAngleLHMassOS;
sAngleMassIS = 4 Pi -sAngleMassRoom-sAngleMassOS;

heat

heatRadMassRoom = hRadMass[tRoom,tMass,sMass,sAngleMassRoom,saEmis];(*radiation comes from holes for laser to final mass[W]*)

heatRadMassOS = hRadMass[tOSCryo,tMass,sMass,sAngleMassOS,saEmis];(*radiation comes from holes for laser to final mass[W]*)

heatRadMassIS = hRadMass[tISCryo,tMass,sMass,sAngleMassIS,saEmis];(*radiation comes from holes for laser to final mass[W]*)

heatRadMass  =heatRadMassRoom+heatRadMassOS+heatRadMassIS;(*total radiation heat in final mass [W]*)

Cooling by sapphire fibers & decide temperature of upper mass

(*heatMass = heatLAbs+heatRadMass;(*total heat in final mass [W]*)*)

heatMass = heatLAbs;(*total heat in final mass [W]*)

heatMassMax = sMHeat heatMass; (*total heat in final mass with safety margin. [W]*)

(*heatMassMax=y;*)

tDeltaMass =tDelta[heatMassMax] ;(*temperature increase due to thermal contact resistance [K]*)

tSaPend = tMass - tDeltaMass; (*temperature of sa-fiber at contact point with final mass [K]*)

solveTUMass = Part[Solve[heatMassMax-hSa[numSaPend,tSaPend,x,diaSaPend,lSaPend] ==0,x],1];

tUMass =x/.solveTUMass

Plot[tUMass,{y,0.4,1},GridLines-> Automatic]

Thermal conduction from 300K

diaUMassPend=2*(Sqrt[((sMSus*(mMass+mUMass)*gaccel)/(numUMassPend*susTensile*Pi))]);(*minimum radius of suspension wire [m]*)

heatTCUMassPend = hSUS[numUMassPend,diaUMassPend/2,lUMassPend];(*[W]*)

Radiation into the upper mass

solid angle of suspension wire holes

sAngleHCWOSMBUMass = numHCWOSMBody*sAngle[rHCWOSMBody,pZOSMBody+lOSMBody+lCWOSMBody-pZMass-lSaPend]; (*solid angle of wire hole from mass. from 300K*)

sAngleSHUMassRoom = sAngleHCWOSMBUMass;(*solid angle of wire hole from mass. from 300K*)

sAngleHCWISMBUMass = numHCWISMBody*sAngle[rHCWISMBody,pZISMBody+lISMBody-pZMass-lSaPend];(*solid angle of wire hole from mass. from 100K*)

sAngleSHUMassOS = sAngleHCWISMBUMass;(*solid angle of wire hole from mass. from 100K*)

total solid angle

sAngleUMassRoom = sAngleSHUMassRoom;
sAngleUMassOS = sAngleSHUMassOS;
sAngleUMassIS = 4 Pi -sAngleUMassRoom-sAngleUMassOS;

heat

heatRadUMassRoom = hRadMass[tRoom,tMass,sMass,sAngleUMassRoom,saEmis];(*radiation comes from holes for laser to upper mass[W]*)

heatRadUMassOS = hRadMass[tOSCryo,tMass,sMass,sAngleUMassOS,saEmis];(*radiation comes from holes for laser to upper mass[W]*)

heatRadUMassIS = hRadMass[tISCryo,tMass,sMass,sAngleUMassIS,saEmis];(*radiation comes from holes for laser to upper mass[W]*)

heatRadUMass  =heatRadUMassRoom+heatRadUMassOS+heatRadUMassIS;(*total radiation heat in final mass [W]*)

Total heat in suspension

heatSus = heatRadUMass+heatTCUMassPend+heatMass;(*estimated heat in suspension without safety value [W]*)

heatSusMax = heatSus*sMHeat; (*estimated heat in suspension with safety value [W]*)

Summary

StringForm["Total laser Absorption heat is `` mW",NumberForm[heatLAbs*1000,3]]
StringForm["laser Absorption in substrate is `` mW",NumberForm[heatLAMass*1000,3]]
StringForm["laser Absorption in coating is `` mW",NumberForm[heatLACoat*1000,3]]
StringForm["Radiation heat from 300K into final mass is `` mW",NumberForm[(heatRadMassRoom)*1000,3]]
StringForm["Radiation heat from outer shield into final mass is `` mW.",NumberForm[(heatRadMassOS)*1000,3]]
StringForm["Radiation heat goes to inner shield from final mass is `` mW",NumberForm[(-heatRadMassIS)*1000,3]]
StringForm["Total radiation heat into final mass is `` mW",NumberForm[heatRadMass*1000,3]]
StringForm["Total heat transfered by fibers without safety value is  `` mW",NumberForm[heatMass*1000,3]]
StringForm["Total heat transfered by fibers with safety value is  `` mW",NumberForm[heatMassMax*1000,3]]
StringForm["Diameter of the sapphire fiber is  `` mm",NumberForm[diaSaPend*1000,3]]
StringForm["Temeperature of the upper mass is  `` K",NumberForm[tUMass,3]]
StringForm["Temeperature increase due to thermal contact resistance is  `` K",NumberForm[tDeltaMass,3]]
StringForm["Temeperature of the end of fiber of final mass side is  `` K",NumberForm[tSaPend,4]]
StringForm["Minimum diameter of suspension wire is `` mm",NumberForm[diaUMassPend*1000,3]]
StringForm["Length of suspension wires are `` m",NumberForm[lUMassPend,3]]
StringForm["Number of suspension wires are `` ",NumberForm[numUMassPend,1]]
StringForm["Safety value is ``",NumberForm[sMSus,3]]
StringForm["Heat transfered by thermal conductivity of suspension wire is `` mW",NumberForm[heatTCUMassPend*1000,3]]
StringForm["Radiation heat from 300K into upper mass is `` mW",NumberForm[(heatRadUMassRoom)*1000,3]]
StringForm["Radiation heat from outer shield into upper mass is `` mW.",NumberForm[(heatRadUMassOS)*1000,3]]
StringForm["Radiation heat goes to inner shield into upper mass is `` mW",NumberForm[(-heatRadUMassIS)*1000,3]]
StringForm["Radiation heat into final mass is `` mW",NumberForm[heatRadUMass*1000,3]]
StringForm["Estimated total heat in suspension without margin is `` mW",NumberForm[(heatSus)*1000,3]]
StringForm["Estimated total heat in suspension with margin is `` mW",NumberForm[(heatSusMax)*1000,3]]

Heat in cryostat system

radiation heat

calcualtion

heatRadOSMBody = hRadRoom[sAOSCryo];(*radiation into outer shield from 300K.*)

heatRadISMBody = hRadArea[tOSCryo,tISCryo,alEmis,sAISCryo]/(numSI+1);(*radiation into inner shield from outer shield.*)

total

heatRadOSCryo = heatRadOSMBody-heatRadISMBody;

heatRadISCryo = heatRadISMBody;

heatRadVPipe = hRadRoom[sASVPipe];

radiation through hole (see note 2002/12/31)

calcuration

from shorter side with vacuum pipe

heatHSSISMBRoom= hRadHole[tRoom,tISCryo,alEmis,rHSSISMBody]*((sAngle[rSVPipe,rOSMBody+lSSOSMBody+lSVPipe-rISMBody])/(2 Pi))((2 Pi)/(4 Pi));(*300K radiation heat into inner shield throgh shorter side laser hole *)

heatHSSISMBOS = hRadHole[tOSCryo,tISCryo,alEmis,rHSSISMBody]*(1-((sAngle[rSVPipe,rOSMBody+lSSOSMBody+lSVPipe-rISMBody])/(2 Pi)))*((2 Pi)/(4 Pi));(*radiation heat into inner shield throgh shorter side laser hole from outer shield *)

heatHSSOSMBRoom = hRadHole[tRoom,tOSCryo,alEmis,rSVPipe]*(1/(2 Pi))(sAngle[rHSSOSMBody,lSVPipe]-sAngle[rHSSISMBody,rOSMBody+lSSOSMBody+lSVPipe-rISMBody])((2 Pi)/(4 Pi));
(*300K radiation heat into outer shield throgh shorter side laser hole *)

heatHSVPRoom = hRadHole[tRoom,tOSCryo,alEmis,rSVPipe]((2 Pi)/(4 Pi))-heatHSSOSMBRoom-heatHSSISMBRoom;(*300K radiation into vacuum pipe*)

heatHSSOSCryo =heatHSSOSMBRoom-heatHSSISMBOS;

heatHSSISCryo = heatHSSISMBRoom+heatHSSISMBOS;

from longer side

heatHLSISMBRoom= hRadHole[tRoom,tISCryo,alEmis,rHLSISMBody]*((sAngle[rHLSOSMBody,rOSMBody+lLSOSMBody-rISMBody])/(2 Pi))((2 Pi)/(4 Pi));(*300K radiation heat into inner shield throgh center wire hole *)

heatHLSISMBOS = hRadHole[tOSCryo,tISCryo,alEmis,rHLSISMBody]*(1-((sAngle[rHLSOSMBody,rOSMBody+lLSOSMBody-rISMBody])/(2 Pi)))*((2 Pi)/(4 Pi));(*radiation heat into inner shield throgh shorter side laser hole from outer shield *)

heatHLSOSMBRoom = hRadHole[tRoom,tOSCryo,alEmis,rHLSOSMBody]*((2 Pi)/(4 Pi))-heatHLSISMBRoom;
(*300K radiation heat into outer shield throgh shorter side laser hole *)

heatHLSOSCryo =heatHLSOSMBRoom-heatHLSISMBOS;

heatHLSISCryo = heatHLSISMBRoom+heatHLSISMBOS;

from center wire hole

heatHCWISMBRoom = numCWOSMBody*numHCWISMBody*hRadHole[tRoom,tISCryo,alEmis,rHCWISMBody]*((sAngle[rHCWOSMBody,pZOSMBody+lOSMBody+lCWOSMBody-(pZISMBody+lISMBody)])/(2 Pi))((2 Pi)/(4 Pi));(*300K radiation heat into inner shield throgh center wire hole *)

heatHCWISMBOS = numCWOSMBody*numHCWISMBody*hRadHole[tOSCryo,tISCryo,alEmis,rHCWISMBody]*(1-((sAngle[rHCWOSMBody,pZOSMBody+lOSMBody+lCWOSMBody-(pZISMBody+lISMBody)])/(2 Pi)))((2 Pi)/(4 Pi));(*radiation heat into inner shield throgh center wire hole from outer shield*)

heatHCWOSMBRoom = numHCWOSMBody*hRadHole[tRoom,tOSCryo,alEmis,rHCWOSMBody]((2 Pi)/(4 Pi))-heatHCWISMBRoom;
(*300K radiation heat into inner shield throgh center wire *)

heatHCWOSCryo =heatHCWOSMBRoom-heatHCWISMBOS;

heatHCWISCryo = heatHCWISMBRoom+heatHCWISMBOS;

from outer wire hole

heatHOWISMBRoom = numOWOSMBody*numHOWISMBody*hRadHole[tRoom,tISCryo,alEmis,rHOWISMBody]*((sAngle[rHOWOSMBody,pZOSMBody+lOSMBody+lOWOSMBody-(pZISMBody+lISMBody)])/(2 Pi))((2 Pi)/(4 Pi));
(*300K radiation heat into inner shield throgh outer wire hole *)

heatHOWISMBOS = numOWOSMBody*numHOWISMBody*hRadHole[tOSCryo,tISCryo,alEmis,rHOWISMBody]*(1-((sAngle[rHOWOSMBody,pZOSMBody+lOSMBody+lOWOSMBody-(pZISMBody+lISMBody)])/(2 Pi)))((2 Pi)/(4 Pi));(*radiation heat into inner shield throgh outer wire hole from outer shiel*)

heatHOWOSMBRoom = numOWOSMBody*hRadHole[tRoom,tOSCryo,alEmis,rHOWOSMBody]*((2 Pi)/(4 Pi))-heatHOWISMBRoom;
(*300K radiation heat into outer shield throgh outer wire hole *)

heatHOWOSCryo =heatHOWOSMBRoom-heatHOWISMBOS;

heatHOWISCryo = heatHOWISMBRoom+heatHOWISMBOS;

total

heatHRadOSCryo = heatHSSOSCryo+heatHLSOSCryo+heatHCWOSCryo+heatHOWOSCryo;

heatHRadISCryo = heatHSSISCryo+heatHLSISCryo+heatHCWISCryo+heatHOWISCryo;

heatHVPipe = heatHSVPRoom;

heat transfered by G10 support

calculation

heatG10OSMBody = hG10300[numG10OSMBody,rG10OSMBody,lG10OSMBody];

heatG10ISMBody = hG104[numG10ISMBody,rG10ISMBody,lG10ISMBody];

total

heatG10OSCryo = heatG10OSMBody-heatG10ISMBody;

heatG10ISCryo = heatG10ISMBody;

heatG10VPipe = hG10300[numG10VPipe,rG10VPipe,lG10VPipe];

heat transfered by signal cable

calcuration

heatSigOSMBody = hSig300[numSigOSMBody+numSigISMBody,lSigOSMBody];

heatSigISMBody = hSig4[numSigISMBody,lSigISMBody];

heatSigOSRUCryo = hSig300[numSigOSRUCryo+numSigISRUCryo,lSigOSRUCryo];

heatSigISRUCryo = hSig4[numSigISRUCryo,lSigISRUCryo];

heatSigSVPipe = hSig300[numSigSVPipe,lSigSVPipe];

heatSigRUVPipe = hSig300[numSigRUVPipe,lSigRUVPipe];

total

heatSigOSCryo = heatSigOSMBody+heatSigOSRUCryo-heatSigISCryo;

heatSigISCryo = heatSigISMBody+heatSigISRUCryo;

heatSigVPipe= heatSigSVPipe+heatSigRUVPipe;

Total

heatOSCryo  = heatRadOSCryo+heatHRadOSCryo+heatG10OSCryo+heatSigOSCryo;

heatISCryo = heatRadISCryo+heatHRadISCryo+heatG10ISCryo+heatSigISCryo;

heatVpipe  = heatRadVPipe+heatHVPipe+heatG10VPipe+heatSigVPipe;

summary

StringForm["Total heat in 40K head in mirror tank `` W",NumberForm[heatOSCryo,3]]

StringForm["Total heat in 40K head in vacuum pipe `` W",NumberForm[heatVpipe,3]]

StringForm["Total heat in 4K head in mirror tank `` W",NumberForm[heatISCryo,3]]

StringForm["Number of radiation shield `` ",NumberForm[numSI,3]]

(*surface aria*)
StringForm["Surface aria of 40K shield of mirror tank `` m^2",NumberForm[sAOSCryo,3]]

StringForm["Surface aria of 4K shield of mirror tank `` m^2",NumberForm[sAISCryo,3]]

StringForm["Surface aria of radiation shield of cryogenic vacuum pipe `` m^2",NumberForm[sASVPipe,3]]

(*40K shield of mirror tank*)

StringForm["heat due to radiation in 40K head in mirror tank `` W",NumberForm[heatRadOSCryo,3]]

StringForm["heat due to G10 support in 40K head in mirror tank `` W",NumberForm[heatG10OSCryo,3]]

StringForm["heat due to signal cable in 40K head in mirror tank `` W",NumberForm[heatSigOSCryo,3]]





(*40K shield of vacuum pipe*)
StringForm["heat due to radiation in 40K head in vacuum pipe `` W",NumberForm[heatRadVPipe,3]]

StringForm["heat due to radiation through holes in 40K head in vacuum pipe `` W",NumberForm[  heatHVPipe,3]]

StringForm["heat due to G10 support in 40K head in vacuum pipe `` W",NumberForm[heatG10VPipe,3]]

StringForm["heat due to signal cable in 40K head in vacuum pipe `` W",NumberForm[heatSigVPipe,3]]





(*4K shield of mirror tank*)
StringForm["heat comes from heat link in 4K head in mirror tank `` W",NumberForm[heatSus,3]]

StringForm["heat due to radiation in 4K head in mirror tank `` W",NumberForm[heatRadISCryo,3]]

StringForm["heat due to radiation through holes in 4K head in mirror tank `` W",NumberForm[  heatHRadISCryo,3]]


StringForm["heat due to G10 support in 4K head in mirror tank `` W",NumberForm[heatG10ISCryo,3]]

StringForm["heat due to signal cable in 4K head in mirror tank `` W",NumberForm[heatSigISCryo,3]]

Heat link

thermal condudtion of Al

kAl[rrr_,t_]:=(1/(1.83 10^(-7)t^2+(1.09/(rrr t))))(*thermal confuctivity of aluminum[W/m/K]*)

hAl[thigh_,tlow_,rrr_,r_,l_] :=((r^2 Pi)/l)(∫_tlow^thigh)kAl[rrr,x]\[DifferentialD]x

hAlU[thigh_,tlow_,rrr_,dia_,r_,deg_] :=((dia^2 Pi)/(4 r deg))(∫_tlow^thigh)kAl[rrr,x]\[DifferentialD]x

hAl2[thigh_,tlow_,rrr_,sl_] :=sl*(∫_tlow^thigh)kAl[rrr,x]\[DifferentialD]x(*sl_; S/l*)

(∫_5^7)kAl[6000,x]\[DifferentialD]x

LogLogPlot[{kAl[6000,temp]},{temp,3,30},{GridLines -> Automatic}]

hAl[13.1,8,6000,1.4 mm,Pi*0.25]

Sqrt[(0.5 mm /2)^2 30]

hAl[13.6,13.1,6000,1.2 mm,Pi*0.25]

Plot[hAl[14,8,6000,x mm,Pi*0.25],{x,0.1 , 2 },GridLines -> Automatic]

Plot[hAl[15,14,6000,x mm,Pi*0.20],{x,1 , 5 },GridLines -> Automatic]

heat transfer

(*heatHlink := nHlink*Integrate[thCondAl,{temp,tinrads,tumass}]*(((diaHlink/2)^2*Pi)/(rHlink degHlink))(*heat transfer of heat links of nHlink. diaHlink is diameter of Al wire. rHlink [deg] is radius of "U"shape of heat link. degHlink is degree of "U"shape.*)
*)

heatHlink := nHlink*hAlU[tumass,tinrads,5000,diaHlink,rHlink,degHlink]

Suspension

LCGT target sensitivity

seismic noise model

dispSeisModel[f_] := 2*10^(-9)/f^2*10^(-3)/f^6

hDispSeisModel[f_] := dispSeisModel[f]/l

1.0hDispSeisModel[3]

Read out noise

shot noise

hShot[f_] :=hshot[f,pCav,fcut]

shot[f_] := hShot[f]*l

hShotOriginal[f_ ] :=hshot[f,pCav,fcut]

shotOriginal[f_] := hShotOriginal[f]*l

radiation pressure noise

hRadia[f_] :=hradia[f,pCav,fcut,l,finesse,mMass]

radia[f_] :=hRadia[f]*l

hRadiaOriginal[f_] :=hradia[f,pCav,fcut,l,finesse,mMass]

radiaOriginal[f_] :=hRadiaOriginal[f]*l

radiaOriginal[10]

hRadiaOriginal[3]

test plot

LogLogPlot[{shot[f],radia[f]},{f,1,10000}]

Mirror thermal noise

noises in cryogenic 20K

thCoat20[f_] := mirrorcoa[f,tMass,dcoa,phicoa,w1,w2,saYoung](*sum up 4 mirros*)

thMassStrucure20[f_] := mirrorhomo[f,tMass,saPoisson,1/saQMass20,w1,w2,saYoung](*sum up 4 mirros*)

thElastic20[f_] := Sqrt[2*(thelastic[f,tMass,saAlpha20,saPoisson,saKappa20,saSpHeat20,w1]+thelastic[f,tMass,saAlpha20,saPoisson,saKappa20,saSpHeat20,w2])](*sum up 4 mirros*)

dispThMass20[f_] := Sqrt[thCoat20[f]^2+thMassStrucure20[f]^2+thElastic20[f]^2](*sum up 4 mirros*)

hDispThMass20[f_] := Sqrt[thCoat20[f]^2+thMassStrucure20[f]^2+thElastic20[f]^2]/l

noises in cryogenic 25K

thCoat25[f_] := mirrorcoa[f,tMass,dcoa,phicoa,w1,w2,saYoung](*sum up 4 mirros*)

thMassStrucure25[f_] := mirrorhomo[f,tMass,saPoisson,1/saQMass25,w1,w2,saYoung](*sum up 4 mirros*)

thElastic25[f_] := Sqrt[2*(thelastic[f,tMass,saAlpha25,saPoisson,saKappa25,saSpHeat25,w1]+thelastic[f,tMass,saAlpha25,saPoisson,saKappa25,saSpHeat25,w2])](*sum up 4 mirros*)

dispThMass25[f_] := Sqrt[thCoat25[f]^2+thMassStrucure25[f]^2+thElastic25[f]^2](*sum up 4 mirros*)

hDispThMass25[f_] := Sqrt[thCoat25[f]^2+thMassStrucure25[f]^2+thElastic25[f]^2]/l

noise in 300K

thCoat300[f_] := mirrorcoa[f,300,dcoa,phicoa,w1,w2,saYoung]

thMassStrucure300[f_] := mirrorhomo[f,300,saPoisson,1/saQMass300,w1,w2,saYoung]

thElastic300[f_] := Sqrt[2*(thelastic[f,300,saAlpha300,saPoisson,saKappa300,saSpHeat300,w1]+thelastic[f,300,saAlpha300,saPoisson,saKappa300,saSpHeat300,w2])]

dispThMass300[f_] := Sqrt[thCoat300[f]^2+thMassStrucure300[f]^2+thElastic300[f]^2]

hDispThMass300[f_] := Sqrt[thCoat300[f]^2+thMassStrucure300[f]^2+thElastic300[f]^2]/l

Model

dispLCGToriginal[f_] := Sqrt[dispSeisModel[f]^2+shotOriginal[f]^2+radiaOriginal[f]^2+dispThMass20[f]^2]

hDispLCGToriginal[f_] := Sqrt[hDispSeisModel[f]^2+hShotOriginal[f]^2+hRadiaOriginal[f]^2+hDispThMass20[f]^2]

dispLCGT20Model[f_] := Sqrt[dispSeisModel[f]^2+shot[f]^2+radia[f]^2+dispThMass20[f]^2]

dispLCGT25Model[f_] := Sqrt[dispSeisModel[f]^2+shot[f]^2+radia[f]^2+dispThMass25[f]^2]

dispLCGTRoomModel[f_] := Sqrt[dispSeisModel[f]^2+shot[f]^2+radia[f]^2+dispThMass300[f]^2]

dispLCGToriginal[100]

dispLCGToriginal[3]

dispLCGToriginal[10]

hDispLCGToriginal[10]

hDispLCGToriginal[3]

plotLCGTmodel= LogLogPlot[dispLCGToriginal[f],{f,1,1000},PlotRange -> All,PlotStyle -> Dashing[{0.03,0.03}]]

hDispLCGToriginal[10]

hDispLCGToriginal[100]

plotLCGTHmodel= LogLogPlot[hDispLCGToriginal[f],{f,1,1000},PlotRange -> All,PlotStyle -> Dashing[{0.03,0.03}]]

plotLCGT25model= LogLogPlot[dispLCGT25Model[f],{f,10,1000}]

plotLCGTRoommodel= LogLogPlot[dispLCGTRoomModel[f],{f,10,1000},PlotStyle -> {RGBColor[1,0,0],Dashing[{0.03,0.03}]}]

plotLCGTMTNRoom= LogLogPlot[dispThMass300[f],{f,10,1000},PlotStyle -> {RGBColor[1,0,0],Dashing[{0.03,0.03}]}]

Full suspension (OLD)

Parameters

intersting item

nItem = 7 ;
(*m1 ~ m7 -> 1 ~ 7,
md2 = 8,
md5 = 9,
Final mass = 7.*)

coupling & vibration amplification in cryostat

coupleZX = 5/100;(*coupling Z -> X*)
coupleYX = 10/100;(*coupling Y -> X*)
ampCryo = 100;(*seismic vibration amplification in cryostat*)
ampStage = 1;(*seismic vibration amplification in cryostat*)

offset of beam centering

offsetRoll = 0 mm;

offsetPitch = 0.1 mm;

offsetYaw = 0.1 mm;

dimensions of mass

m1

m1Dens = alDens;
m1X = 100mm;
m1Y = 100 mm;
m1Z = 70 mm;
mCube[alDens,m1X,m1Y,m1Z]

m2

m2Dens = alDens;
m2X = 100mm;
m2Y = 100 mm;
m2Z = 70 mm;
mCube[alDens,m2X,m2Y,m2Z]

m3

m3Dens = alDens;
m3X = 100mm;
m3Y = 100 mm;
m3Z = 70 mm;
mCube[alDens,m3X,m3Y,m3Z]

m4

m4Dens = alDens;
m4X = 100mm;
m4Y = 100 mm;
m4Z = 70 mm;
mCube[alDens,m4X,m4Y,m4Z]

m5

m5Dens = alDens;
m5X = 100mm;
m5Y = 100 mm;
m5Z = 70 mm;
mCube[alDens,m5X,m5Y,m5Z]

m6

m6Dens = UMassDens;
m6X = UMassX;
m6Y = UMassY;
m6Z = UMassZ;
mCube[alDens,m6X,m6Y,m6Z]

m7

m7Dens = saDens;
m7r = rMass;
m7l = lMass;

mMass

md2

md2Dens = alDens;
md2X = 100mm;
md2Y = 100 mm;
md2Z = 70 mm;
mCube[alDens,md2X,md2Y,md2Z]

md5

md5Dens = alDens;
md5X = 100mm;
md5Y = 100 mm;
md5Z = 70 mm;
mCube[alDens,md5X,md5Y,md5Z]

spring

kA

kAUYoung = alYoung;
kAUShear = alShear;
kAURad = Pi;
kAUDia = 0.2*10^(-3)m;
kAURadius = 7.5 cm;
kANum = 1;

kB

kBUYoung = alYoung;
kBUShear = alShear;
kBURad = Pi;
kBUDia = 0.2*10^(-3)m;
kBURadius = 7.5 cm;
kBNum = 1;

kC

kCUYoung = alYoung;
kCUShear = alShear;
kCURad = Pi;
kCUDia = 0.2*10^(-3)m;
kCURadius = 15 cm;
kCNum = 1;

heat check

kUsl := 1/(((lU[kAURad,kAURadius])/(kANum*aC[kAUDia]))+((lU[kBURad,kBURadius])/(kBNum*aC[kBUDia]))+((lU[kCURad,kCURadius])/(kCNum*aC[kCUDia])))

hAl2[tUMass,tISCryo,3000,kUsl](*heat transfered by heat link [W]*)

hAl2[tUMass,tISCryo,3000,kUsl]/heatSusMax(*show safety margin*)

g1

g1Length = 1m;
g1VFreq = 4Hz;

g2

g2Length =0.25m;
g2VFreq = 4Hz;

g3

g3Length = 1m;
g3VFreq = 4Hz;

g4

g4Length = 3 cm;
g4VFreq = 4 Hz;

g5

g5Length = 0.25m;
g5VFreq = 4 Hz;

g6

g6Length = lUMassPend;
g6VFreq = 4 Hz;

g7

g7Length = lSaPend;

gm2

gm2Length = 0.3m;
gm2VFreq = 4  Hz;

gm5

gm5Length = 0.3m;
gm5VFreq =4 Hz;

position of wire clamp from COM (4 wires + symmetrical distribution)

heat link clamp

pk01X = 1 mm;
pk01Y = 1 mm /2;
pk01Z = 0 mm;

pk10X = 1 mm;
pk10Y = 1 mm /2;
pk10Z = - m1Z/2;

pk13X = 1 mm;
pk13Y = 1 mm /2;
pk13Z = - m1Z/2;

pk31X = 1 mm;
pk31Y = 1 mm/2;
pk31Z = - m3Z/2 ;

pk36X = 1 mm;
pk36Y = 1 mm /2;
pk36Z = - m3Z/2;

pk63X = 1 mm;
pk63Y = 1 mm /2;
pk63Z = - m6Z/2;

suspension wires

pg01X = 20 mm;
pg01Y = 20 mm;
pg01Z = -0 mm;

pg10X = pg01X;
pg10Y = pg01Y;
pg10Z = +m1Z/2 ;

pg02X = 20 mm;
pg02Y = 20 mm;
pg02Z = +0mm;

pg20X = pg02X;
pg20Y = pg02Y;
pg20Z = +m2Z/2;

pg23X = 20 mm;
pg23Y = 20 mm;
pg23Z = -m2Z/2;

pg32X = pg23X;
pg32Y = pg23Y;
pg32Z = +m3Z/2;

pg04X = 20 mm;
pg04Y = 20 mm;
pg04Z = +0mm;

pg40X = pg04X;
pg40Y = pg04Y;
pg40Z = +m4Z/2;

pg45X = 20 mm;
pg45Y = 20 mm;
pg45Z = -m4Z/2;

pg54X = pg45X;
pg54Y = pg45Y;
pg54Z = +m5Z/2;

pg56X = 20 mm;
pg56Y = 20 mm;
pg56Z = -m5Z/2;

pg65X = pg56X;
pg65Y = pg56Y;
pg65Z = +m6Z/2;

pg67X = 10 mm;
pg67Y = rMass;
pg67Z = -0mm;

pg76X=pg67X;
pg76Y=pg67Y;
pg76Z=+0mm;

pgm02X=20 mm;
pgm02Y=20 mm;
pgm02Z=+0mm;

pgm20X=pgm02X;
pgm20Y=pgm02Y;
pgm20Z=+md2Z/2;

pgm05X=20 mm;
pgm05Y=20 mm;
pgm05Z=+0mm;

pgm50X=pgm05X;
pgm50Y=pgm05Y;
pgm50Z=+md5Z/2;

dissipation

qRoomH = 10^6;
qCryoH =  10^7;
qRoomV =  10^4;
qCryoV  = 10^5;
qUAl =  10^3;

qSaH =  10^8;
qSaV =  10^6;

qg1V = qRoomV;
qg3V = qRoomV;
qg6V = qCryoV;

g1TempV = tRoom;(*縦防振の板ばねをcryoに入れるときはm1Temp,それ以外はtRoom*)
g3TempV = m2Temp;(*縦防振の板ばねをcryoに入れるときはm3Temp,それ以外はm2Temp*)
g6TempV = m6Temp;(*縦防振の板ばねをcryoに入れるときはm6Temp,それ以外はm5Temp*)

in spring

kAPhi =   1/qUAl;
kBPhi =   1/qUAl;
kCPhi =   1/qUAl;

g10HPhi =  1/qRoomH;
g10VPhi =  1/qg1V;

g20HPhi =  1/qRoomH;
g20VPhi =  1/qRoomV;

g23HPhi = 1/qCryoH;
g23VPhi =  1/qg3V;

g32HPhi =  1/qRoomH;
g32VPhi =  1/qg3V;

g40HPhi = 1/qRoomH;
g40VPhi = 1/qRoomV;

g45HPhi = 1/qRoomH;
g45VPhi = 1/qRoomV;

g54HPhi =  1/qRoomH;
g54VPhi =  1/qRoomV;

g56HPhi =  1/qCryoH;
g56VPhi = 1/qg6V;

g65HPhi =  1/qRoomH;
g65VPhi =  1/qg6V;

g67HPhi =  1/qSaH;
g67VPhi =  1/qSaV;

g76HPhi =  1/qSaH;
g76VPhi =  1/qSaV;

gm20HPhi = 1/qRoomH;
gm20VPhi =1/qRoomV;

gm50HPhi = 1/qRoomH;
gm50VPhi =  1/qRoomV;

magnet damping

d1DampF = 5  Hz;
d1DampQ = 10;

d2DampF = 5 Hz;
d2DampQ = 10;

d3DampF = 0 Hz;
d3DampQ = 5;

d4DampF = 0Hz;
d4DampQ = 5;

d5DampF = 5 Hz;
d5DampQ = 10;

temperature

m1Temp = 8 K ;
m2Temp = 300K;
m3Temp =  8K;

m4Temp = 300K;
m5Temp = 300K;
m6Temp =  tUMass ;
m7Temp = tMass;

md2Temp = 300K;
md5Temp = 300K;

Preparation

mass & moment

m1

mass1 = mCube[m1Dens, m1X,m1Y, m1Z];

iRoll1 = mIRollCube[m1Dens, m1X,m1Y, m1Z];

iPitch1 = mIPitchCube[m1Dens, m1X,m1Y, m1Z];

iYaw1 = mIYawCube[m1Dens, m1X,m1Y, m1Z];

m2

mass2 = mCube[m2Dens, m2X,m2Y, m2Z];

iRoll2 = mIRollCube[m2Dens, m2X,m2Y, m2Z];

iPitch2 = mIPitchCube[m2Dens, m2X,m2Y, m2Z];

iYaw2 = mIYawCube[m2Dens, m2X,m2Y, m2Z];

m3

mass3 = mCube[m3Dens, m3X,m3Y, m3Z];

iRoll3 = mIRollCube[m3Dens, m3X,m3Y, m3Z];

iPitch3 = mIPitchCube[m3Dens, m3X,m3Y, m3Z];

iYaw3 = mIYawCube[m3Dens, m3X,m3Y, m3Z];

m4

mass4 = mCube[m4Dens, m4X,m4Y, m4Z];

iRoll4 = mIRollCube[m4Dens, m4X,m4Y, m4Z];

iPitch4 = mIPitchCube[m4Dens, m4X,m4Y, m4Z];

iYaw4 = mIYawCube[m4Dens, m4X,m4Y, m4Z];

m5

mass5 = mCube[m5Dens, m5X,m5Y, m5Z];

iRoll5 = mIRollCube[m5Dens, m5X,m5Y, m5Z];

iPitch5 = mIPitchCube[m5Dens, m5X,m5Y, m5Z];

iYaw5 = mIYawCube[m5Dens, m5X,m5Y, m5Z];

m6

mass6 = mCube[m6Dens, m6X,m6Y, m6Z];

iRoll6 = mIRollCube[m6Dens, m6X,m6Y, m6Z];

iPitch6 = mIPitchCube[m6Dens, m6X,m6Y, m6Z];

iYaw6 = mIYawCube[m6Dens, m6X,m6Y, m6Z];

m7

mass7 = mMass; (*see Parameters/Dimensions of final suspension/final mass*)

iRoll7 = mILCyl[m7Dens, m7r,m7l];

iPitch7 = mIRCyl[m7Dens, m7r,m7l];

iYaw7 = mIRCyl[m7Dens, m7r,m7l];

md2

massd2 = mCube[md2Dens, md2X,md2Y, md2Z];

iRolld2 = mIRollCube[md2Dens, md2X,md2Y, md2Z];

iPitchd2 = mIPitchCube[md2Dens, md2X,md2Y, md2Z];

iYawd2 = mIYawCube[md2Dens, md2X,md2Y, md2Z];

md5

massd5 = mCube[md5Dens, md5X,md5Y, md5Z];

iRolld5 = mIRollCube[md5Dens, md5X,md5Y, md5Z];

iPitchd5 = mIPitchCube[md5Dens, md5X,md5Y, md5Z];

iYawd5 = mIYawCube[md5Dens, md5X,md5Y, md5Z];

heat link

kA

kAXsc = kANum*scUX[kAUYoung,kAURad,kAUDia,kAURadius];
kAYsc = kANum*scUY[kAUShear,kAUDia,kAURadius];
kAZsc = kANum*scUZ[kAUYoung,kAURad,kAUDia,kAURadius];

kB

kBXsc = kBNum*scUX[kBUYoung,kBURad,kBUDia,kBURadius];
kBYsc = kBNum*scUY[kBUShear,kBUDia,kBURadius];
kBZsc = kBNum*scUZ[kBUYoung,kBURad,kBUDia,kBURadius];

kC

kCXsc = kCNum*scUX[kCUYoung,kCURad,kCUDia,kCURadius];
kCYsc = kCNum*scUY[kCUShear,kCUDia,kCURadius];
kCZsc = kCNum*scUZ[kCUYoung,kCURad,kCUDia,kCURadius];

k10

k10X = kAXsc(1+ I kAPhi);
k10Y = kAYsc(1+ I kAPhi);
k10Z = kAZsc(1+ I kAPhi);

k10XThermal = kAXsc(1+ tISCryo I kAPhi);
k10YThermal = kAYsc(1+ tISCryo I kAPhi);
k10ZThermal = kAZsc(1+ tISCryo I kAPhi);

tk10Roll = tURoll[pk10X,pk10Y,pk10Z,kAXsc,kAYsc,kAZsc,kAPhi];
tk10Pitch = tUPitch[pk10X,pk10Y,pk10Z,kAXsc,kAYsc,kAZsc,kAPhi];
tk10Yaw = tUYaw[pk10X,pk10Y,pk10Z,kAXsc,kAYsc,kAZsc,kAPhi];

tk10RollThermal = tURoll[pk10X,pk10Y,pk10Z,kAXsc,kAYsc,kAZsc,tISCryo kAPhi];
tk10PitchThermal = tUPitch[pk10X,pk10Y,pk10Z,kAXsc,kAYsc,kAZsc,tISCryo kAPhi];
tk10YawThermal = tUYaw[pk10X,pk10Y,pk10Z,kAXsc,kAYsc,kAZsc,tISCryo kAPhi];

ctk10Roll = ctURoll[pk10X,pk10Y,pk10Z,pk01X,pk01Y,pk01Z,kAXsc,kAYsc,kAZsc,kAPhi];
ctk10Pitch = ctUPitch[pk10X,pk10Y,pk10Z,pk01X,pk01Y,pk01Z,kAXsc,kAYsc,kAZsc,kAPhi];
ctk10Yaw = ctUYaw[pk10X,pk10Y,pk10Z,pk01X,pk01Y,pk01Z,kAXsc,kAYsc,kAZsc,kAPhi];

ctk10RollThermal = ctURoll[pk10X,pk10Y,pk10Z,pk01X,pk01Y,pk01Z,kAXsc,kAYsc,kAZsc,tISCryo kAPhi];
ctk10PitchThermal = ctUPitch[pk10X,pk10Y,pk10Z,pk01X,pk01Y,pk01Z,kAXsc,kAYsc,kAZsc,tISCryo kAPhi];
ctk10YawThermal = ctUYaw[pk10X,pk10Y,pk10Z,pk01X,pk01Y,pk01Z,kAXsc,kAYsc,kAZsc,tISCryo kAPhi];

k13

k13X = kBXsc(1+ I kBPhi);
k13Y = kBYsc(1+ I kBPhi);
k13Z = kBZsc(1+ I kBPhi);

k13XThermal = kBXsc(1+ m3Temp I kBPhi);
k13YThermal = kBYsc(1+ m3Temp I kBPhi);
k13ZThermal = kBZsc(1+ m3Temp I kBPhi);

tk13Roll = tURoll[pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,kBPhi];
tk13Pitch = tUPitch[pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,kBPhi];
tk13Yaw = tUYaw[pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,kBPhi];

tk13RollThermal = tURoll[pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,m3Temp kBPhi];
tk13PitchThermal = tUPitch[pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,m3Temp kBPhi];
tk13YawThermal = tUYaw[pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,m3Temp kBPhi];

ctk13Roll = ctURoll[pk13X,pk13Y,pk13Z,pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,kBPhi];
ctk13Pitch = ctUPitch[pk13X,pk13Y,pk13Z,pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,kBPhi];
ctk13Yaw = ctUYaw[pk13X,pk13Y,pk13Z,pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,kBPhi];

ctk13RollThermal = ctURoll[pk13X,pk13Y,pk13Z,pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,m3Temp kBPhi];
ctk13PitchThermal = ctUPitch[pk13X,pk13Y,pk13Z,pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,m3Temp kBPhi];
ctk13YawThermal = ctUYaw[pk13X,pk13Y,pk13Z,pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,m3Temp kBPhi];

k31

k31X = kBXsc(1+ I kBPhi);
k31Y = kBYsc(1+ I kBPhi);
k31Z = kBZsc(1+ I kBPhi);

k31XThermal = kBXsc(1+ m1Temp I kBPhi);
k31YThermal = kBYsc(1+ m1Temp I kBPhi);
k31ZThermal = kBZsc(1+ m1Temp I kBPhi);

tk31Roll = tURoll[pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,kBPhi];
tk31Pitch = tUPitch[pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,kBPhi];
tk31Yaw = tUYaw[pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,kBPhi];

tk31RollThermal = tURoll[pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,m1Temp kBPhi];
tk31PitchThermal = tUPitch[pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,m1Temp kBPhi];
tk31YawThermal = tUYaw[pk31X,pk31Y,pk31Z,kBXsc,kBYsc,kBZsc,m1Temp kBPhi];

ctk31Roll = ctURoll[pk31X,pk31Y,pk31Z,pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,kBPhi];
ctk31Pitch = ctUPitch[pk31X,pk31Y,pk31Z,pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,kBPhi];
ctk31Yaw = ctUYaw[pk31X,pk31Y,pk31Z,pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,kBPhi];

ctk31RollThermal = ctURoll[pk31X,pk31Y,pk31Z,pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,m1Temp kBPhi];
ctk31PitchThermal = ctUPitch[pk31X,pk31Y,pk31Z,pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,m1Temp kBPhi];
ctk31YawThermal = ctUYaw[pk31X,pk31Y,pk31Z,pk13X,pk13Y,pk13Z,kBXsc,kBYsc,kBZsc,m1Temp kBPhi];

k36

k36X = kCXsc(1+ I kCPhi);
k36Y = kCYsc(1+ I kCPhi);
k36Z = kCZsc(1+ I kCPhi);

k36XThermal = kCXsc(1+ m6Temp I kCPhi);
k36YThermal = kCYsc(1+ m6Temp I kCPhi);
k36ZThermal = kCZsc(1+ m6Temp I kCPhi);

tk36Roll = tURoll[pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,kCPhi];
tk36Pitch = tUPitch[pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,kCPhi];
tk36Yaw = tUYaw[pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,kCPhi];

tk36RollThermal = tURoll[pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,m6Temp kCPhi];
tk36PitchThermal = tUPitch[pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,m6Temp kCPhi];
tk36YawThermal = tUYaw[pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,m6Temp kCPhi];

ctk36Roll = ctURoll[pk36X,pk36Y,pk36Z,pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,kCPhi];
ctk36Pitch = ctUPitch[pk36X,pk36Y,pk36Z,pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,kCPhi];
ctk36Yaw = ctUYaw[pk36X,pk36Y,pk36Z,pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,kCPhi];

ctk36RollThermal = ctURoll[pk36X,pk36Y,pk36Z,pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,m6Temp kCPhi];
ctk36PitchThermal = ctUPitch[pk36X,pk36Y,pk36Z,pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,m6Temp kCPhi];
ctk36YawThermal = ctUYaw[pk36X,pk36Y,pk36Z,pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,m6Temp kCPhi];

k63

k63X = kCXsc(1+ I kCPhi);
k63Y = kCYsc(1+ I kCPhi);
k63Z = kCZsc(1+ I kCPhi);

k63XThermal = kCXsc(1+ m3Temp I kCPhi);
k63YThermal = kCYsc(1+ m3Temp I kCPhi);
k63ZThermal = kCZsc(1+ m3Temp I kCPhi);

tk63Roll = tURoll[pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,kCPhi];
tk63Pitch = tUPitch[pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,kCPhi];
tk63Yaw = tUYaw[pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,kCPhi];

tk63RollThermal = tURoll[pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,m3Temp kCPhi];
tk63PitchThermal = tUPitch[pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,m3Temp kCPhi];
tk63YawThermal = tUYaw[pk63X,pk63Y,pk63Z,kCXsc,kCYsc,kCZsc,m3Temp kCPhi];

ctk63Roll = ctURoll[pk63X,pk63Y,pk63Z,pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,kCPhi];
ctk63Pitch = ctUPitch[pk63X,pk63Y,pk63Z,pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,kCPhi];
ctk63Yaw = ctUYaw[pk63X,pk63Y,pk63Z,pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,kCPhi];

ctk63RollThermal = ctURoll[pk63X,pk63Y,pk63Z,pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,m3Temp kCPhi];
ctk63PitchThermal = ctUPitch[pk63X,pk63Y,pk63Z,pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,m3Temp kCPhi];
ctk63YawThermal = ctUYaw[pk63X,pk63Y,pk63Z,pk36X,pk36Y,pk36Z,kCXsc,kCYsc,kCZsc,m3Temp kCPhi];

suspension wire

horizontal

g1HSc = scPend[mass1,g1Length];
g2HSc = scPend[mass2+mass3,g2Length];
g3HSc = scPend[mass3,g3Length];
g4HSc = scPend[mass4+mass5+mass6+mass7,g4Length];
g5HSc = scPend[mass5+mass6+mass7,g5Length];
g6HSc = scPend[mass6+mass7,g6Length];
g7HSc = scPend[mass7,g7Length];

gm2HSc = scPend[massd2,gm2Length];
gm5HSc = scPend[massd5,gm5Length];

vertical

g1VSc = scFreq[mass1,g1VFreq];
g2VSc = scFreq[mass2+mass3,g2VFreq];
g3VSc = scFreq[mass3,g3VFreq];
g4VSc = scFreq[mass4+mass5+mass6+mass7,g4VFreq];
g5VSc = scFreq[mass5+mass6+mass7,g5VFreq];
g6VSc = scFreq[mass6+mass7,g6VFreq];
g7VSc = numSaPend*scVert[saYoung,diaSaPend,lSaPend];

gm2VSc = scFreq[massd2,gm2VFreq];
gm5VSc = scFreq[massd5,gm5VFreq];

g10

g10X = g1HSc(1 +I g10HPhi);
g10Y = g1HSc(1 +I g10HPhi);
g10Z = g1VSc(1 +I g10VPhi);

g10XThermal = g1HSc(1 +tRoom I g10HPhi);
g10YThermal = g1HSc(1 +tRoom I g10HPhi);
g10ZThermal = g1VSc(1 +g1TempV I g10VPhi);

t10Roll = tRoll[pg10X,pg10Y,pg10Z,g1HSc,g10HPhi,g1VSc,g10VPhi];
t10Pitch = tPitch[pg10X,pg10Y,pg10Z,g1HSc,g10HPhi,g1VSc,g10VPhi];
t10Yaw = tYaw[pg10X,pg10Y,pg10Z,g1HSc,g10HPhi,g1VSc,g10VPhi];

t10RollThermal = tRoll[pg10X,pg10Y,pg10Z,g1HSc,tRoom g10HPhi,g1VSc,g1TempV g10VPhi];
t10PitchThermal = tPitch[pg10X,pg10Y,pg10Z,g1HSc,tRoom g10HPhi,g1VSc,g1TempV g10VPhi];
t10YawThermal = tYaw[pg10X,pg10Y,pg10Z,g1HSc,tRoom g10HPhi,g1VSc,g1TempV g10VPhi];

ct10Roll = ctRoll[pg10X,pg10Y,pg10Z,pg01X,pg01Y,pg01Z,g1HSc,g10HPhi,g1VSc,g10VPhi];
ct10Pitch = ctPitch[pg10X,pg10Y,pg10Z,pg01X,pg01Y,pg01Z,g1HSc,g10HPhi,g1VSc,g10VPhi];
ct10Yaw = ctYaw[pg10X,pg10Y,pg10Z,pg01X,pg01Y,pg01Z,g1HSc,g10HPhi,g1VSc,g10VPhi];

ct10RollThermal = ctRoll[pg10X,pg10Y,pg10Z,pg01X,pg01Y,pg01Z,g1HSc,tRoom g10HPhi,g1VSc,g1TempV g10VPhi];
ct10PitchThermal = ctPitch[pg10X,pg10Y,pg10Z,pg01X,pg01Y,pg01Z,g1HSc,tRoom g10HPhi,g1VSc,g1TempV g10VPhi];
ct10YawThermal = ctYaw[pg10X,pg10Y,pg10Z,pg01X,pg01Y,pg01Z,g1HSc,tRoom g10HPhi,g1VSc,g1TempV g10VPhi];

g20

g20X = g2HSc(1 +I g20HPhi);
g20Y = g2HSc(1 +I g20HPhi);
g20Z = g2VSc(1 +I g20VPhi);

g20XThermal = g2HSc(1 +tRoom I g20HPhi);
g20YThermal = g2HSc(1 +tRoom I g20HPhi);
g20ZThermal = g2VSc(1 +tRoom I g20VPhi);

t20Roll = tRoll[pg20X,pg20Y,pg20Z,g2HSc,g20HPhi,g2VSc,g20VPhi];
t20Pitch = tPitch[pg20X,pg20Y,pg20Z,g2HSc,g20HPhi,g2VSc,g20VPhi];
t20Yaw = tYaw[pg20X,pg20Y,pg20Z,g2HSc,g20HPhi,g2VSc,g20VPhi];

t20RollThermal = tRoll[pg20X,pg20Y,pg20Z,g2HSc,tRoom g20HPhi,g2VSc,tRoom g20VPhi];
t20PitchThermal = tPitch[pg20X,pg20Y,pg20Z,g2HSc,tRoom g20HPhi,g2VSc,tRoom g20VPhi];
t20YawThermal = tYaw[pg20X,pg20Y,pg20Z,g2HSc,tRoom g20HPhi,g2VSc,tRoom g20VPhi];

ct20Roll = ctRoll[pg20X,pg20Y,pg20Z,pg02X,pg02Y,pg02Z,g2HSc,g20HPhi,g2VSc,g20VPhi];
ct20Pitch = ctPitch[pg20X,pg20Y,pg20Z,pg02X,pg02Y,pg02Z,g2HSc,g20HPhi,g2VSc,g20VPhi];
ct20Yaw = ctYaw[pg20X,pg20Y,pg20Z,pg02X,pg02Y,pg02Z,g2HSc,g20HPhi,g2VSc,g20VPhi];

ct20RollThermal = ctRoll[pg20X,pg20Y,pg20Z,pg02X,pg02Y,pg02Z,g2HSc,tRoom g20HPhi,g2VSc,tRoom g20VPhi];
ct20PitchThermal = ctPitch[pg20X,pg20Y,pg20Z,pg02X,pg02Y,pg02Z,g2HSc,tRoom g20HPhi,g2VSc,tRoom g20VPhi];
ct20YawThermal = ctYaw[pg20X,pg20Y,pg20Z,pg02X,pg02Y,pg02Z,g2HSc,tRoom g20HPhi,g2VSc,tRoom g20VPhi];

g23

g23X = g3HSc(1 +I g23HPhi);
g23Y = g3HSc(1 +I g23HPhi);
g23Z = g3VSc(1 +I g23VPhi);

g23XThermal = g3HSc(1 +m3Temp I g23HPhi);
g23YThermal = g3HSc(1 +m3Temp I g23HPhi);
g23ZThermal = g3VSc(1 +g3TempV I g23VPhi);

t23Roll = tRoll[pg23X,pg23Y,pg23Z,g3HSc,g23HPhi,g3VSc,g23VPhi];
t23Pitch = tPitch[pg23X,pg23Y,pg23Z,g3HSc,g23HPhi,g3VSc,g23VPhi];
t23Yaw = tYaw[pg23X,pg23Y,pg23Z,g3HSc,g23HPhi,g3VSc,g23VPhi];

t23RollThermal = tRoll[pg23X,pg23Y,pg23Z,g3HSc,m3Temp g23HPhi,g3VSc,g3TempV g23VPhi];
t23PitchThermal = tPitch[pg23X,pg23Y,pg23Z,g3HSc,m3Temp g23HPhi,g3VSc,g3TempV g23VPhi];
t23YawThermal = tYaw[pg23X,pg23Y,pg23Z,g3HSc,m3Temp g23HPhi,g3VSc,g3TempV g23VPhi];

ct23Roll = ctRoll[pg23X,pg23Y,pg23Z,pg32X,pg32Y,pg32Z,g3HSc,g23HPhi,g3VSc,g23VPhi];
ct23Pitch = ctPitch[pg23X,pg23Y,pg23Z,pg32X,pg32Y,pg32Z,g3HSc,g23HPhi,g3VSc,g23VPhi];
ct23Yaw = ctYaw[pg23X,pg23Y,pg23Z,pg32X,pg32Y,pg32Z,g3HSc,g23HPhi,g3VSc,g23VPhi];

ct23RollThermal = ctRoll[pg23X,pg23Y,pg23Z,pg32X,pg32Y,pg32Z,g3HSc,m3Temp g23HPhi,g3VSc,g3TempV g23VPhi];
ct23PitchThermal = ctPitch[pg23X,pg23Y,pg23Z,pg32X,pg32Y,pg32Z,g3HSc,m3Temp g23HPhi,g3VSc,g3TempV g23VPhi];
ct23YawThermal = ctYaw[pg23X,pg23Y,pg23Z,pg32X,pg32Y,pg32Z,g3HSc,m3Temp g23HPhi,g3VSc,g3TempV g23VPhi];

g32

g32X = g3HSc(1 +I g32HPhi);
g32Y = g3HSc(1 +I g32HPhi);
g32Z = g3VSc(1 +I g32VPhi);

g32XThermal = g3HSc(1 +m2Temp I g32HPhi);
g32YThermal = g3HSc(1 +m2Temp I g32HPhi);
g32ZThermal = g3VSc(1 +g3TempV I g32VPhi);

t32Roll = tRoll[pg32X,pg32Y,pg32Z,g3HSc,g32HPhi,g3VSc,g32VPhi];
t32Pitch = tPitch[pg32X,pg32Y,pg32Z,g3HSc,g32HPhi,g3VSc,g32VPhi];
t32Yaw = tYaw[pg32X,pg32Y,pg32Z,g3HSc,g32HPhi,g3VSc,g32VPhi];

t32RollThermal = tRoll[pg32X,pg32Y,pg32Z,g3HSc,m2Temp g32HPhi,g3VSc,g3TempV g32VPhi];
t32PitchThermal = tPitch[pg32X,pg32Y,pg32Z,g3HSc,m2Temp g32HPhi,g3VSc,g3TempV g32VPhi];
t32YawThermal = tYaw[pg32X,pg32Y,pg32Z,g3HSc,m2Temp g32HPhi,g3VSc,g3TempV g32VPhi];

ct32Roll = ctRoll[pg32X,pg32Y,pg32Z,pg23X,pg23Y,pg23Z,g3HSc,g32HPhi,g3VSc,g32VPhi];
ct32Pitch = ctPitch[pg32X,pg32Y,pg32Z,pg23X,pg23Y,pg23Z,g3HSc,g32HPhi,g3VSc,g32VPhi];
ct32Yaw = ctYaw[pg32X,pg32Y,pg32Z,pg23X,pg23Y,pg23Z,g3HSc,g32HPhi,g3VSc,g32VPhi];

ct32RollThermal = ctRoll[pg32X,pg32Y,pg32Z,pg23X,pg23Y,pg23Z,g3HSc,m2Temp g32HPhi,g3VSc,g3TempV g32VPhi];
ct32PitchThermal = ctPitch[pg32X,pg32Y,pg32Z,pg23X,pg23Y,pg23Z,g3HSc,m2Temp g32HPhi,g3VSc,g3TempV g32VPhi];
ct32YawThermal = ctYaw[pg32X,pg32Y,pg32Z,pg23X,pg23Y,pg23Z,g3HSc,m2Temp g32HPhi,g3VSc,g3TempV g32VPhi];

g40

g40X = g4HSc(1 +I g40HPhi);
g40Y = g4HSc(1 +I g40HPhi);
g40Z = g4VSc(1 +I g40VPhi);

g40XThermal = g4HSc(1 +tRoom I g40HPhi);
g40YThermal = g4HSc(1 +tRoom I g40HPhi);
g40ZThermal = g4VSc(1 +tRoom I g40VPhi);

t40Roll = tRoll[pg40X,pg40Y,pg40Z,g4HSc,g40HPhi,g4VSc,g40VPhi];
t40Pitch = tPitch[pg40X,pg40Y,pg40Z,g4HSc,g40HPhi,g4VSc,g40VPhi];
t40Yaw = tYaw[pg40X,pg40Y,pg40Z,g4HSc,g40HPhi,g4VSc,g40VPhi];

t40RollThermal = tRoll[pg40X,pg40Y,pg40Z,g4HSc,tRoom g40HPhi,g4VSc,tRoom g40VPhi];
t40PitchThermal = tPitch[pg40X,pg40Y,pg40Z,g4HSc,tRoom g40HPhi,g4VSc,tRoom g40VPhi];
t40YawThermal = tYaw[pg40X,pg40Y,pg40Z,g4HSc,tRoom g40HPhi,g4VSc,tRoom g40VPhi];

ct40Roll = ctRoll[pg40X,pg40Y,pg40Z,pg04X,pg04Y,pg04Z,g4HSc,g40HPhi,g4VSc,g40VPhi];
ct40Pitch = ctPitch[pg40X,pg40Y,pg40Z,pg04X,pg04Y,pg04Z,g4HSc,g40HPhi,g4VSc,g40VPhi];
ct40Yaw = ctYaw[pg40X,pg40Y,pg40Z,pg04X,pg04Y,pg04Z,g4HSc,g40HPhi,g4VSc,g40VPhi];

ct40RollThermal = ctRoll[pg40X,pg40Y,pg40Z,pg04X,pg04Y,pg04Z,g4HSc,tRoom g40HPhi,g4VSc,tRoom g40VPhi];
ct40PitchThermal = ctPitch[pg40X,pg40Y,pg40Z,pg04X,pg04Y,pg04Z,g4HSc,tRoom g40HPhi,g4VSc,tRoom g40VPhi];
ct40YawThermal = ctYaw[pg40X,pg40Y,pg40Z,pg04X,pg04Y,pg04Z,g4HSc,tRoom g40HPhi,g4VSc,tRoom g40VPhi];

g45

g45X = g5HSc(1 +I g45HPhi);
g45Y = g5HSc(1 +I g45HPhi);
g45Z = g5VSc(1 +I g45VPhi);

g45XThermal = g5HSc(1 +m5Temp I g45HPhi);
g45YThermal = g5HSc(1 +m5Temp I g45HPhi);
g45ZThermal = g5VSc(1 +m5Temp I g45VPhi);

t45Roll = tRoll[pg45X,pg45Y,pg45Z,g5HSc,g45HPhi,g5VSc,g45VPhi];
t45Pitch = tPitch[pg45X,pg45Y,pg45Z,g5HSc,g45HPhi,g5VSc,g45VPhi];
t45Yaw = tYaw[pg45X,pg45Y,pg45Z,g5HSc,g45HPhi,g5VSc,g45VPhi];

t45RollThermal = tRoll[pg45X,pg45Y,pg45Z,g5HSc,m5Temp g45HPhi,g5VSc,m5Temp g45VPhi];
t45PitchThermal = tPitch[pg45X,pg45Y,pg45Z,g5HSc,m5Temp g45HPhi,g5VSc,m5Temp g45VPhi];
t45YawThermal = tYaw[pg45X,pg45Y,pg45Z,g5HSc,m5Temp g45HPhi,g5VSc,m5Temp g45VPhi];

ct45Roll = ctRoll[pg45X,pg45Y,pg45Z,pg54X,pg54Y,pg54Z,g5HSc,g45HPhi,g5VSc,g45VPhi];
ct45Pitch = ctPitch[pg45X,pg45Y,pg45Z,pg54X,pg54Y,pg54Z,g5HSc,g45HPhi,g5VSc,g45VPhi];
ct45Yaw = ctYaw[pg45X,pg45Y,pg45Z,pg54X,pg54Y,pg54Z,g5HSc,g45HPhi,g5VSc,g45VPhi];

ct45RollThermal = ctRoll[pg45X,pg45Y,pg45Z,pg54X,pg54Y,pg54Z,g5HSc,m5Temp g45HPhi,g5VSc,m5Temp g45VPhi];
ct45PitchThermal = ctPitch[pg45X,pg45Y,pg45Z,pg54X,pg54Y,pg54Z,g5HSc,m5Temp g45HPhi,g5VSc,m5Temp g45VPhi];
ct45YawThermal = ctYaw[pg45X,pg45Y,pg45Z,pg54X,pg54Y,pg54Z,g5HSc,m5Temp g45HPhi,g5VSc,m5Temp g45VPhi];

g54

g54X = g5HSc(1 +I g54HPhi);
g54Y = g5HSc(1 +I g54HPhi);
g54Z = g5VSc(1 +I g54VPhi);

g54XThermal = g5HSc(1 +m4Temp I g54HPhi);
g54YThermal = g5HSc(1 +m4Temp I g54HPhi);
g54ZThermal = g5VSc(1 +m4Temp I g54VPhi);

t54Roll = tRoll[pg54X,pg54Y,pg54Z,g5HSc,g54HPhi,g5VSc,g54VPhi];
t54Pitch = tPitch[pg54X,pg54Y,pg54Z,g5HSc,g54HPhi,g5VSc,g54VPhi];
t54Yaw = tYaw[pg54X,pg54Y,pg54Z,g5HSc,g54HPhi,g5VSc,g54VPhi];

t54RollThermal = tRoll[pg54X,pg54Y,pg54Z,g5HSc,m4Temp g54HPhi,g5VSc,m4Temp g54VPhi];
t54PitchThermal = tPitch[pg54X,pg54Y,pg54Z,g5HSc,m4Temp g54HPhi,g5VSc,m4Temp g54VPhi];
t54YawThermal = tYaw[pg54X,pg54Y,pg54Z,g5HSc,m4Temp g54HPhi,g5VSc,m4Temp g54VPhi];

ct54Roll = ctRoll[pg54X,pg54Y,pg54Z,pg45X,pg45Y,pg45Z,g5HSc,g54HPhi,g5VSc,g54VPhi];
ct54Pitch = ctPitch[pg54X,pg54Y,pg54Z,pg45X,pg45Y,pg45Z,g5HSc,g54HPhi,g5VSc,g54VPhi];
ct54Yaw = ctYaw[pg54X,pg54Y,pg54Z,pg45X,pg45Y,pg45Z,g5HSc,g54HPhi,g5VSc,g54VPhi];

ct54RollThermal = ctRoll[pg54X,pg54Y,pg54Z,pg45X,pg45Y,pg45Z,g5HSc,m4Temp g54HPhi,g5VSc,m4Temp g54VPhi];
ct54PitchThermal = ctPitch[pg54X,pg54Y,pg54Z,pg45X,pg45Y,pg45Z,g5HSc,m4Temp g54HPhi,g5VSc,m4Temp g54VPhi];
ct54YawThermal = ctYaw[pg54X,pg54Y,pg54Z,pg45X,pg45Y,pg45Z,g5HSc,m4Temp g54HPhi,g5VSc,m4Temp g54VPhi];

g56

g56X = g6HSc(1 +I g56HPhi);
g56Y = g6HSc(1 +I g56HPhi);
g56Z = g6VSc(1 +I g56VPhi);

g56XThermal = g6HSc(1 +m6Temp I g56HPhi);
g56YThermal = g6HSc(1 +m6Temp I g56HPhi);
g56ZThermal = g6VSc(1 +g6TempV I g56VPhi);

t56Roll = tRoll[pg56X,pg56Y,pg56Z,g6HSc,g56HPhi,g6VSc,g56VPhi];
t56Pitch = tPitch[pg56X,pg56Y,pg56Z,g6HSc,g56HPhi,g6VSc,g56VPhi];
t56Yaw = tYaw[pg56X,pg56Y,pg56Z,g6HSc,g56HPhi,g6VSc,g56VPhi];

t56RollThermal = tRoll[pg56X,pg56Y,pg56Z,g6HSc,m6Temp g56HPhi,g6VSc,g6TempV g56VPhi];
t56PitchThermal = tPitch[pg56X,pg56Y,pg56Z,g6HSc,m6Temp g56HPhi,g6VSc,g6TempV g56VPhi];
t56YawThermal = tYaw[pg56X,pg56Y,pg56Z,g6HSc,m6Temp g56HPhi,g6VSc,g6TempV g56VPhi];

ct56Roll = ctRoll[pg56X,pg56Y,pg56Z,pg65X,pg65Y,pg65Z,g6HSc,g56HPhi,g6VSc,g56VPhi];
ct56Pitch = ctPitch[pg56X,pg56Y,pg56Z,pg65X,pg65Y,pg65Z,g6HSc,g56HPhi,g6VSc,g56VPhi];
ct56Yaw = ctYaw[pg56X,pg56Y,pg56Z,pg65X,pg65Y,pg65Z,g6HSc,g56HPhi,g6VSc,g56VPhi];

ct56RollThermal = ctRoll[pg56X,pg56Y,pg56Z,pg65X,pg65Y,pg65Z,g6HSc,m6Temp g56HPhi,g6VSc,g6TempV g56VPhi];
ct56PitchThermal = ctPitch[pg56X,pg56Y,pg56Z,pg65X,pg65Y,pg65Z,g6HSc,m6Temp g56HPhi,g6VSc,g6TempV g56VPhi];
ct56YawThermal = ctYaw[pg56X,pg56Y,pg56Z,pg65X,pg65Y,pg65Z,g6HSc,m6Temp g56HPhi,g6VSc,g6TempV g56VPhi];

g65

g65X = g6HSc(1 +I g65HPhi);
g65Y = g6HSc(1 +I g65HPhi);
g65Z = g6VSc(1 +I g65VPhi);

g65XThermal = g6HSc(1 +m5Temp I g65HPhi);
g65YThermal = g6HSc(1 +m5Temp I g65HPhi);
g65ZThermal = g6VSc(1 +g6TempV I g65VPhi);

t65Roll = tRoll[pg65X,pg65Y,pg65Z,g6HSc,g65HPhi,g6VSc,g65VPhi];
t65Pitch = tPitch[pg65X,pg65Y,pg65Z,g6HSc,g65HPhi,g6VSc,g65VPhi];
t65Yaw = tYaw[pg65X,pg65Y,pg65Z,g6HSc,g65HPhi,g6VSc,g65VPhi];

t65RollThermal = tRoll[pg65X,pg65Y,pg65Z,g6HSc,m5Temp g65HPhi,g6VSc,g6TempV g65VPhi];
t65PitchThermal = tPitch[pg65X,pg65Y,pg65Z,g6HSc,m5Temp g65HPhi,g6VSc,g6TempV g65VPhi];
t65YawThermal = tYaw[pg65X,pg65Y,pg65Z,g6HSc,m5Temp g65HPhi,g6VSc,g6TempV g65VPhi];

ct65Roll = ctRoll[pg65X,pg65Y,pg65Z,pg56X,pg56Y,pg56Z,g6HSc,g65HPhi,g6VSc,g65VPhi];
ct65Pitch = ctPitch[pg65X,pg65Y,pg65Z,pg56X,pg56Y,pg56Z,g6HSc,g65HPhi,g6VSc,g65VPhi];
ct65Yaw = ctYaw[pg65X,pg65Y,pg65Z,pg56X,pg56Y,pg56Z,g6HSc,g65HPhi,g6VSc,g65VPhi];

ct65RollThermal = ctRoll[pg65X,pg65Y,pg65Z,pg56X,pg56Y,pg56Z,g6HSc,m5Temp g65HPhi,g6VSc,g6TempV g65VPhi];
ct65PitchThermal = ctPitch[pg65X,pg65Y,pg65Z,pg56X,pg56Y,pg56Z,g6HSc,m5Temp g65HPhi,g6VSc,g6TempV g65VPhi];
ct65YawThermal = ctYaw[pg65X,pg65Y,pg65Z,pg56X,pg56Y,pg56Z,g6HSc,m5Temp g65HPhi,g6VSc,g6TempV g65VPhi];

g67

g67X = g7HSc(1 +I g67HPhi);
g67Y = g7HSc(1 +I g67HPhi);
g67Z = g7VSc(1 +I g67VPhi);

g67XThermal = g7HSc(1 +m7Temp I g67HPhi);
g67YThermal = g7HSc(1 +m7Temp I g67HPhi);
g67ZThermal = g7VSc(1 +m7Temp I g67VPhi);

t67Roll = tRoll[pg67X,pg67Y,pg67Z,g7HSc,g67HPhi,g7VSc,g67VPhi];
t67Pitch = tPitch[pg67X,pg67Y,pg67Z,g7HSc,g67HPhi,g7VSc,g67VPhi];
t67Yaw = tYaw[pg67X,pg67Y,pg67Z,g7HSc,g67HPhi,g7VSc,g67VPhi];

t67RollThermal = tRoll[pg67X,pg67Y,pg67Z,g7HSc,m7Temp g67HPhi,g7VSc,m7Temp g67VPhi];
t67PitchThermal = tPitch[pg67X,pg67Y,pg67Z,g7HSc,m7Temp g67HPhi,g7VSc,m7Temp g67VPhi];
t67YawThermal = tYaw[pg67X,pg67Y,pg67Z,g7HSc,m7Temp g67HPhi,g7VSc,m7Temp g67VPhi];

ct67Roll = ctRoll[pg67X,pg67Y,pg67Z,pg76X,pg76Y,pg76Z,g7HSc,g67HPhi,g7VSc,g67VPhi];
ct67Pitch = ctPitch[pg67X,pg67Y,pg67Z,pg76X,pg76Y,pg76Z,g7HSc,g67HPhi,g7VSc,g67VPhi];
ct67Yaw = ctYaw[pg67X,pg67Y,pg67Z,pg76X,pg76Y,pg76Z,g7HSc,g67HPhi,g7VSc,g67VPhi];

ct67RollThermal = ctRoll[pg67X,pg67Y,pg67Z,pg76X,pg76Y,pg76Z,g7HSc,m7Temp g67HPhi,g7VSc,m7Temp g67VPhi];
ct67PitchThermal = ctPitch[pg67X,pg67Y,pg67Z,pg76X,pg76Y,pg76Z,g7HSc,m7Temp g67HPhi,g7VSc,m7Temp g67VPhi];
ct67YawThermal = ctYaw[pg67X,pg67Y,pg67Z,pg76X,pg76Y,pg76Z,g7HSc,m7Temp g67HPhi,g7VSc,m7Temp g67VPhi];

g76 (*Z方向はm7Tempをつかう。*)

g76X = g7HSc(1 +I g76HPhi);
g76Y = g7HSc(1 +I g76HPhi);
g76Z = g7VSc(1 +I g76VPhi);

g76XThermal = g7HSc(1 +m6Temp I g76HPhi);
g76YThermal = g7HSc(1 +m6Temp I g76HPhi);
g76ZThermal = g7VSc(1 +m7Temp I g76VPhi);

t76Roll = tRoll[pg76X,pg76Y,pg76Z,g7HSc,g76HPhi,g7VSc,g76VPhi];
t76Pitch = tPitch[pg76X,pg76Y,pg76Z,g7HSc,g76HPhi,g7VSc,g76VPhi];
t76Yaw = tYaw[pg76X,pg76Y,pg76Z,g7HSc,g76HPhi,g7VSc,g76VPhi];

t76RollThermal = tRoll[pg76X,pg76Y,pg76Z,g7HSc,m6Temp g76HPhi,g7VSc,m7Temp g76VPhi];
t76PitchThermal = tPitch[pg76X,pg76Y,pg76Z,g7HSc,m6Temp g76HPhi,g7VSc,m7Temp g76VPhi];
t76YawThermal = tYaw[pg76X,pg76Y,pg76Z,g7HSc,m6Temp g76HPhi,g7VSc,m7Temp g76VPhi];

ct76Roll = ctRoll[pg76X,pg76Y,pg76Z,pg67X,pg67Y,pg67Z,g7HSc,g76HPhi,g7VSc,g76VPhi];
ct76Pitch = ctPitch[pg76X,pg76Y,pg76Z,pg67X,pg67Y,pg67Z,g7HSc,g76HPhi,g7VSc,g76VPhi];
ct76Yaw = ctYaw[pg76X,pg76Y,pg76Z,pg67X,pg67Y,pg67Z,g7HSc,g76HPhi,g7VSc,g76VPhi];

ct76RollThermal = ctRoll[pg76X,pg76Y,pg76Z,pg67X,pg67Y,pg67Z,g7HSc,m6Temp g76HPhi,g7VSc,m7Temp g76VPhi];
ct76PitchThermal = ctPitch[pg76X,pg76Y,pg76Z,pg67X,pg67Y,pg67Z,g7HSc,m6Temp g76HPhi,g7VSc,m7Temp g76VPhi];
ct76YawThermal = ctYaw[pg76X,pg76Y,pg76Z,pg67X,pg67Y,pg67Z,g7HSc,m6Temp g76HPhi,g7VSc,m7Temp g76VPhi];

gm20

gm20X = gm2HSc(1 +I gm20HPhi);
gm20Y = gm2HSc(1 +I gm20HPhi);
gm20Z = gm2VSc(1 +I gm20VPhi);

gm20XThermal = gm2HSc(1 +tRoom I gm20HPhi);
gm20YThermal = gm2HSc(1 +tRoom I gm20HPhi);
gm20ZThermal = gm2VSc(1 +tRoom I gm20VPhi);

tm20Roll = tRoll[pgm20X,pgm20Y,pgm20Z,gm2HSc,gm20HPhi,gm2VSc,gm20VPhi];
tm20Pitch = tPitch[pgm20X,pgm20Y,pgm20Z,gm2HSc,gm20HPhi,gm2VSc,gm20VPhi];
tm20Yaw = tYaw[pgm20X,pgm20Y,pgm20Z,gm2HSc,gm20HPhi,gm2VSc,gm20VPhi];

tm20RollThermal = tRoll[pgm20X,pgm20Y,pgm20Z,gm2HSc,tRoom gm20HPhi,gm2VSc,tRoom gm20VPhi];
tm20PitchThermal = tPitch[pgm20X,pgm20Y,pgm20Z,gm2HSc,tRoom gm20HPhi,gm2VSc,tRoom gm20VPhi];
tm20YawThermal = tYaw[pgm20X,pgm20Y,pgm20Z,gm2HSc,tRoom gm20HPhi,gm2VSc,tRoom gm20VPhi];

ctm20Roll = ctRoll[pgm20X,pgm20Y,pgm20Z,pgm02X,pgm02Y,pgm02Z,gm2HSc,gm20HPhi,gm2VSc,gm20VPhi];
ctm20Pitch = ctPitch[pgm20X,pgm20Y,pgm20Z,pgm02X,pgm02Y,pgm02Z,gm2HSc,gm20HPhi,gm2VSc,gm20VPhi];
ctm20Yaw = ctYaw[pgm20X,pgm20Y,pgm20Z,pgm02X,pgm02Y,pgm02Z,gm2HSc,gm20HPhi,gm2VSc,gm20VPhi];

ctm20RollThermal = ctRoll[pgm20X,pgm20Y,pgm20Z,pgm02X,pgm02Y,pgm02Z,gm2HSc,tRoom gm20HPhi,gm2VSc,tRoom gm20VPhi];
ctm20PitchThermal = ctPitch[pgm20X,pgm20Y,pgm20Z,pgm02X,pgm02Y,pgm02Z,gm2HSc,tRoom gm20HPhi,gm2VSc,tRoom gm20VPhi];
ctm20YawThermal = ctYaw[pgm20X,pgm20Y,pgm20Z,pgm02X,pgm02Y,pgm02Z,gm2HSc,tRoom gm20HPhi,gm2VSc,tRoom gm20VPhi];

gm50

gm50X = gm5HSc(1 +I gm50HPhi);
gm50Y = gm5HSc(1 +I gm50HPhi);
gm50Z = gm5VSc(1 +I gm50VPhi);

gm50XThermal = gm5HSc(1 +tRoom I gm50HPhi);
gm50YThermal = gm5HSc(1 +tRoom I gm50HPhi);
gm50ZThermal = gm5VSc(1 +tRoom I gm50VPhi);

tm50Roll = tRoll[pgm50X,pgm50Y,pgm50Z,gm5HSc,gm50HPhi,gm5VSc,gm50VPhi];
tm50Pitch = tPitch[pgm50X,pgm50Y,pgm50Z,gm5HSc,gm50HPhi,gm5VSc,gm50VPhi];
tm50Yaw = tYaw[pgm50X,pgm50Y,pgm50Z,gm5HSc,gm50HPhi,gm5VSc,gm50VPhi];

tm50RollThermal = tRoll[pgm50X,pgm50Y,pgm50Z,gm5HSc,tRoom gm50HPhi,gm5VSc,tRoom gm50VPhi];
tm50PitchThermal = tPitch[pgm50X,pgm50Y,pgm50Z,gm5HSc,tRoom gm50HPhi,gm5VSc,tRoom gm50VPhi];
tm50YawThermal = tYaw[pgm50X,pgm50Y,pgm50Z,gm5HSc,tRoom gm50HPhi,gm5VSc,tRoom gm50VPhi];

ctm50Roll = ctRoll[pgm50X,pgm50Y,pgm50Z,pgm05X,pgm05Y,pgm05Z,gm5HSc,gm50HPhi,gm5VSc,gm50VPhi];
ctm50Pitch = ctPitch[pgm50X,pgm50Y,pgm50Z,pgm05X,pgm05Y,pgm05Z,gm5HSc,gm50HPhi,gm5VSc,gm50VPhi];
ctm50Yaw = ctYaw[pgm50X,pgm50Y,pgm50Z,pgm05X,pgm05Y,pgm05Z,gm5HSc,gm50HPhi,gm5VSc,gm50VPhi];

ctm50RollThermal = ctRoll[pgm50X,pgm50Y,pgm50Z,pgm05X,pgm05Y,pgm05Z,gm5HSc,tRoom gm50HPhi,gm5VSc,tRoom gm50VPhi];
ctm50PitchThermal = ctPitch[pgm50X,pgm50Y,pgm50Z,pgm05X,pgm05Y,pgm05Z,gm5HSc,tRoom gm50HPhi,gm5VSc,tRoom gm50VPhi];
ctm50YawThermal = ctYaw[pgm50X,pgm50Y,pgm50Z,pgm05X,pgm05Y,pgm05Z,gm5HSc,tRoom gm50HPhi,gm5VSc,tRoom gm50VPhi];

damping

d1Damp[f_] := Damp[f,d1DampF,d1DampQ];
d2Damp[f_] := Damp[f,d2DampF,d2DampQ];
d3Damp[f_] := Damp[f,d3DampF,d3DampQ];
d4Damp[f_] := Damp[f,d4DampF,d4DampQ];
d5Damp[f_] := Damp[f,d5DampF,d5DampQ];

parameter set

Test

parXPtest={f,mass1,iPitch1,g10X,t10Pitch,ct10Pitch,pg01Z,pg10Z,d1Damp[f]}

parXPThermaltest={f,mass1,iPitch1,g10XThermal,t10PitchThermal,ct10PitchThermal,pg01Z,pg10Z,d1Damp[f]}

parYRtest={f,mass1,iRoll1,g10Y,t10Roll,ct10Roll,pg01Z,pg10Z,d1Damp[f]}

parYRThermaltest={f,mass1,iRoll1,g10YThermal,t10RollThermal,ct10RollThermal,pg01Z,pg10Z,d1Damp[f]}

X - Pitch

parXP = {f,
mass1,iPitch1,mass2,iPitch2,mass3,iPitch3,mass4,iPitch4,mass5,iPitch5,mass6,iPitch6,mass7,iPitch7,massd2,iPitchd2,massd5,iPitchd5,
k10X,k13X,k31X,k36X,k63X,
g10X,g20X,g23X,g32X,g40X,g45X,g54X,g56X,g65X,g67X,g76X,gm20X,gm50X,
tk10Pitch,tk13Pitch,tk31Pitch,tk36Pitch,tk63Pitch,
t10Pitch,t20Pitch,t23Pitch,t32Pitch,t40Pitch,t45Pitch,t54Pitch,t56Pitch,t65Pitch,t67Pitch,t76Pitch,tm20Pitch,tm50Pitch,
ctk10Pitch,ctk13Pitch,ctk31Pitch,ctk36Pitch,ctk63Pitch,
ct10Pitch,ct20Pitch,ct23Pitch,ct32Pitch,ct40Pitch,ct45Pitch,ct54Pitch,ct56Pitch,ct65Pitch,ct67Pitch,ct76Pitch,ctm20Pitch,ctm50Pitch,
pk01Z,pk10Z,pk13Z,pk31Z,pk36Z,pk63Z,
pg01Z,pg10Z,pg02Z,pg20Z,pg23Z,pg32Z,pg04Z,pg40Z,pg45Z,pg54Z,pg56Z,pg65Z,pg67Z,pg76Z,pgm02Z,pgm20Z,pgm05Z,pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]}

parXPThermal = {f,
mass1,iPitch1,mass2,iPitch2,mass3,iPitch3,mass4,iPitch4,mass5,iPitch5,mass6,iPitch6,mass7,iPitch7,massd2,iPitchd2,massd5,iPitchd5,
k10XThermal,k13XThermal,k31XThermal,k36XThermal,k63XThermal,
g10XThermal,g20XThermal,g23XThermal,g32XThermal,g40XThermal,g45XThermal,g54XThermal,g56XThermal,g65XThermal,g67XThermal,g76XThermal,gm20XThermal,gm50XThermal,
tk10PitchThermal,tk13PitchThermal,tk31PitchThermal,tk36PitchThermal,tk63PitchThermal,
t10PitchThermal,t20PitchThermal,t23PitchThermal,t32PitchThermal,t40PitchThermal,t45PitchThermal,t54PitchThermal,t56PitchThermal,t65PitchThermal,t67PitchThermal,t76PitchThermal,tm20PitchThermal,tm50PitchThermal,
tk10PitchThermal,tk13PitchThermal,tk31PitchThermal,tk36PitchThermal,tk63PitchThermal,
ct10PitchThermal,ct20PitchThermal,ct23PitchThermal,ct32PitchThermal,ct40PitchThermal,ct45PitchThermal,ct54PitchThermal,ct56PitchThermal,ct65PitchThermal,ct67PitchThermal,ct76PitchThermal,ctm20PitchThermal,ctm50PitchThermal,
pk01Z,pk10Z,pk13Z,pk31Z,pk36Z,pk63Z,
pg01Z,pg10Z,pg02Z,pg20Z,pg23Z,pg32Z,pg04Z,pg40Z,pg45Z,pg54Z,pg56Z,pg65Z,pg67Z,pg76Z,pgm02Z,pgm20Z,pgm05Z,pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]}

Y - Roll

parYR= {f,
mass1,iRoll1,mass2,iRoll2,mass3,iRoll3,mass4,iRoll4,mass5,iRoll5,mass6,iRoll6,mass7,iRoll7,massd2,iRolld2,massd5,iRolld5,
k10Y,k13Y,k31Y,k36Y,k63Y,
g10Y,g20Y,g23Y,g32Y,g40Y,g45Y,g54Y,g56Y,g65Y,g67Y,g76Y,gm20Y,gm50Y,
tk10Roll,tk13Roll,tk31Roll,tk36Roll,tk63Roll,
t10Roll,t20Roll,t23Roll,t32Roll,t40Roll,t45Roll,t54Roll,t56Roll,t65Roll,t67Roll,t76Roll,tm20Roll,tm50Roll,
ctk10Roll,ctk13Roll,ctk31Roll,ctk36Roll,ctk63Roll,
ct10Roll,ct20Roll,ct23Roll,ct32Roll,ct40Roll,ct45Roll,ct54Roll,ct56Roll,ct65Roll,ct67Roll,ct76Roll,ctm20Roll,ctm50Roll,
-pk01Z,-pk10Z,-pk13Z,-pk31Z,-pk36Z,-pk63Z,
-pg01Z,-pg10Z,-pg02Z,-pg20Z,-pg23Z,-pg32Z,-pg04Z,-pg40Z,-pg45Z,-pg54Z,-pg56Z,-pg65Z,-pg67Z,-pg76Z,-pgm02Z,-pgm20Z,-pgm05Z,-pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]}

parYRThermal = {f,
mass1,iRoll1,mass2,iRoll2,mass3,iRoll3,mass4,iRoll4,mass5,iRoll5,mass6,iRoll6,mass7,iRoll7,massd2,iRolld2,massd5,iRolld5,
k10YThermal,k13YThermal,k31YThermal,k36YThermal,k63YThermal,
g10YThermal,g20YThermal,g23YThermal,g32YThermal,g40YThermal,g45YThermal,g54YThermal,g56YThermal,g65YThermal,g67YThermal,g76YThermal,gm20YThermal,gm50YThermal,
tk10RollThermal,tk13RollThermal,tk31RollThermal,tk36RollThermal,tk63RollThermal,
t10RollThermal,t20RollThermal,t23RollThermal,t32RollThermal,t40RollThermal,t45RollThermal,t54RollThermal,t56RollThermal,t65RollThermal,t67RollThermal,t76RollThermal,tm20RollThermal,tm50RollThermal,
ctk10RollThermal,ctk13RollThermal,ctk31RollThermal,ctk36RollThermal,ctk63RollThermal,
ct10RollThermal,ct20RollThermal,ct23RollThermal,ct32RollThermal,ct40RollThermal,ct45RollThermal,ct54RollThermal,ct56RollThermal,ct65RollThermal,ct67RollThermal,ct76RollThermal,ctm20RollThermal,ctm50RollThermal,
-pk01Z,-pk10Z,-pk13Z,-pk31Z,-pk36Z,-pk63Z,
-pg01Z,-pg10Z,-pg02Z,-pg20Z,-pg23Z,-pg32Z,-pg04Z,-pg40Z,-pg45Z,-pg54Z,-pg56Z,-pg65Z,-pg67Z,-pg76Z,-pgm02Z,-pgm20Z,-pgm05Z,-pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]}

Z

parZ = {f,
mass1,mass2,mass3,mass4,mass5,mass6,mass7,massd2,massd5,
k10Z,k13Z,k31Z,k36Z,k63Z,
g10Z,g20Z,g23Z,g32Z,g40Z,g45Z,g54Z,g56Z,g65Z,g67Z,g76Z,gm20Z,gm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]}

parZThermal = {f,
mass1,mass2,mass3,mass4,mass5,mass6,mass7,massd2,massd5,
k10ZThermal,k13ZThermal,k31ZThermal,k36ZThermal,k63ZThermal,
g10ZThermal,g20ZThermal,g23ZThermal,g32ZThermal,g40ZThermal,g45ZThermal,g54ZThermal,g56ZThermal,g65ZThermal,g67ZThermal,g76ZThermal,gm20ZThermal,gm50ZThermal,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]}

Yaw

parYaw = {f,
iYaw1,iYaw2,iYaw3,iYaw4,iYaw5,iYaw6,iYaw7,iYawd2,iYawd5,
tk10Yaw,tk13Yaw,tk31Yaw,tk36Yaw,tk63Yaw,
t10Yaw,t20Yaw,t23Yaw,t32Yaw,t40Yaw,t45Yaw,t54Yaw,t56Yaw,t65Yaw,t67Yaw,t76Yaw,tm20Yaw,tm50Yaw,
ctk10Yaw,ctk13Yaw,ctk31Yaw,ctk36Yaw,ctk63Yaw,
ct10Yaw,ct20Yaw,ct23Yaw,ct32Yaw,ct40Yaw,ct45Yaw,ct54Yaw,ct56Yaw,ct65Yaw,ct67Yaw,ct76Yaw,ctm20Yaw,ctm50Yaw,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]}

parYawThermal = {f,
iYaw1,iYaw2,iYaw3,iYaw4,iYaw5,iYaw6,iYaw7,iYawd2,iYawd5,
tk10YawThermal,tk13YawThermal,tk31YawThermal,tk36YawThermal,tk63YawThermal,
t10YawThermal,t20YawThermal,t23YawThermal,t32YawThermal,t40YawThermal,t45YawThermal,t54YawThermal,t56YawThermal,t65YawThermal,t67YawThermal,t76YawThermal,tm20YawThermal,tm50YawThermal,
ctk10YawThermal,ctk13YawThermal,ctk31YawThermal,ctk36YawThermal,ctk63YawThermal,
ct10YawThermal,ct20YawThermal,ct23YawThermal,ct32YawThermal,ct40YawThermal,ct45YawThermal,ct54YawThermal,ct56YawThermal,ct65YawThermal,ct67YawThermal,ct76YawThermal,ctm20YawThermal,ctm50YawThermal,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]}

calculation for single mirror

Test

trfXtest[f_] := trfXYtest[1,f,mass1,iPitch1,g10X,t10Pitch,ct10Pitch,pg01Z,pg10Z,d1Damp[f]]

trfPitchtest[f_] := trfPRtest[2,f,mass1,iPitch1,g10X,t10Pitch,ct10Pitch,pg01Z,pg10Z,d1Damp[f]]

trfYtest[f_] := trfXYtest[1,f,mass1,iRoll1,g10Y,t10Roll,ct10Roll,pg01Z,pg10Z,d1Damp[f]]

trfRolltest[f_] := trfPRtest[2,f,mass1,iRoll1,g10Y,t10Roll,ct10Roll,pg01Z,pg10Z,d1Damp[f]]

dispXtest[f_] :=dispXYtest[1,f,mass1,iPitch1,g10X,t10Pitch,ct10Pitch,pg01Z,pg10Z,d1Damp[f]]

tNoiseXtest[f_] := tNoiseXYtest[1,
f,mass1,iPitch1,g10XThermal,t10PitchThermal,ct10PitchThermal,pg01Z,pg10Z,d1Damp[f]]

dispPitchtest[f_] :=dispPRtest[offsetPitch,2,f,mass1,iPitch1,g10X,t10Pitch,ct10Pitch,pg01Z,pg10Z,d1Damp[f]]

tNoisePitchtest[f_] := tNoisePRtest[offsetPitch,2,
f,mass1,iPitch1,g10XThermal,t10PitchThermal,ct10PitchThermal,pg01Z,pg10Z,d1Damp[f]]

X

trfCryoX[f_] :=trfCryoXY[2*nItem-1,f,
mass1,iPitch1,mass2,iPitch2,mass3,iPitch3,mass4,iPitch4,mass5,iPitch5,mass6,iPitch6,mass7,iPitch7,massd2,iPitchd2,massd5,iPitchd5,
k10X,k13X,k31X,k36X,k63X,
g10X,g20X,g23X,g32X,g40X,g45X,g54X,g56X,g65X,g67X,g76X,gm20X,gm50X,
tk10Pitch,tk13Pitch,tk31Pitch,tk36Pitch,tk63Pitch,
t10Pitch,t20Pitch,t23Pitch,t32Pitch,t40Pitch,t45Pitch,t54Pitch,t56Pitch,t65Pitch,t67Pitch,t76Pitch,tm20Pitch,tm50Pitch,
ctk10Pitch,ctk13Pitch,ctk31Pitch,ctk36Pitch,ctk63Pitch,
ct10Pitch,ct20Pitch,ct23Pitch,ct32Pitch,ct40Pitch,ct45Pitch,ct54Pitch,ct56Pitch,ct65Pitch,ct67Pitch,ct76Pitch,ctm20Pitch,ctm50Pitch,
pk01Z,pk10Z,pk13Z,pk31Z,pk36Z,pk63Z,
pg01Z,pg10Z,pg02Z,pg20Z,pg23Z,pg32Z,pg04Z,pg40Z,pg45Z,pg54Z,pg56Z,pg65Z,pg67Z,pg76Z,pgm02Z,pgm20Z,pgm05Z,pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

trfStageX[f_] := trfStageXY[2*nItem-1,
f,
mass1,iPitch1,mass2,iPitch2,mass3,iPitch3,mass4,iPitch4,mass5,iPitch5,mass6,iPitch6,mass7,iPitch7,massd2,iPitchd2,massd5,iPitchd5,
k10X,k13X,k31X,k36X,k63X,
g10X,g20X,g23X,g32X,g40X,g45X,g54X,g56X,g65X,g67X,g76X,gm20X,gm50X,
tk10Pitch,tk13Pitch,tk31Pitch,tk36Pitch,tk63Pitch,
t10Pitch,t20Pitch,t23Pitch,t32Pitch,t40Pitch,t45Pitch,t54Pitch,t56Pitch,t65Pitch,t67Pitch,t76Pitch,tm20Pitch,tm50Pitch,
ctk10Pitch,ctk13Pitch,ctk31Pitch,ctk36Pitch,ctk63Pitch,
ct10Pitch,ct20Pitch,ct23Pitch,ct32Pitch,ct40Pitch,ct45Pitch,ct54Pitch,ct56Pitch,ct65Pitch,ct67Pitch,ct76Pitch,ctm20Pitch,ctm50Pitch,
pk01Z,pk10Z,pk13Z,pk31Z,pk36Z,pk63Z,
pg01Z,pg10Z,pg02Z,pg20Z,pg23Z,pg32Z,pg04Z,pg40Z,pg45Z,pg54Z,pg56Z,pg65Z,pg67Z,pg76Z,pgm02Z,pgm20Z,pgm05Z,pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispXSeis[f_] := dispXY[ampCryo,ampStage,2*nItem-1,f,
mass1,iPitch1,mass2,iPitch2,mass3,iPitch3,mass4,iPitch4,mass5,iPitch5,mass6,iPitch6,mass7,iPitch7,massd2,iPitchd2,massd5,iPitchd5,
k10X,k13X,k31X,k36X,k63X,
g10X,g20X,g23X,g32X,g40X,g45X,g54X,g56X,g65X,g67X,g76X,gm20X,gm50X,
tk10Pitch,tk13Pitch,tk31Pitch,tk36Pitch,tk63Pitch,
t10Pitch,t20Pitch,t23Pitch,t32Pitch,t40Pitch,t45Pitch,t54Pitch,t56Pitch,t65Pitch,t67Pitch,t76Pitch,tm20Pitch,tm50Pitch,
ctk10Pitch,ctk13Pitch,ctk31Pitch,ctk36Pitch,ctk63Pitch,
ct10Pitch,ct20Pitch,ct23Pitch,ct32Pitch,ct40Pitch,ct45Pitch,ct54Pitch,ct56Pitch,ct65Pitch,ct67Pitch,ct76Pitch,ctm20Pitch,ctm50Pitch,
pk01Z,pk10Z,pk13Z,pk31Z,pk36Z,pk63Z,
pg01Z,pg10Z,pg02Z,pg20Z,pg23Z,pg32Z,pg04Z,pg40Z,pg45Z,pg54Z,pg56Z,pg65Z,pg67Z,pg76Z,pgm02Z,pgm20Z,pgm05Z,pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispXTNoise[f_] := tNoiseXY[2*nItem-1,f,
mass1,iPitch1,mass2,iPitch2,mass3,iPitch3,mass4,iPitch4,mass5,iPitch5,mass6,iPitch6,mass7,iPitch7,massd2,iPitchd2,massd5,iPitchd5,
k10XThermal,k13XThermal,k31XThermal,k36XThermal,k63XThermal,
g10XThermal,g20XThermal,g23XThermal,g32XThermal,g40XThermal,g45XThermal,g54XThermal,g56XThermal,g65XThermal,g67XThermal,g76XThermal,gm20XThermal,gm50XThermal,
tk10PitchThermal,tk13PitchThermal,tk31PitchThermal,tk36PitchThermal,tk63PitchThermal,
t10PitchThermal,t20PitchThermal,t23PitchThermal,t32PitchThermal,t40PitchThermal,t45PitchThermal,t54PitchThermal,t56PitchThermal,t65PitchThermal,t67PitchThermal,t76PitchThermal,tm20PitchThermal,tm50PitchThermal,
tk10PitchThermal,tk13PitchThermal,tk31PitchThermal,tk36PitchThermal,tk63PitchThermal,
ct10PitchThermal,ct20PitchThermal,ct23PitchThermal,ct32PitchThermal,ct40PitchThermal,ct45PitchThermal,ct54PitchThermal,ct56PitchThermal,ct65PitchThermal,ct67PitchThermal,ct76PitchThermal,ctm20PitchThermal,ctm50PitchThermal,
pk01Z,pk10Z,pk13Z,pk31Z,pk36Z,pk63Z,
pg01Z,pg10Z,pg02Z,pg20Z,pg23Z,pg32Z,pg04Z,pg40Z,pg45Z,pg54Z,pg56Z,pg65Z,pg67Z,pg76Z,pgm02Z,pgm20Z,pgm05Z,pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

Y

trfCryoY[f_] :=trfCryoXY[2*nItem-1,f,
mass1,iRoll1,mass2,iRoll2,mass3,iRoll3,mass4,iRoll4,mass5,iRoll5,mass6,iRoll6,mass7,iRoll7,massd2,iRolld2,massd5,iRolld5,
k10Y,k13Y,k31Y,k36Y,k63Y,
g10Y,g20Y,g23Y,g32Y,g40Y,g45Y,g54Y,g56Y,g65Y,g67Y,g76Y,gm20Y,gm50Y,
tk10Roll,tk13Roll,tk31Roll,tk36Roll,tk63Roll,
t10Roll,t20Roll,t23Roll,t32Roll,t40Roll,t45Roll,t54Roll,t56Roll,t65Roll,t67Roll,t76Roll,tm20Roll,tm50Roll,
ctk10Roll,ctk13Roll,ctk31Roll,ctk36Roll,ctk63Roll,
ct10Roll,ct20Roll,ct23Roll,ct32Roll,ct40Roll,ct45Roll,ct54Roll,ct56Roll,ct65Roll,ct67Roll,ct76Roll,ctm20Roll,ctm50Roll,
-pk01Z,-pk10Z,-pk13Z,-pk31Z,-pk36Z,-pk63Z,
-pg01Z,-pg10Z,-pg02Z,-pg20Z,-pg23Z,-pg32Z,-pg04Z,-pg40Z,-pg45Z,-pg54Z,-pg56Z,-pg65Z,-pg67Z,-pg76Z,-pgm02Z,-pgm20Z,-pgm05Z,-pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

trfStageY[f_] := trfStageXY[2*nItem-1,f,
mass1,iRoll1,mass2,iRoll2,mass3,iRoll3,mass4,iRoll4,mass5,iRoll5,mass6,iRoll6,mass7,iRoll7,massd2,iRolld2,massd5,iRolld5,
k10Y,k13Y,k31Y,k36Y,k63Y,
g10Y,g20Y,g23Y,g32Y,g40Y,g45Y,g54Y,g56Y,g65Y,g67Y,g76Y,gm20Y,gm50Y,
tk10Roll,tk13Roll,tk31Roll,tk36Roll,tk63Roll,
t10Roll,t20Roll,t23Roll,t32Roll,t40Roll,t45Roll,t54Roll,t56Roll,t65Roll,t67Roll,t76Roll,tm20Roll,tm50Roll,
ctk10Roll,ctk13Roll,ctk31Roll,ctk36Roll,ctk63Roll,
ct10Roll,ct20Roll,ct23Roll,ct32Roll,ct40Roll,ct45Roll,ct54Roll,ct56Roll,ct65Roll,ct67Roll,ct76Roll,ctm20Roll,ctm50Roll,
-pk01Z,-pk10Z,-pk13Z,-pk31Z,-pk36Z,-pk63Z,
-pg01Z,-pg10Z,-pg02Z,-pg20Z,-pg23Z,-pg32Z,-pg04Z,-pg40Z,-pg45Z,-pg54Z,-pg56Z,-pg65Z,-pg67Z,-pg76Z,-pgm02Z,-pgm20Z,-pgm05Z,-pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispYSeis[f_] :=coupleYX* dispXY[ampCryo,ampStage,2*nItem-1,f,
mass1,iRoll1,mass2,iRoll2,mass3,iRoll3,mass4,iRoll4,mass5,iRoll5,mass6,iRoll6,mass7,iRoll7,massd2,iRolld2,massd5,iRolld5,
k10Y,k13Y,k31Y,k36Y,k63Y,
g10Y,g20Y,g23Y,g32Y,g40Y,g45Y,g54Y,g56Y,g65Y,g67Y,g76Y,gm20Y,gm50Y,
tk10Roll,tk13Roll,tk31Roll,tk36Roll,tk63Roll,
t10Roll,t20Roll,t23Roll,t32Roll,t40Roll,t45Roll,t54Roll,t56Roll,t65Roll,t67Roll,t76Roll,tm20Roll,tm50Roll,
ctk10Roll,ctk13Roll,ctk31Roll,ctk36Roll,ctk63Roll,
ct10Roll,ct20Roll,ct23Roll,ct32Roll,ct40Roll,ct45Roll,ct54Roll,ct56Roll,ct65Roll,ct67Roll,ct76Roll,ctm20Roll,ctm50Roll,
-pk01Z,-pk10Z,-pk13Z,-pk31Z,-pk36Z,-pk63Z,
-pg01Z,-pg10Z,-pg02Z,-pg20Z,-pg23Z,-pg32Z,-pg04Z,-pg40Z,-pg45Z,-pg54Z,-pg56Z,-pg65Z,-pg67Z,-pg76Z,-pgm02Z,-pgm20Z,-pgm05Z,-pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispYTNoise[f_] := coupleYX*tNoiseXY[2*nItem-1,f,
mass1,iRoll1,mass2,iRoll2,mass3,iRoll3,mass4,iRoll4,mass5,iRoll5,mass6,iRoll6,mass7,iRoll7,massd2,iRolld2,massd5,iRolld5,
k10YThermal,k13YThermal,k31YThermal,k36YThermal,k63YThermal,
g10YThermal,g20YThermal,g23YThermal,g32YThermal,g40YThermal,g45YThermal,g54YThermal,g56YThermal,g65YThermal,g67YThermal,g76YThermal,gm20YThermal,gm50YThermal,
tk10RollThermal,tk13RollThermal,tk31RollThermal,tk36RollThermal,tk63RollThermal,
t10RollThermal,t20RollThermal,t23RollThermal,t32RollThermal,t40RollThermal,t45RollThermal,t54RollThermal,t56RollThermal,t65RollThermal,t67RollThermal,t76RollThermal,tm20RollThermal,tm50RollThermal,
ctk10RollThermal,ctk13RollThermal,ctk31RollThermal,ctk36RollThermal,ctk63RollThermal,
ct10RollThermal,ct20RollThermal,ct23RollThermal,ct32RollThermal,ct40RollThermal,ct45RollThermal,ct54RollThermal,ct56RollThermal,ct65RollThermal,ct67RollThermal,ct76RollThermal,ctm20RollThermal,ctm50RollThermal,
-pk01Z,-pk10Z,-pk13Z,-pk31Z,-pk36Z,-pk63Z,
-pg01Z,-pg10Z,-pg02Z,-pg20Z,-pg23Z,-pg32Z,-pg04Z,-pg40Z,-pg45Z,-pg54Z,-pg56Z,-pg65Z,-pg67Z,-pg76Z,-pgm02Z,-pgm20Z,-pgm05Z,-pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

Z

trfCryoZ[f_] := trfCryoZ[nItem,f,
mass1,mass2,mass3,mass4,mass5,mass6,mass7,massd2,massd5,
k10Z,k13Z,k31Z,k36Z,k63Z,
g10Z,g20Z,g23Z,g32Z,g40Z,g45Z,g54Z,g56Z,g65Z,g67Z,g76Z,gm20Z,gm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

trfStageZ[f_]:= trfStageZ[nItem,f,
mass1,mass2,mass3,mass4,mass5,mass6,mass7,massd2,massd5,
k10Z,k13Z,k31Z,k36Z,k63Z,
g10Z,g20Z,g23Z,g32Z,g40Z,g45Z,g54Z,g56Z,g65Z,g67Z,g76Z,gm20Z,gm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispZSeis[f_] := coupleZX*dispZ[ampCryo,ampStage,nItem,f,
mass1,mass2,mass3,mass4,mass5,mass6,mass7,massd2,massd5,
k10Z,k13Z,k31Z,k36Z,k63Z,
g10Z,g20Z,g23Z,g32Z,g40Z,g45Z,g54Z,g56Z,g65Z,g67Z,g76Z,gm20Z,gm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispZTNoise[f_] := coupleZX*tNoiseZ[nItem,f,
mass1,mass2,mass3,mass4,mass5,mass6,mass7,massd2,massd5,
k10ZThermal,k13ZThermal,k31ZThermal,k36ZThermal,k63ZThermal,
g10ZThermal,g20ZThermal,g23ZThermal,g32ZThermal,g40ZThermal,g45ZThermal,g54ZThermal,g56ZThermal,g65ZThermal,g67ZThermal,g76ZThermal,gm20ZThermal,gm50ZThermal,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

Roll

trfCryoRoll[f_] :=trfCryoPR[2*nItem,f,
mass1,iRoll1,mass2,iRoll2,mass3,iRoll3,mass4,iRoll4,mass5,iRoll5,mass6,iRoll6,mass7,iRoll7,massd2,iRolld2,massd5,iRolld5,
k10Y,k13Y,k31Y,k36Y,k63Y,
g10Y,g20Y,g23Y,g32Y,g40Y,g45Y,g54Y,g56Y,g65Y,g67Y,g76Y,gm20Y,gm50Y,
tk10Roll,tk13Roll,tk31Roll,tk36Roll,tk63Roll,
t10Roll,t20Roll,t23Roll,t32Roll,t40Roll,t45Roll,t54Roll,t56Roll,t65Roll,t67Roll,t76Roll,tm20Roll,tm50Roll,
ctk10Roll,ctk13Roll,ctk31Roll,ctk36Roll,ctk63Roll,
ct10Roll,ct20Roll,ct23Roll,ct32Roll,ct40Roll,ct45Roll,ct54Roll,ct56Roll,ct65Roll,ct67Roll,ct76Roll,ctm20Roll,ctm50Roll,
-pk01Z,-pk10Z,-pk13Z,-pk31Z,-pk36Z,-pk63Z,
-pg01Z,-pg10Z,-pg02Z,-pg20Z,-pg23Z,-pg32Z,-pg04Z,-pg40Z,-pg45Z,-pg54Z,-pg56Z,-pg65Z,-pg67Z,-pg76Z,-pgm02Z,-pgm20Z,-pgm05Z,-pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

trfStageRoll[f_] := trfStagePR[2*nItem,f,
mass1,iRoll1,mass2,iRoll2,mass3,iRoll3,mass4,iRoll4,mass5,iRoll5,mass6,iRoll6,mass7,iRoll7,massd2,iRolld2,massd5,iRolld5,
k10Y,k13Y,k31Y,k36Y,k63Y,
g10Y,g20Y,g23Y,g32Y,g40Y,g45Y,g54Y,g56Y,g65Y,g67Y,g76Y,gm20Y,gm50Y,
tk10Roll,tk13Roll,tk31Roll,tk36Roll,tk63Roll,
t10Roll,t20Roll,t23Roll,t32Roll,t40Roll,t45Roll,t54Roll,t56Roll,t65Roll,t67Roll,t76Roll,tm20Roll,tm50Roll,
ctk10Roll,ctk13Roll,ctk31Roll,ctk36Roll,ctk63Roll,
ct10Roll,ct20Roll,ct23Roll,ct32Roll,ct40Roll,ct45Roll,ct54Roll,ct56Roll,ct65Roll,ct67Roll,ct76Roll,ctm20Roll,ctm50Roll,
-pk01Z,-pk10Z,-pk13Z,-pk31Z,-pk36Z,-pk63Z,
-pg01Z,-pg10Z,-pg02Z,-pg20Z,-pg23Z,-pg32Z,-pg04Z,-pg40Z,-pg45Z,-pg54Z,-pg56Z,-pg65Z,-pg67Z,-pg76Z,-pgm02Z,-pgm20Z,-pgm05Z,-pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispRollSeis[f_] := dispPR[offsetRoll,ampCryo,ampStage,2*nItem,f,
mass1,iRoll1,mass2,iRoll2,mass3,iRoll3,mass4,iRoll4,mass5,iRoll5,mass6,iRoll6,mass7,iRoll7,massd2,iRolld2,massd5,iRolld5,
k10Y,k13Y,k31Y,k36Y,k63Y,
g10Y,g20Y,g23Y,g32Y,g40Y,g45Y,g54Y,g56Y,g65Y,g67Y,g76Y,gm20Y,gm50Y,
tk10Roll,tk13Roll,tk31Roll,tk36Roll,tk63Roll,
t10Roll,t20Roll,t23Roll,t32Roll,t40Roll,t45Roll,t54Roll,t56Roll,t65Roll,t67Roll,t76Roll,tm20Roll,tm50Roll,
ctk10Roll,ctk13Roll,ctk31Roll,ctk36Roll,ctk63Roll,
ct10Roll,ct20Roll,ct23Roll,ct32Roll,ct40Roll,ct45Roll,ct54Roll,ct56Roll,ct65Roll,ct67Roll,ct76Roll,ctm20Roll,ctm50Roll,
-pk01Z,-pk10Z,-pk13Z,-pk31Z,-pk36Z,-pk63Z,
-pg01Z,-pg10Z,-pg02Z,-pg20Z,-pg23Z,-pg32Z,-pg04Z,-pg40Z,-pg45Z,-pg54Z,-pg56Z,-pg65Z,-pg67Z,-pg76Z,-pgm02Z,-pgm20Z,-pgm05Z,-pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispRollTNoise[f_] := tNoisePR[offsetRoll,2*nItem,f,
mass1,iRoll1,mass2,iRoll2,mass3,iRoll3,mass4,iRoll4,mass5,iRoll5,mass6,iRoll6,mass7,iRoll7,massd2,iRolld2,massd5,iRolld5,
k10YThermal,k13YThermal,k31YThermal,k36YThermal,k63YThermal,
g10YThermal,g20YThermal,g23YThermal,g32YThermal,g40YThermal,g45YThermal,g54YThermal,g56YThermal,g65YThermal,g67YThermal,g76YThermal,gm20YThermal,gm50YThermal,
tk10RollThermal,tk13RollThermal,tk31RollThermal,tk36RollThermal,tk63RollThermal,
t10RollThermal,t20RollThermal,t23RollThermal,t32RollThermal,t40RollThermal,t45RollThermal,t54RollThermal,t56RollThermal,t65RollThermal,t67RollThermal,t76RollThermal,tm20RollThermal,tm50RollThermal,
ctk10RollThermal,ctk13RollThermal,ctk31RollThermal,ctk36RollThermal,ctk63RollThermal,
ct10RollThermal,ct20RollThermal,ct23RollThermal,ct32RollThermal,ct40RollThermal,ct45RollThermal,ct54RollThermal,ct56RollThermal,ct65RollThermal,ct67RollThermal,ct76RollThermal,ctm20RollThermal,ctm50RollThermal,
-pk01Z,-pk10Z,-pk13Z,-pk31Z,-pk36Z,-pk63Z,
-pg01Z,-pg10Z,-pg02Z,-pg20Z,-pg23Z,-pg32Z,-pg04Z,-pg40Z,-pg45Z,-pg54Z,-pg56Z,-pg65Z,-pg67Z,-pg76Z,-pgm02Z,-pgm20Z,-pgm05Z,-pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

Pitch

trfCryoPitch[f_] :=trfCryoPR[2*nItem,f,
mass1,iPitch1,mass2,iPitch2,mass3,iPitch3,mass4,iPitch4,mass5,iPitch5,mass6,iPitch6,mass7,iPitch7,massd2,iPitchd2,massd5,iPitchd5,
k10X,k13X,k31X,k36X,k63X,
g10X,g20X,g23X,g32X,g40X,g45X,g54X,g56X,g65X,g67X,g76X,gm20X,gm50X,
tk10Pitch,tk13Pitch,tk31Pitch,tk36Pitch,tk63Pitch,
t10Pitch,t20Pitch,t23Pitch,t32Pitch,t40Pitch,t45Pitch,t54Pitch,t56Pitch,t65Pitch,t67Pitch,t76Pitch,tm20Pitch,tm50Pitch,
ctk10Pitch,ctk13Pitch,ctk31Pitch,ctk36Pitch,ctk63Pitch,
ct10Pitch,ct20Pitch,ct23Pitch,ct32Pitch,ct40Pitch,ct45Pitch,ct54Pitch,ct56Pitch,ct65Pitch,ct67Pitch,ct76Pitch,ctm20Pitch,ctm50Pitch,
pk01Z,pk10Z,pk13Z,pk31Z,pk36Z,pk63Z,
pg01Z,pg10Z,pg02Z,pg20Z,pg23Z,pg32Z,pg04Z,pg40Z,pg45Z,pg54Z,pg56Z,pg65Z,pg67Z,pg76Z,pgm02Z,pgm20Z,pgm05Z,pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

trfStagePitch[f_] := trfStagePR[2*nItem,f,
mass1,iPitch1,mass2,iPitch2,mass3,iPitch3,mass4,iPitch4,mass5,iPitch5,mass6,iPitch6,mass7,iPitch7,massd2,iPitchd2,massd5,iPitchd5,
k10X,k13X,k31X,k36X,k63X,
g10X,g20X,g23X,g32X,g40X,g45X,g54X,g56X,g65X,g67X,g76X,gm20X,gm50X,
tk10Pitch,tk13Pitch,tk31Pitch,tk36Pitch,tk63Pitch,
t10Pitch,t20Pitch,t23Pitch,t32Pitch,t40Pitch,t45Pitch,t54Pitch,t56Pitch,t65Pitch,t67Pitch,t76Pitch,tm20Pitch,tm50Pitch,
ctk10Pitch,ctk13Pitch,ctk31Pitch,ctk36Pitch,ctk63Pitch,
ct10Pitch,ct20Pitch,ct23Pitch,ct32Pitch,ct40Pitch,ct45Pitch,ct54Pitch,ct56Pitch,ct65Pitch,ct67Pitch,ct76Pitch,ctm20Pitch,ctm50Pitch,
pk01Z,pk10Z,pk13Z,pk31Z,pk36Z,pk63Z,
pg01Z,pg10Z,pg02Z,pg20Z,pg23Z,pg32Z,pg04Z,pg40Z,pg45Z,pg54Z,pg56Z,pg65Z,pg67Z,pg76Z,pgm02Z,pgm20Z,pgm05Z,pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispPitchSeis[f_] := dispPR[offsetPitch,ampCryo,ampStage,2*nItem,f,
mass1,iPitch1,mass2,iPitch2,mass3,iPitch3,mass4,iPitch4,mass5,iPitch5,mass6,iPitch6,mass7,iPitch7,massd2,iPitchd2,massd5,iPitchd5,
k10X,k13X,k31X,k36X,k63X,
g10X,g20X,g23X,g32X,g40X,g45X,g54X,g56X,g65X,g67X,g76X,gm20X,gm50X,
tk10Pitch,tk13Pitch,tk31Pitch,tk36Pitch,tk63Pitch,
t10Pitch,t20Pitch,t23Pitch,t32Pitch,t40Pitch,t45Pitch,t54Pitch,t56Pitch,t65Pitch,t67Pitch,t76Pitch,tm20Pitch,tm50Pitch,
ctk10Pitch,ctk13Pitch,ctk31Pitch,ctk36Pitch,ctk63Pitch,
ct10Pitch,ct20Pitch,ct23Pitch,ct32Pitch,ct40Pitch,ct45Pitch,ct54Pitch,ct56Pitch,ct65Pitch,ct67Pitch,ct76Pitch,ctm20Pitch,ctm50Pitch,
pk01Z,pk10Z,pk13Z,pk31Z,pk36Z,pk63Z,
pg01Z,pg10Z,pg02Z,pg20Z,pg23Z,pg32Z,pg04Z,pg40Z,pg45Z,pg54Z,pg56Z,pg65Z,pg67Z,pg76Z,pgm02Z,pgm20Z,pgm05Z,pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispPitchTNoise[f_] := tNoisePR[offsetPitch,2*nItem,f,
mass1,iPitch1,mass2,iPitch2,mass3,iPitch3,mass4,iPitch4,mass5,iPitch5,mass6,iPitch6,mass7,iPitch7,massd2,iPitchd2,massd5,iPitchd5,
k10XThermal,k13XThermal,k31XThermal,k36XThermal,k63XThermal,
g10XThermal,g20XThermal,g23XThermal,g32XThermal,g40XThermal,g45XThermal,g54XThermal,g56XThermal,g65XThermal,g67XThermal,g76XThermal,gm20XThermal,gm50XThermal,
tk10PitchThermal,tk13PitchThermal,tk31PitchThermal,tk36PitchThermal,tk63PitchThermal,
t10PitchThermal,t20PitchThermal,t23PitchThermal,t32PitchThermal,t40PitchThermal,t45PitchThermal,t54PitchThermal,t56PitchThermal,t65PitchThermal,t67PitchThermal,t76PitchThermal,tm20PitchThermal,tm50PitchThermal,
tk10PitchThermal,tk13PitchThermal,tk31PitchThermal,tk36PitchThermal,tk63PitchThermal,
ct10PitchThermal,ct20PitchThermal,ct23PitchThermal,ct32PitchThermal,ct40PitchThermal,ct45PitchThermal,ct54PitchThermal,ct56PitchThermal,ct65PitchThermal,ct67PitchThermal,ct76PitchThermal,ctm20PitchThermal,ctm50PitchThermal,
pk01Z,pk10Z,pk13Z,pk31Z,pk36Z,pk63Z,
pg01Z,pg10Z,pg02Z,pg20Z,pg23Z,pg32Z,pg04Z,pg40Z,pg45Z,pg54Z,pg56Z,pg65Z,pg67Z,pg76Z,pgm02Z,pgm20Z,pgm05Z,pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

Yaw

trfCryoYaw[f_] := trfCryoYaw[nItem,f,
iYaw1,iYaw2,iYaw3,iYaw4,iYaw5,iYaw6,iYaw7,iYawd2,iYawd5,
tk10Yaw,tk13Yaw,tk31Yaw,tk36Yaw,tk63Yaw,
t10Yaw,t20Yaw,t23Yaw,t32Yaw,t40Yaw,t45Yaw,t54Yaw,t56Yaw,t65Yaw,t67Yaw,t76Yaw,tm20Yaw,tm50Yaw,
ctk10Yaw,ctk13Yaw,ctk31Yaw,ctk36Yaw,ctk63Yaw,
ct10Yaw,ct20Yaw,ct23Yaw,ct32Yaw,ct40Yaw,ct45Yaw,ct54Yaw,ct56Yaw,ct65Yaw,ct67Yaw,ct76Yaw,ctm20Yaw,ctm50Yaw,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

trfStageYaw[f_]:= trfStageYaw[nItem,f,
iYaw1,iYaw2,iYaw3,iYaw4,iYaw5,iYaw6,iYaw7,iYawd2,iYawd5,
tk10Yaw,tk13Yaw,tk31Yaw,tk36Yaw,tk63Yaw,
t10Yaw,t20Yaw,t23Yaw,t32Yaw,t40Yaw,t45Yaw,t54Yaw,t56Yaw,t65Yaw,t67Yaw,t76Yaw,tm20Yaw,tm50Yaw,
ctk10Yaw,ctk13Yaw,ctk31Yaw,ctk36Yaw,ctk63Yaw,
ct10Yaw,ct20Yaw,ct23Yaw,ct32Yaw,ct40Yaw,ct45Yaw,ct54Yaw,ct56Yaw,ct65Yaw,ct67Yaw,ct76Yaw,ctm20Yaw,ctm50Yaw,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispYawSeis[f_] := dispYaw[offsetYaw,ampCryo,ampStage,nItem,f,
iYaw1,iYaw2,iYaw3,iYaw4,iYaw5,iYaw6,iYaw7,iYawd2,iYawd5,
tk10Yaw,tk13Yaw,tk31Yaw,tk36Yaw,tk63Yaw,
t10Yaw,t20Yaw,t23Yaw,t32Yaw,t40Yaw,t45Yaw,t54Yaw,t56Yaw,t65Yaw,t67Yaw,t76Yaw,tm20Yaw,tm50Yaw,
ctk10Yaw,ctk13Yaw,ctk31Yaw,ctk36Yaw,ctk63Yaw,
ct10Yaw,ct20Yaw,ct23Yaw,ct32Yaw,ct40Yaw,ct45Yaw,ct54Yaw,ct56Yaw,ct65Yaw,ct67Yaw,ct76Yaw,ctm20Yaw,ctm50Yaw,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

dispYawTNoise[f_] := tNoiseYaw[offsetYaw,nItem,f,
iYaw1,iYaw2,iYaw3,iYaw4,iYaw5,iYaw6,iYaw7,iYawd2,iYawd5,
tk10YawThermal,tk13YawThermal,tk31YawThermal,tk36YawThermal,tk63YawThermal,
t10YawThermal,t20YawThermal,t23YawThermal,t32YawThermal,t40YawThermal,t45YawThermal,t54YawThermal,t56YawThermal,t65YawThermal,t67YawThermal,t76YawThermal,tm20YawThermal,tm50YawThermal,
ctk10YawThermal,ctk13YawThermal,ctk31YawThermal,ctk36YawThermal,ctk63YawThermal,
ct10YawThermal,ct20YawThermal,ct23YawThermal,ct32YawThermal,ct40YawThermal,ct45YawThermal,ct54YawThermal,ct56YawThermal,ct65YawThermal,ct67YawThermal,ct76YawThermal,ctm20YawThermal,ctm50YawThermal,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]

seismic noise

dispParallel[f_]:= Sqrt[4*(dispXSeis[f]^2+dispYSeis[f]^2+dispZSeis[f]^2)]; (*4 mirrors displacement in parallel motion.*)

dispRotation[f_] :=Sqrt[4*(dispRollSeis[f]^2+dispPitchSeis[f]^2+dispYawSeis[f]^2)]

dispSeis[f_] := Sqrt[dispParallel[f]^2+dispRotation[f]^2]

hDispSeis[f_] := Sqrt[dispParallel[f]^2+dispRotation[f]^2]/l

suspension thermal noise (without violin mode)

tNoiseParallel[f_]:=Sqrt[4*(dispXTNoise[f]^2+dispYTNoise[f]^2+dispZTNoise[f]^2)]

tNoiseRotation[f_]:=Sqrt[4*(dispRollTNoise[f]^2+dispPitchTNoise[f]^2+dispYawTNoise[f]^2)]

dispSTNoise [f_] :=Sqrt[tNoiseParallel[f]^2+tNoiseRotation[f]^2]

hDispSTNoise [f_] :=Sqrt[tNoiseParallel[f]^2+tNoiseRotation[f]^2]/l

Results

Test

Q & resonant frequency

resXPtest=f  /. NSolve[Det[matXPYRtest[f,mass1,iPitch1,g10X,t10Pitch,ct10Pitch,pg10Z,d1Damp[f]]]==0,f];

Sort[resXPtest/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

resYRtest=f  /. NSolve[Det[matXPYRtest[f,mass1,iRoll1,g10Y,t10Roll,pg10Z,d1Damp[f]]]==0,f];

Sort[resYRtest/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

Eigenvalues[matXPYRtest[f,mass1,iPitch1,g10X,t10Pitch,pg10Z,d1Damp[f]]]

TRF plot

LogLogPlot[{trfXtest[f],trfPitchtest[f]},{f,0.01,10},PlotStyle -> {RGBColor[0,0,1],RGBColor[0,1,0]}]

displacement

LogLogPlot[{dispXtest[f],dispPitchtest[f],seisK[f]},{f,0.1,10},PlotStyle -> {RGBColor[0,0,1],RGBColor[1,0,0],RGBColor[0,1,0]}]

LogLogPlot[{tNoiseXtest[f],tNoisePitchtest[f]},{f,0.01,10},PlotStyle -> {RGBColor[0,0,1],RGBColor[0,1,0]}]

X - Pitch

Q & resonant frequency

resXP=f  /. NSolve[Det[matXPYR[f,
mass1,iPitch1,mass2,iPitch2,mass3,iPitch3,mass4,iPitch4,mass5,iPitch5,mass6,iPitch6,mass7,iPitch7,massd2,iPitchd2,massd5,iPitchd5,
k10X,k13X,k31X,k36X,k63X,
g10X,g20X,g23X,g32X,g40X,g45X,g54X,g56X,g65X,g67X,g76X,gm20X,gm50X,
tk10Pitch,tk13Pitch,tk31Pitch,tk36Pitch,tk63Pitch,
t10Pitch,t20Pitch,t23Pitch,t32Pitch,t40Pitch,t45Pitch,t54Pitch,t56Pitch,t65Pitch,t67Pitch,t76Pitch,tm20Pitch,tm50Pitch,
ctk10Pitch,ctk13Pitch,ctk31Pitch,ctk36Pitch,ctk63Pitch,
ct10Pitch,ct20Pitch,ct23Pitch,ct32Pitch,ct40Pitch,ct45Pitch,ct54Pitch,ct56Pitch,ct65Pitch,ct67Pitch,ct76Pitch,ctm20Pitch,ctm50Pitch,
pk10Z,pk13Z,pk31Z,pk36Z,pk63Z,
pg10Z,pg20Z,pg23Z,pg32Z,pg40Z,pg45Z,pg54Z,pg56Z,pg65Z,pg67Z,pg76Z,pgm20Z,pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]]==0,f];

Sort[resXP/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

TRF plot

LogLogPlot[{trfStageX[f],trfCryoX[f]},{f,0.1,10}]

LogLogPlot[{trfStagePitch[f]},{f,0.01,30}]

displacement

LogLogPlot[{dispXSeis[f],dispXTNoise[f]},{f,0.1,30}]

LogLogPlot[{dispPitchSeis[f],dispPitchTNoise[f]},{f,0.1,40}]

Y - Roll

Q & resonant frequency

resYR=f  /. NSolve[Det[matXPYR[f,
mass1,iRoll1,mass2,iRoll2,mass3,iRoll3,mass4,iRoll4,mass5,iRoll5,mass6,iRoll6,mass7,iRoll7,massd2,iRolld2,massd5,iRolld5,
k10Y,k13Y,k31Y,k36Y,k63Y,
g10Y,g20Y,g23Y,g32Y,g40Y,g45Y,g54Y,g56Y,g65Y,g67Y,g76Y,gm20Y,gm50Y,
tk10Roll,tk13Roll,tk31Roll,tk36Roll,tk63Roll,
t10Roll,t20Roll,t23Roll,t32Roll,t40Roll,t45Roll,t54Roll,t56Roll,t65Roll,t67Roll,t76Roll,tm20Roll,tm50Roll,
ctk10Roll,ctk13Roll,ctk31Roll,ctk36Roll,ctk63Roll,
ct10Roll,ct20Roll,ct23Roll,ct32Roll,ct40Roll,ct45Roll,ct54Roll,ct56Roll,ct65Roll,ct67Roll,ct76Roll,ctm20Roll,ctm50Roll,
-pk10Z,-pk13Z,-pk31Z,-pk36Z,-pk63Z,
-pg10Z,-pg20Z,-pg23Z,-pg32Z,-pg40Z,-pg45Z,-pg54Z,-pg56Z,-pg65Z,-pg67Z,-pg76Z,-pgm20Z,-pgm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]]==0,f];

Sort[resYR/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

TRF plot

LogLogPlot[{trfCryoY[f],trfStageY[f]},{f,0.1,10}]

LogLogPlot[{trfStageRoll[f]},{f,0.01,10}]

displacement

LogLogPlot[{dispYSeis[f],dispYTNoise[f]},{f,0.1,10}]

Z

Q & resonant frequency

resZ=f  /. NSolve[Det[matZ[f,
mass1,mass2,mass3,mass4,mass5,mass6,mass7,massd2,massd5,
k10Z,k13Z,k31Z,k36Z,k63Z,
g10Z,g20Z,g23Z,g32Z,g40Z,g45Z,g54Z,g56Z,g65Z,g67Z,g76Z,gm20Z,gm50Z,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]]==0,f];

Sort[resZ/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

TRF plot

LogLogPlot[{trfCryoZ[f],trfStageZ[f]},{f,1,30}]

LogLogPlot[{trfCryoZ[f],trfStageZ[f]},{f,30,300}]

displacement

LogLogPlot[{dispZSeis[f],dispZTNoise[f]},{f,1,30}]

LogLogPlot[{dispZSeis[f],dispZTNoise[f]},{f,10,300}]

Yaw

Q & resonant frequency

resYaw=f  /. NSolve[Det[matYaw[f,
iYaw1,iYaw2,iYaw3,iYaw4,iYaw5,iYaw6,iYaw7,iYawd2,iYawd5,
tk10Yaw,tk13Yaw,tk31Yaw,tk36Yaw,tk63Yaw,
t10Yaw,t20Yaw,t23Yaw,t32Yaw,t40Yaw,t45Yaw,t54Yaw,t56Yaw,t65Yaw,t67Yaw,t76Yaw,tm20Yaw,tm50Yaw,
ctk10Yaw,ctk13Yaw,ctk31Yaw,ctk36Yaw,ctk63Yaw,
ct10Yaw,ct20Yaw,ct23Yaw,ct32Yaw,ct40Yaw,ct45Yaw,ct54Yaw,ct56Yaw,ct65Yaw,ct67Yaw,ct76Yaw,ctm20Yaw,ctm50Yaw,
d1Damp[f],d2Damp[f],d3Damp[f],d4Damp[f],d5Damp[f]]]==0,f];

Sort[resYaw/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

TRF plot

LogLogPlot[{trfStageYaw[f],trfCryoYaw[f]},{f,.1,5}]

displacement

LogLogPlot[{dispYawSeis[f],dispYawTNoise[f]},{f,0.01,10}]

Total sensitivity (OLD)

seismic noise model

dispSeisModel[f_] := 2*seisK[f]/f^4

hDispSeisModel[f_] := dispSeisModel[f]/l

Read out noise

shot noise

hShot[f_] :=hshot[f,p,tau]

shot[f_] := hShot[f]*l

radiation pressure noise

hRadia[f_] :=hradia[f,p,fcut,l,finesse,mMass]

radia[f_] :=hRadia[f]*l

test plot

LogLogPlot[{shot[f],radia[f]},{f,1,10000}]

Mirror thermal noise

noises in cryogenic

thCoat20[f_] := mirrorcoa[f,tMass,dcoa,phicoa,w1,w2,saYoung]

thMassStrucure20[f_] := mirrorhomo[f,tMass,saPoisson,1/saQMass20,w1,w2,saYoung]

thElastic20[f_] := Sqrt[2*(thelastic[f,tMass,saAlpha20,saPoisson,saKappa20,saSpHeat20,w1]+thelastic[f,tMass,saAlpha20,saPoisson,saKappa20,saSpHeat20,w2])]

dispThMass20[f_] := Sqrt[thCoat20[f]^2+thMassStrucure20[f]^2+thElastic20[f]^2]

hDispThMass20[f_] := Sqrt[thCoat20[f]^2+thMassStrucure20[f]^2+thElastic20[f]^2]/l

noise in 300K

thCoat300[f_] := mirrorcoa[f,300,dcoa,phicoa,w1,w2,saYoung]

thMassStrucure300[f_] := mirrorhomo[f,300,saPoisson,1/saQMass300,w1,w2,saYoung]

thElastic300[f_] := Sqrt[2*(thelastic[f,300,saAlpha300,saPoisson,saKappa300,saSpHeat300,w1]+thelastic[f,300,saAlpha300,saPoisson,saKappa300,saSpHeat300,w2])]

dispThMass300[f_] := Sqrt[thCoat300[f]^2+thMassStrucure300[f]^2+thElastic300[f]^2]

hDispThMass300[f_] := Sqrt[thCoat300[f]^2+thMassStrucure300[f]^2+thElastic300[f]^2]/l

sum up

dispCLIO[f_] := Sqrt[dispSeis[f]^2+dispSTNoise [f]^2+shot[f]^2+radia[f]^2+dispThMass20[f]^2]

dispCLIORoom[f_] := Sqrt[dispSeis[f]^2+dispSTNoise [f]^2+shot[f]^2+radia[f]^2+dispThMass300[f]^2]

dispCLIOModel[f_] := Sqrt[dispSeisModel[f]^2+shot[f]^2+radia[f]^2+dispThMass20[f]^2]

hDispCLIO[f_] := Sqrt[hDispSeis[f]^2+hDispSTNoise [f]^2+hShot[f]^2+hRadia[f]^2+hDispThMass20[f]^2]

CLIO sensitivity

seminar seismic noise

plotCLIO1 =LogLogPlot[{dispCLIOModel[f],dispCLIO[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,0,1]}]

plotCLIO2 =LogLogPlot[{dispCLIOModel[f],dispCLIO[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,0,1]}]

Show[plotCLIO1,plotCLIO2,PlotRange -> All]

plotCLIO3 =LogLogPlot[{dispSeis[f],dispSTNoise [f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,1,0],RGBColor[0,1,1]}]

plotCLIO4 =LogLogPlot[{dispSeis[f],dispSTNoise [f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,1,0],RGBColor[0,1,1]}]

Show[plotCLIO1,plotCLIO2,plotCLIO3,plotCLIO4,PlotRange -> All]

plotCLIO5 =LogLogPlot[{dispSeis[f], dispXSeis[f],dispYSeis[f],dispZSeis[f],dispPitchSeis[f], dispYawSeis[f]},
{f,1,60},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1],RGBColor[1,1,0],RGBColor[0,1,1],RGBColor[1,0.5,0]}]

plotCLIO6 =LogLogPlot[{dispSeis[f],dispZSeis[f]},
{f,1,60},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,1,0]}]

plotCLIO7 =LogLogPlot[{dispZSeis[f]},
{f,1,60},
PlotRange-> All,
PlotStyle -> {RGBColor[0,0,1]}](*Cryostat only*)

plotCLIO8 =LogLogPlot[{dispZSeis[f]},
{f,1,60},
PlotRange-> All,
PlotStyle -> {RGBColor[1,1,0]}](*main only*)

Show[plotCLIO6,plotCLIO7,plotCLIO8,PlotRange -> All]

plotCLIO9 =LogLogPlot[{dispCLIOModel[f],dispSeis[f],dispZSeis[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0,0,1],RGBColor[1,0,0],RGBColor[0,1,0]}]

plotCLIO10 =LogLogPlot[{dispCLIOModel[f],dispSeis[f],dispZSeis[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0,0,1],RGBColor[1,0,0],RGBColor[0,1,0]}]

plotCLIO11 =LogLogPlot[{dispSeis[f],dispZSeis[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,1],RGBColor[1,1,0]}](*improved*)

plotCLIO12 =LogLogPlot[{dispSeis[f],dispZSeis[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,1],RGBColor[1,1,0]}](*improved*)

Show[plotCLIO9,plotCLIO10,plotCLIO11,plotCLIO12,PlotRange -> All]

Show[plotCLIO10,plotCLIO12]

seminar suspension thermal

plotCLIO100 =LogLogPlot[{dispCLIOModel[f],dispSeis[f],dispSTNoise [f] },
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]}]

plotCLIO101 =LogLogPlot[{dispCLIOModel[f],dispSeis[f],dispSTNoise [f] },
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1]}]

plotCLIO136 =LogLogPlot[{dispCLIOModel[f],dispSTNoise [f] },
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,1,0]}]

plotCLIO137 =LogLogPlot[{dispCLIOModel[f],dispSTNoise [f] },
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,1,0]}]

Show[plotCLIO100,plotCLIO101,PlotRange -> All]

plotCLIO102 =LogLogPlot[{dispSTNoise[f], dispXTNoise[f],dispYTNoise[f],dispZTNoise[f],dispPitchTNoise[f], dispYawTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1],RGBColor[1,1,0],RGBColor[0,1,1],RGBColor[1,0.5,0]}]

plotCLIO103 =LogLogPlot[{dispSTNoise[f], dispXTNoise[f],dispYTNoise[f],dispZTNoise[f],dispPitchTNoise[f], dispYawTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,1,0],RGBColor[0,0,1],RGBColor[1,1,0],RGBColor[0,1,1],RGBColor[1,0.5,0]}]

Show[plotCLIO102,plotCLIO103,PlotRange -> All]

plotCLIO104 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,1,0]}] (*heat link only*)

plotCLIO105 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0],RGBColor[0,1,0]}] (*heat link only*)

plotCLIO106 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,0]}] (*g4 only*)

plotCLIO107 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,0]}] (*g4 only*)

plotCLIO108 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0,0,1]}] (*g5 only*)

plotCLIO109 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0,0,1]}] (*g5 only*)

plotCLIO110 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,1,0]}] (*g6 only*)

plotCLIO111 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,1,0]}] (*g6 only*)

plotCLIO112 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,1]}] (*g7 only*)

plotCLIO113 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,1]}] (*g7 only*)

plotCLIO114 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,1]}] (*damping only*)

plotCLIO115 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,1]}] (*damping only*)

plotCLIO116 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0.5,0]}] (*magnet damping only*)

plotCLIO117 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0.5,0]}] (*magnet damping only*)

plotCLIO118 =LogLogPlot[{dispCLIOModel[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0,0.5,1]}]

plotCLIO119 =LogLogPlot[{dispCLIOModel[f]},
{f,10,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0,0.5,1]}]

Show[plotCLIO104,plotCLIO105,plotCLIO106,plotCLIO107,plotCLIO108,plotCLIO109,plotCLIO110,plotCLIO111,plotCLIO112,plotCLIO113,plotCLIO114,plotCLIO115,plotCLIO116,plotCLIO117,plotCLIO119,PlotRange -> All]

plotCLIO120 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,0]}] (*g6 improved only. q=10^4*)

plotCLIO121 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,0]}] (*g6 improved only. q=10^4*)

plotCLIO122 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0]}] (*g6 improved only. q=10^5*)

plotCLIO123 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0]}] (*g6 improved only. q=10^5*)

Show[plotCLIO110,plotCLIO111,plotCLIO119,plotCLIO120,plotCLIO121,plotCLIO122,plotCLIO123,PlotRange-> All]

plotCLIO124 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0]}] (*g7 improved only. 0.25 -> 0.20*)

plotCLIO125 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0]}] (*g7 improved only. 0.25 -> 0.20*)

plotCLIO126 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,0]}] (*g7 improved only. 10% -> 3%*)

plotCLIO127 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,0]}] (*g7 improved only. 10% -> 3%*)

Show[plotCLIO112,plotCLIO113,plotCLIO119,plotCLIO124,plotCLIO125,plotCLIO126,plotCLIO127,PlotRange-> All]

plotCLIO128 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0]}] (*g7 improved only*)

plotCLIO129 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0,0]}] (*g7 improved only*)

plotCLIO130 =LogLogPlot[{dispSTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0,0,1]}] (*total improved *)

plotCLIO131 =LogLogPlot[{dispSTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0,0,1]}] (*total improved *)

plotCLIO132 =LogLogPlot[{dispZTNoise[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,0]}] (*g6 improved only*)

plotCLIO133 =LogLogPlot[{dispZTNoise[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,0]}] (*g6 improved only*)

Show[plotCLIO119,plotCLIO136,plotCLIO137,plotCLIO128,plotCLIO129,plotCLIO132,plotCLIO133,plotCLIO130,plotCLIO131]

plotCLIO134 =LogLogPlot[{dispCLIO[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,0]}] (**)

plotCLIO135 =LogLogPlot[{dispCLIO[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0,1,0]}] (**)

Show[plotCLIO1,plotCLIO2,plotCLIO134,plotCLIO135,PlotRange-> All]

Show[plotCLIO2,plotCLIO135,PlotRange-> All]

plotCLIO138 =LogLogPlot[{dispCLIORoom[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0,0,1]}] (*300K*)

plotCLIO139 =LogLogPlot[{dispCLIORoom[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0,0,1]}] (*300K*)

plotCLIO140 =LogLogPlot[{dispCLIOModel[f]},
{f,1,300},
PlotRange-> All,
PlotStyle -> {RGBColor[1,0.,0]}]

plotCLIO141 =LogLogPlot[{dispThMass300[f]},
{f,0.1,30},
PlotRange-> All,
PlotStyle -> {RGBColor[0.5,0,1]}] (*300K*)

plotCLIO142 =LogLogPlot[{dispThMass300[f]},
{f,30,300},
PlotRange-> All,
PlotStyle -> {RGBColor[0.5,0,1]}] (*300K*)

Show[plotCLIO119,plotCLIO134,plotCLIO135,plotCLIO138,plotCLIO139,plotCLIO141,plotCLIO142]

Show[plotCLIO119,plotCLIO134,plotCLIO135,plotCLIO138,plotCLIO139,plotCLIO141,plotCLIO142,plotLISM030214]

Triple pendulum (OLD)

Parameters

intersting item

nItem3Pend = 3 ;
(*m1 ~ m3 -> 1 ~ 3,
Final mass = 3.*)

coupling & vibration amplification in cryostat

coupleZX3Pend = 3/100;(*coupling Z -> X*)
coupleYX3Pend = 10/100;(*coupling Y -> X*)

offset of beam centering

offsetRoll3Pend = 0 mm;
offsetPitch3Pend = 0.1 mm;
offsetYaw3Pend = 0.1 mm;

final suspension

numSaPend3Pend = 4;
diaSaPend3Pend = 1.8 mm;
lSaPend3Pend = 0.5m;

dimensions of mass for triple pendulum

m1

m1Dens3Pend = alDens;
m1X3Pend = 300mm;
m1Y3Pend = 300 mm;
m1Z3Pend = 210 mm;
mCube[m1Dens3Pend,m1X3Pend,m1Y3Pend,m1Z3Pend]

m2

m2Dens3Pend = alDens;
m2X3Pend = 300mm;
m2Y3Pend = 300 mm;
m2Z3Pend = 210 mm;
mCube[m2Dens3Pend,m2X3Pend,m2Y3Pend,m2Z3Pend]

m3

m3Dens3Pend = saDens;
m3R3Pend = 300/2mm;
m3L3Pend = 180 mm;
mCyl[m3Dens3Pend,m3R3Pend,m3L3Pend]

spring for triple pendulum

g1

g1Length3Pend = 0.25m;
g1VFreq3Pend = 0.3 Hz;

g2

g2Length3Pend =1m;
g2VFreq3Pend = 3.5Hz;

g3

lSaPend3Pend = 0.5 m;
g3VFreq3Pend = 3.5Hz;

position of wire clamp from COM (4 wires + symmetrical distribution) for triple pendulum

suspension wires

pg01X3Pend = 20 mm;
pg01Y3Pend = 20 mm;
pg01Z3Pend = +0 mm;

pg10X3Pend = pg01X3Pend;
pg10Y3Pend = pg01Y3Pend ;
pg10Z3Pend = m1Z3Pend/2;

pg12X3Pend = 20 mm;
pg12Y3Pend = 20 mm;
pg12Z3Pend = -m1Z3Pend;

pg21X3Pend = pg12X3Pend;
pg21Y3Pend = pg12Y3Pend;
pg21Z3Pend = m2Z3Pend/2;

pg23X3Pend = 30 mm;
pg23Y3Pend = m3R3Pend /2;
pg23Z3Pend = -0mm;

pg32X3Pend = pg23X3Pend ;
pg32Y3Pend = pg23Y3Pend;
pg32Z3Pend = +0mm;

dissipation for triple pendulum

in spring

g1HPhi3Pend = 1/10^6;
g1VPhi3Pend = 1/10^4;

g2HPhi3Pend = 1/10^6;
g2VPhi3Pend =   1/10^5;

g3HPhi3Pend = 1/10^8;
g3VPhi3Pend = 1/10^6;

temperature for triple pendulum

m1Temp3Pend = 300 K;
m2Temp3Pend = 10K;
m3Temp3Pend = 20K;

g2TempV3Pend = m2Temp3Pend;

Preparation

mass & moment inertia for triple pendulum

m1

mass13Pend = mCube[m1Dens3Pend, m1X3Pend,m1Y3Pend, m1Z3Pend];

iRoll13Pend = mIRollCube[m1Dens3Pend, m1X3Pend,m1Y3Pend, m1Z3Pend];

iPitch13Pend = mIPitchCube[m1Dens3Pend, m1X3Pend,m1Y3Pend, m1Z3Pend];

iYaw13Pend = mIYawCube[m1Dens3Pend, m1X3Pend,m1Y3Pend, m1Z3Pend];

m1

mass23Pend = mCube[m2Dens3Pend, m2X3Pend,m2Y3Pend, m2Z3Pend];

iRoll23Pend = mIRollCube[m2Dens3Pend, m2X3Pend,m2Y3Pend, m2Z3Pend];

iPitch23Pend = mIPitchCube[m2Dens3Pend, m2X3Pend,m2Y3Pend, m2Z3Pend];

iYaw23Pend = mIYawCube[m2Dens3Pend, m2X3Pend,m2Y3Pend, m2Z3Pend];

m3

mass33Pend = mCyl[m3Dens3Pend,m3R3Pend,m3L3Pend];

iRoll33Pend = mILCyl[m3Dens3Pend,m3R3Pend,m3L3Pend];

iPitch33Pend = mIRCyl[m3Dens3Pend,m3R3Pend,m3L3Pend];

iYaw33Pend = mIRCyl[m3Dens3Pend,m3R3Pend,m3L3Pend];

suspension wire for triple pendulum

horizontal

g1HSc3Pend = scPend[mass13Pend+mass23Pend+mass33Pend,g1Length3Pend];
g2HSc3Pend = scPend[mass23Pend+mass33Pend,g2Length3Pend];
g3HSc3Pend = scPend[mass33Pend,lSaPend3Pend];

vertical

g1VSc3Pend = scFreq[mass13Pend+mass23Pend+mass33Pend,g1VFreq3Pend];
g2VSc3Pend = scFreq[mass23Pend+mass33Pend,g2VFreq3Pend];
g3VSc3Pend = numSaPend3Pend*scVert[saYoung,diaSaPend3Pend,lSaPend3Pend];

g10

g10X3Pend = g1HSc3Pend(1 +I g1HPhi3Pend);
g10Y3Pend = g1HSc3Pend(1 +I g1HPhi3Pend);
g10Z3Pend = g1VSc3Pend(1 +I g1VPhi3Pend);

g10XThermal3Pend = g1HSc3Pend(1 +tRoom I g1HPhi3Pend);
g10YThermal3Pend = g1HSc3Pend(1 +tRoom I g1HPhi3Pend);
g10ZThermal3Pend = g1VSc3Pend(1 +tRoom I g1VPhi3Pend);

t10Roll3Pend = tRoll[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,g1HSc3Pend,g1HPhi3Pend,g1VSc3Pend,g1VPhi3Pend];
t10Pitch3Pend = tPitch[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,g1HSc3Pend,g1HPhi3Pend,g1VSc3Pend,g1VPhi3Pend];
t10Yaw3Pend = tYaw[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,g1HSc3Pend,g1HPhi3Pend,g1VSc3Pend,g1VPhi3Pend];

t10RollThermal3Pend = tRoll[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,g1HSc3Pend,tRoom g1HPhi3Pend,g1VSc3Pend,tRoom g1VPhi3Pend];
t10PitchThermal3Pend = tPitch[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,g1HSc3Pend,tRoom g1HPhi3Pend,g1VSc3Pend,tRoom g1VPhi3Pend];
t10YawThermal3Pend = tYaw[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,g1HSc3Pend,tRoom g1HPhi3Pend,g1VSc3Pend,tRoom g1VPhi3Pend];

ct10Roll3Pend = ctRoll[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,pg01X3Pend,pg01Y3Pend,pg01Z3Pend,g1HSc3Pend,g1HPhi3Pend,g1VSc3Pend,g1VPhi3Pend];
ct10Pitch3Pend = ctPitch[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,pg01X3Pend,pg01Y3Pend,pg01Z3Pend,g1HSc3Pend,g1HPhi3Pend,g1VSc3Pend,g1VPhi3Pend];
ct10Yaw3Pend = ctYaw[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,pg01X3Pend,pg01Y3Pend,pg01Z3Pend,g1HSc3Pend,g1HPhi3Pend,g1VSc3Pend,g1VPhi3Pend];

ct10RollThermal3Pend = ctRoll[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,pg01X3Pend,pg01Y3Pend,pg01Z3Pend,g1HSc3Pend,tRoom g1HPhi3Pend,g1VSc3Pend,tRoom g1VPhi3Pend];
ct10PitchThermal3Pend = ctPitch[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,pg01X3Pend,pg01Y3Pend,pg01Z3Pend,g1HSc3Pend,tRoom g1HPhi3Pend,g1VSc3Pend,tRoom g1VPhi3Pend];
ct10YawThermal3Pend = ctYaw[pg10X3Pend,pg10Y3Pend,pg10Z3Pend,pg01X3Pend,pg01Y3Pend,pg01Z3Pend,g1HSc3Pend,tRoom g1HPhi3Pend,g1VSc3Pend,tRoom g1VPhi3Pend];

g12

g12X3Pend = g2HSc3Pend(1 +I g2HPhi3Pend);
g12Y3Pend = g2HSc3Pend(1 +I g2HPhi3Pend);
g12Z3Pend = g2VSc3Pend(1 +I g2VPhi3Pend);

g12XThermal3Pend = g2HSc3Pend(1 +m2Temp3Pend I g2HPhi3Pend);
g12YThermal3Pend = g2HSc3Pend(1 +m2Temp3Pend I g2HPhi3Pend);
g12ZThermal3Pend = g2VSc3Pend(1 +g2TempV3Pend I g2VPhi3Pend);

t12Roll3Pend = tRoll[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];
t12Pitch3Pend = tPitch[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];
t12Yaw3Pend = tYaw[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];

t12RollThermal3Pend = tRoll[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,m2Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];
t12PitchThermal3Pend = tPitch[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,m2Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];
t12YawThermal3Pend = tYaw[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,m2Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];

ct12Roll3Pend = ctRoll[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];
ct12Pitch3Pend = ctPitch[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];
ct12Yaw3Pend = ctYaw[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];

ct12RollThermal3Pend = ctRoll[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,m2Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];
ct12PitchThermal3Pend = ctPitch[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,m2Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];
ct12YawThermal3Pend = ctYaw[pg12X3Pend,pg12Y3Pend,pg12Z3Pend,pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,m2Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];

g21

g21X3Pend = g2HSc3Pend(1 +I g2HPhi3Pend);
g21Y3Pend = g2HSc3Pend(1 +I g2HPhi3Pend);
g21Z3Pend = g2VSc3Pend(1 +I g2VPhi3Pend);

g21XThermal3Pend = g2HSc3Pend(1 +m1Temp3Pend I g2HPhi3Pend);
g21YThermal3Pend = g2HSc3Pend(1 +m1Temp3Pend I g2HPhi3Pend);
g21ZThermal3Pend = g2VSc3Pend(1 +g2TempV3Pend I g2VPhi3Pend);

t21Roll3Pend = tRoll[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];
t21Pitch3Pend = tPitch[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];
t21Yaw3Pend = tYaw[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];

t21RollThermal3Pend = tRoll[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,m1Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];
t21PitchThermal3Pend = tPitch[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,m1Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];
t21YawThermal3Pend = tYaw[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,g2HSc3Pend,m1Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];

ct21Roll3Pend = ctRoll[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];
ct21Pitch3Pend = ctPitch[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];
ct21Yaw3Pend = ctYaw[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,g2HPhi3Pend,g2VSc3Pend,g2VPhi3Pend];

ct21RollThermal3Pend = ctRoll[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,m1Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];
ct21PitchThermal3Pend = ctPitch[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,m1Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];
ct21YawThermal3Pend = ctYaw[pg21X3Pend,pg21Y3Pend,pg21Z3Pend,pg12X3Pend,pg12Y3Pend,pg12Z3Pend,g2HSc3Pend,m1Temp3Pend g2HPhi3Pend,g2VSc3Pend,g2TempV3Pend g2VPhi3Pend];

g23

g23X3Pend = g3HSc3Pend(1 +I g3HPhi3Pend);
g23Y3Pend = g3HSc3Pend(1 +I g3HPhi3Pend);
g23Z3Pend = g3VSc3Pend(1 +I g3VPhi3Pend);

g23XThermal3Pend = g3HSc3Pend(1 +m3Temp3Pend I g3HPhi3Pend);
g23YThermal3Pend = g3HSc3Pend(1 +m3Temp3Pend I g3HPhi3Pend);
g23ZThermal3Pend = g3VSc3Pend(1 +m3Temp3Pend I g3VPhi3Pend);

t23Roll3Pend = tRoll[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];
t23Pitch3Pend = tPitch[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];
t23Yaw3Pend = tYaw[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];

t23RollThermal3Pend = tRoll[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,m3Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];
t23PitchThermal3Pend = tPitch[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,m3Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];
t23YawThermal3Pend = tYaw[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,m3Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];

ct23Roll3Pend = ctRoll[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];
ct23Pitch3Pend = ctPitch[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];
ct23Yaw3Pend = ctYaw[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];

ct23RollThermal3Pend = ctRoll[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,m3Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];
ct23PitchThermal3Pend = ctPitch[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,m3Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];
ct23YawThermal3Pend = ctYaw[pg23X3Pend,pg23Y3Pend,pg23Z3Pend,pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,m3Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];

g32

g32X3Pend = g3HSc3Pend(1 +I g3HPhi3Pend);
g32Y3Pend = g3HSc3Pend(1 +I g3HPhi3Pend);
g32Z3Pend = g3VSc3Pend(1 +I g3VPhi3Pend);

g32XThermal3Pend = g3HSc3Pend(1 +m2Temp3Pend I g3HPhi3Pend);
g32YThermal3Pend = g3HSc3Pend(1 +m2Temp3Pend I g3HPhi3Pend);
g32ZThermal3Pend = g3VSc3Pend(1 +m3Temp3Pend I g3VPhi3Pend);

t32Roll3Pend = tRoll[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];
t32Pitch3Pend = tPitch[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];
t32Yaw3Pend = tYaw[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];

t32RollThermal3Pend = tRoll[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,m2Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];
t32PitchThermal3Pend = tPitch[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,m2Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];
t32YawThermal3Pend = tYaw[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,g3HSc3Pend,m2Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];

ct32Roll3Pend = ctRoll[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];
ct32Pitch3Pend = ctPitch[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];
ct32Yaw3Pend = ctYaw[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,g3HPhi3Pend,g3VSc3Pend,g3VPhi3Pend];

ct32RollThermal3Pend = ctRoll[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,m2Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];
ct32PitchThermal3Pend = ctPitch[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,m2Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];
ct32YawThermal3Pend = ctYaw[pg32X3Pend,pg32Y3Pend,pg32Z3Pend,pg23X3Pend,pg23Y3Pend,pg23Z3Pend,g3HSc3Pend,m2Temp3Pend g3HPhi3Pend,g3VSc3Pend,m3Temp3Pend g3VPhi3Pend];

parameter set for triple pendulum

X - Pitch

parXP3Pend = {f,
mass13Pend,iPitch13Pend,mass23Pend,iPitch23Pend,mass33Pend,iPitch33Pend,
g10X3Pend,g12X3Pend,g21X3Pend,g23X3Pend,g32X3Pend,
t10Pitch3Pend,t12Pitch3Pend,t21Pitch3Pend,t23Pitch3Pend,t32Pitch3Pend,
ct10Pitch3Pend,ct12Pitch3Pend,ct21Pitch3Pend,ct23Pitch3Pend,ct32Pitch3Pend,
pg01Z3Pend,pg10Z3Pend,pg12Z3Pend,pg21Z3Pend,pg23Z3Pend,pg32Z3Pend
}

parXP3PendThermal = {f,
mass13Pend,iPitch13Pend,mass23Pend,iPitch23Pend,mass33Pend,iPitch33Pend,
g10XThermal3Pend,g12XThermal3Pend,g21XThermal3Pend,g23XThermal3Pend,g32XThermal3Pend,
t10PitchThermal3Pend,t12PitchThermal3Pend,t21PitchThermal3Pend,t23PitchThermal3Pend,t32PitchThermal3Pend,
ct10PitchThermal3Pend,ct12PitchThermal3Pend,ct21PitchThermal3Pend,ct23PitchThermal3Pend,ct32PitchThermal3Pend,
pg01Z3Pend,pg10Z3Pend,pg12Z3Pend,pg21Z3Pend,pg23Z3Pend,pg32Z3Pend
}

Y - Roll

parYR3Pend = {f,
mass13Pend,iRoll13Pend,mass23Pend,iRoll23Pend,mass33Pend,iRoll33Pend,
g10Y3Pend,g12Y3Pend,g21Y3Pend,g23Y3Pend,g32Y3Pend,
t10Roll3Pend,t12Roll3Pend,t21Roll3Pend,t23Roll3Pend,t32Roll3Pend,
ct10Roll3Pend,ct12Roll3Pend,ct21Roll3Pend,ct23Roll3Pend,ct32Roll3Pend,
-pg01Z3Pend,-pg10Z3Pend,-pg12Z3Pend,-pg21Z3Pend,-pg23Z3Pend,-pg32Z3Pend
}

parYP3PendThermal = {f,
mass13Pend,iRoll13Pend,mass23Pend,iRoll23Pend,mass33Pend,iRoll33Pend,
g10YThermal3Pend,g12YThermal3Pend,g21YThermal3Pend,g23YThermal3Pend,g32YThermal3Pend,
t10RollThermal3Pend,t12RollThermal3Pend,t21RollThermal3Pend,t23RollThermal3Pend,t32RollThermal3Pend,
ct10RollThermal3Pend,ct12RollThermal3Pend,ct21RollThermal3Pend,ct23RollThermal3Pend,ct32RollThermal3Pend,
-pg01Z3Pend,-pg10Z3Pend,-pg12Z3Pend,-pg21Z3Pend,-pg23Z3Pend,-pg32Z3Pend
}

Z

parZ3Pend = {f,
mass13Pend,mass23Pend,mass33Pend,
g10Z3Pend,g12Z3Pend,g21Z3Pend,g23Z3Pend,g32Z3Pend}

parZ3PendThermal = {f,
mass13Pend,mass23Pend,mass33Pend,
g10ZThermal3Pend,g12ZThermal3Pend,g21ZThermal3Pend,g23ZThermal3Pend,g32ZThermal3Pend}

Yaw

parYaw3Pend = {f,
iYaw13Pend,iYaw23Pend,iYaw33Pend,
t10Yaw3Pend,t12Yaw3Pend,t21Yaw3Pend,t23Yaw3Pend,t32Yaw3Pend,
ct10Yaw3Pend,ct12Yaw3Pend,ct21Yaw3Pend,ct23Yaw3Pend,ct32Yaw3Pend}

parYawThermal3Pend = {f,
iYaw13Pend,iYaw23Pend,iYaw33Pend,
t10YawThermal3Pend,t12YawThermal3Pend,t21YawThermal3Pend,t23YawThermal3Pend,t32YawThermal3Pend,
ct10YawThermal3Pend,ct12YawThermal3Pend,ct21YawThermal3Pend,ct23YawThermal3Pend,ct32YawThermal3Pend}

calculation for single mirror for triple pendulum

X

trfX3Pend[f_] :=trfXY3Pend[2*nItem3Pend-1,f,
mass13Pend,iPitch13Pend,mass23Pend,iPitch23Pend,mass33Pend,iPitch33Pend,
g10X3Pend,g12X3Pend,g21X3Pend,g23X3Pend,g32X3Pend,
t10Pitch3Pend,t12Pitch3Pend,t21Pitch3Pend,t23Pitch3Pend,t32Pitch3Pend,
ct10Pitch3Pend,ct12Pitch3Pend,ct21Pitch3Pend,ct23Pitch3Pend,ct32Pitch3Pend,
pg01Z3Pend,pg10Z3Pend,pg12Z3Pend,pg21Z3Pend,pg23Z3Pend,pg32Z3Pend]

dispXSeis3Pend[f_] := dispXY3Pend[2*nItem3Pend-1,f,
mass13Pend,iPitch13Pend,mass23Pend,iPitch23Pend,mass33Pend,iPitch33Pend,
g10X3Pend,g12X3Pend,g21X3Pend,g23X3Pend,g32X3Pend,
t10Pitch3Pend,t12Pitch3Pend,t21Pitch3Pend,t23Pitch3Pend,t32Pitch3Pend,
ct10Pitch3Pend,ct12Pitch3Pend,ct21Pitch3Pend,ct23Pitch3Pend,ct32Pitch3Pend,
pg01Z3Pend,pg10Z3Pend,pg12Z3Pend,pg21Z3Pend,pg23Z3Pend,pg32Z3Pend]

dispXTNoise3Pend[f_] := tNoiseXY3Pend[2*nItem3Pend-1,f,
mass13Pend,iPitch13Pend,mass23Pend,iPitch23Pend,mass33Pend,iPitch33Pend,
g10XThermal3Pend,g12XThermal3Pend,g21XThermal3Pend,g23XThermal3Pend,g32XThermal3Pend,
t10PitchThermal3Pend,t12PitchThermal3Pend,t21PitchThermal3Pend,t23PitchThermal3Pend,t32PitchThermal3Pend,
ct10PitchThermal3Pend,ct12PitchThermal3Pend,ct21PitchThermal3Pend,ct23PitchThermal3Pend,ct32PitchThermal3Pend,
pg01Z3Pend,pg10Z3Pend,pg12Z3Pend,pg21Z3Pend,pg23Z3Pend,pg32Z3Pend]

Y

trfY3Pend[f_] :=trfXY3Pend[2*nItem3Pend-1,f,
mass13Pend,iRoll13Pend,mass23Pend,iRoll23Pend,mass33Pend,iRoll33Pend,
g10Y3Pend,g12Y3Pend,g21Y3Pend,g23Y3Pend,g32Y3Pend,
t10Roll3Pend,t12Roll3Pend,t21Roll3Pend,t23Roll3Pend,t32Roll3Pend,
ct10Roll3Pend,ct12Roll3Pend,ct21Roll3Pend,ct23Roll3Pend,ct32Roll3Pend,
-pg01Z3Pend,-pg10Z3Pend,-pg12Z3Pend,-pg21Z3Pend,-pg23Z3Pend,-pg32Z3Pend]

dispYSeis3Pend[f_] :=coupleYX3Pend* dispXY3Pend[2*nItem3Pend-1,f,
mass13Pend,iRoll13Pend,mass23Pend,iRoll23Pend,mass33Pend,iRoll33Pend,
g10Y3Pend,g12Y3Pend,g21Y3Pend,g23Y3Pend,g32Y3Pend,
t10Roll3Pend,t12Roll3Pend,t21Roll3Pend,t23Roll3Pend,t32Roll3Pend,
ct10Roll3Pend,ct12Roll3Pend,ct21Roll3Pend,ct23Roll3Pend,ct32Roll3Pend,
-pg01Z3Pend,-pg10Z3Pend,-pg12Z3Pend,-pg21Z3Pend,-pg23Z3Pend,-pg32Z3Pend]

dispYTNoise3Pend[f_] := coupleYX3Pend*tNoiseXY3Pend[2*nItem3Pend-1,f,
mass13Pend,iRoll13Pend,mass23Pend,iRoll23Pend,mass33Pend,iRoll33Pend,
g10YThermal3Pend,g12YThermal3Pend,g21YThermal3Pend,g23YThermal3Pend,g32YThermal3Pend,
t10RollThermal3Pend,t12RollThermal3Pend,t21RollThermal3Pend,t23RollThermal3Pend,t32RollThermal3Pend,
ct10RollThermal3Pend,ct12RollThermal3Pend,ct21RollThermal3Pend,ct23RollThermal3Pend,ct32RollThermal3Pend,
-pg01Z3Pend,-pg10Z3Pend,-pg12Z3Pend,-pg21Z3Pend,-pg23Z3Pend,-pg32Z3Pend]

Z

trfZ3Pend[f_] := trfZ3Pend[nItem3Pend,f,
mass13Pend,mass23Pend,mass33Pend,
g10Z3Pend,g12Z3Pend,g21Z3Pend,g23Z3Pend,g32Z3Pend]

dispZSeis3Pend[f_] := coupleZX3Pend*dispZ3Pend[nItem3Pend,f,
mass13Pend,mass23Pend,mass33Pend,
g10Z3Pend,g12Z3Pend,g21Z3Pend,g23Z3Pend,g32Z3Pend]

dispZTNoise3Pend[f_] := coupleZX3Pend*tNoiseZ3Pend[nItem3Pend,f,
mass13Pend,mass23Pend,mass33Pend,
g10ZThermal3Pend,g12ZThermal3Pend,g21ZThermal3Pend,g23ZThermal3Pend,g32ZThermal3Pend]

Roll

trfRoll3Pend[f_] :=trfPR3Pend[2*nItem3Pend,f,
mass13Pend,iRoll13Pend,mass23Pend,iRoll23Pend,mass33Pend,iRoll33Pend,
g10Y3Pend,g12Y3Pend,g21Y3Pend,g23Y3Pend,g32Y3Pend,
t10Roll3Pend,t12Roll3Pend,t21Roll3Pend,t23Roll3Pend,t32Roll3Pend,
ct10Roll3Pend,ct12Roll3Pend,ct21Roll3Pend,ct23Roll3Pend,ct32Roll3Pend,
-pg01Z3Pend,-pg10Z3Pend,-pg12Z3Pend,-pg21Z3Pend,-pg23Z3Pend,-pg32Z3Pend]

dispRollSeis3Pend[f_] := dispPR3Pend[offsetRoll3Pend,2*nItem3Pend,f,
mass13Pend,iRoll13Pend,mass23Pend,iRoll23Pend,mass33Pend,iRoll33Pend,
g10Y3Pend,g12Y3Pend,g21Y3Pend,g23Y3Pend,g32Y3Pend,
t10Roll3Pend,t12Roll3Pend,t21Roll3Pend,t23Roll3Pend,t32Roll3Pend,
ct10Roll3Pend,ct12Roll3Pend,ct21Roll3Pend,ct23Roll3Pend,ct32Roll3Pend,
-pg01Z3Pend,-pg10Z3Pend,-pg12Z3Pend,-pg21Z3Pend,-pg23Z3Pend,-pg32Z3Pend]

dispRollTNoise3Pend[f_] := tNoisePR3Pend[offsetRoll3Pend,2*nItem3Pend,f,
mass13Pend,iRoll13Pend,mass23Pend,iRoll23Pend,mass33Pend,iRoll33Pend,
g10YThermal3Pend,g12YThermal3Pend,g21YThermal3Pend,g23YThermal3Pend,g32YThermal3Pend,
t10RollThermal3Pend,t12RollThermal3Pend,t21RollThermal3Pend,t23RollThermal3Pend,t32RollThermal3Pend,
ct10RollThermal3Pend,ct12RollThermal3Pend,ct21RollThermal3Pend,ct23RollThermal3Pend,ct32RollThermal3Pend,
-pg01Z3Pend,-pg10Z3Pend,-pg12Z3Pend,-pg21Z3Pend,-pg23Z3Pend,-pg32Z3Pend]

Pitch

trfPitch3Pend[f_] :=trfPR3Pend[2*nItem3Pend,f,
mass13Pend,iPitch13Pend,mass23Pend,iPitch23Pend,mass33Pend,iPitch33Pend,
g10X3Pend,g12X3Pend,g21X3Pend,g23X3Pend,g32X3Pend,
t10Pitch3Pend,t12Pitch3Pend,t21Pitch3Pend,t23Pitch3Pend,t32Pitch3Pend,
ct10Pitch3Pend,ct12Pitch3Pend,ct21Pitch3Pend,ct23Pitch3Pend,ct32Pitch3Pend,
pg01Z3Pend,pg10Z3Pend,pg12Z3Pend,pg21Z3Pend,pg23Z3Pend,pg32Z3Pend]

dispPitchSeis3Pend[f_] := dispPR3Pend[offsetPitch3Pend,2*nItem3Pend,f,
mass13Pend,iPitch13Pend,mass23Pend,iPitch23Pend,mass33Pend,iPitch33Pend,
g10X3Pend,g12X3Pend,g21X3Pend,g23X3Pend,g32X3Pend,
t10Pitch3Pend,t12Pitch3Pend,t21Pitch3Pend,t23Pitch3Pend,t32Pitch3Pend,
ct10Pitch3Pend,ct12Pitch3Pend,ct21Pitch3Pend,ct23Pitch3Pend,ct32Pitch3Pend,
pg01Z3Pend,pg10Z3Pend,pg12Z3Pend,pg21Z3Pend,pg23Z3Pend,pg32Z3Pend]

dispPitchTNoise3Pend[f_] := tNoisePR3Pend[offsetPitch3Pend,2*nItem3Pend,f,
mass13Pend,iPitch13Pend,mass23Pend,iPitch23Pend,mass33Pend,iPitch33Pend,
g10XThermal3Pend,g12XThermal3Pend,g21XThermal3Pend,g23XThermal3Pend,g32XThermal3Pend,
t10PitchThermal3Pend,t12PitchThermal3Pend,t21PitchThermal3Pend,t23PitchThermal3Pend,t32PitchThermal3Pend,
ct10PitchThermal3Pend,ct12PitchThermal3Pend,ct21PitchThermal3Pend,ct23PitchThermal3Pend,ct32PitchThermal3Pend,
pg01Z3Pend,pg10Z3Pend,pg12Z3Pend,pg21Z3Pend,pg23Z3Pend,pg32Z3Pend]

Yaw

trfYaw3Pend[f_] := trfYaw3Pend[nItem3Pend,f,
iYaw13Pend,iYaw23Pend,iYaw33Pend,
t10Yaw3Pend,t12Yaw3Pend,t21Yaw3Pend,t23Yaw3Pend,t32Yaw3Pend,
ct10Yaw3Pend,ct12Yaw3Pend,ct21Yaw3Pend,ct23Yaw3Pend,ct32Yaw3Pend]

dispYawSeis3Pend[f_] := dispYaw3Pend[offsetYaw3Pend,nItem3Pend,f,
iYaw13Pend,iYaw23Pend,iYaw33Pend,
t10Yaw3Pend,t12Yaw3Pend,t21Yaw3Pend,t23Yaw3Pend,t32Yaw3Pend,
ct10Yaw3Pend,ct12Yaw3Pend,ct21Yaw3Pend,ct23Yaw3Pend,ct32Yaw3Pend]

dispYawTNoise3Pend[f_] := tNoiseYaw3Pend[offsetYaw3Pend,nItem3Pend,
f,
iYaw13Pend,iYaw23Pend,iYaw33Pend,
t10YawThermal3Pend,t12YawThermal3Pend,t21YawThermal3Pend,t23YawThermal3Pend,t32YawThermal3Pend,
ct10YawThermal3Pend,ct12YawThermal3Pend,ct21YawThermal3Pend,ct23YawThermal3Pend,ct32YawThermal3Pend]

Results

X - Pitch

Q & resonant frequency

resXP3Pend=f  /. NSolve[Det[matXPYR3Pend[f,
mass13Pend,iPitch13Pend,mass23Pend,iPitch23Pend,mass33Pend,iPitch33Pend,
g10X3Pend,g12X3Pend,g21X3Pend,g23X3Pend,g32X3Pend,
t10Pitch3Pend,t12Pitch3Pend,t21Pitch3Pend,t23Pitch3Pend,t32Pitch3Pend,
ct10Pitch3Pend,ct12Pitch3Pend,ct21Pitch3Pend,ct23Pitch3Pend,ct32Pitch3Pend,
pg01Z3Pend,pg10Z3Pend,pg12Z3Pend,pg21Z3Pend,pg23Z3Pend,pg32Z3Pend]]==0,f];

Sort[resXP3Pend/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

TRF plot

LogLogPlot[{trfX3Pend[f]},{f,0.1,50}]

LogLogPlot[{trfPitch3Pend[f]},{f,1,300}]

displacement

LogLogPlot[{dispXSeis3Pend[f],dispXTNoise3Pend[f]},{f,0.1,10}]

LogLogPlot[{dispPitchSeis3Pend[f],dispPitchTNoise3Pend[f]},{f,0.1,400}]

Y - Roll

Q & resonant frequency

resYR3Pend=f  /. NSolve[Det[matXPYR3Pend[f,
mass13Pend,iRoll13Pend,mass23Pend,iRoll23Pend,mass33Pend,iRoll33Pend,
g10Y3Pend,g12Y3Pend,g21Y3Pend,g23Y3Pend,g32Y3Pend,
t10Roll3Pend,t12Roll3Pend,t21Roll3Pend,t23Roll3Pend,t32Roll3Pend,
ct10Roll3Pend,ct12Roll3Pend,ct21Roll3Pend,ct23Roll3Pend,ct32Roll3Pend,
-pg01Z3Pend,-pg10Z3Pend,-pg12Z3Pend,-pg21Z3Pend,-pg23Z3Pend,-pg32Z3Pend]]==0,f];

Sort[resYR3Pend/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

TRF plot

LogLogPlot[{trfY3Pend[f]},{f,0.01,10}]

LogLogPlot[{trfRoll3Pend[f]},{f,0.01,10}]

displacement

LogLogPlot[{dispYSeis3Pend[f],dispYTNoise3Pend[f]},{f,0.1,10}]

Z

Q & resonant frequency

resZ3Pend=f  /. NSolve[Det[matZ3Pend[f,
mass13Pend,mass23Pend,mass33Pend,
g10Z3Pend,g12Z3Pend,g21Z3Pend,g23Z3Pend,g32Z3Pend]]==0,f];

Sort[resZ3Pend/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

TRF plot

LogLogPlot[{trfZ3Pend[f]},{f,1,30}]

displacement

LogLogPlot[{dispZSeis3Pend[f],dispZTNoise3Pend[f]},{f,1,30}]

LogLogPlot[{dispZSeis3Pend[f],dispZTNoise3Pend[f]},{f,10,2000}]

Yaw

Q & resonant frequency

resYaw3Pend=f  /. NSolve[Det[matYaw3Pend[f,
iYaw13Pend,iYaw23Pend,iYaw33Pend,
t10Yaw3Pend,t12Yaw3Pend,t21Yaw3Pend,t23Yaw3Pend,t32Yaw3Pend,
ct10Yaw3Pend,ct12Yaw3Pend,ct21Yaw3Pend,ct23Yaw3Pend,ct32Yaw3Pend]]==0,f];

Sort[resYaw3Pend/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

TRF plot

LogLogPlot[{trfYaw3Pend[f]},{f,.1,5}]

displacement

LogLogPlot[{dispYawSeis3Pend[f],dispYawTNoise3Pend[f]},{f,0.1,5}]

seismic noise

dispParallel3Pend[f_]:= Sqrt[4*(dispXSeis3Pend[f]^2+dispYSeis3Pend[f]^2+dispZSeis3Pend[f]^2)]; (*4 mirrors displacement in parallel motion.*)

dispRotation3Pend[f_] :=Sqrt[4*(dispRollSeis3Pend[f]^2+dispPitchSeis3Pend[f]^2+dispYawSeis3Pend[f]^2)]

dispSeis3Pend[f_] := Sqrt[dispParallel3Pend[f]^2+dispRotation3Pend[f]^2]

hDispSeis3Pend[f_] := Sqrt[dispParallel3Pend[f]^2+dispRotation3Pend[f]^2]/l

dispSeisModel3Pend[f_] := 2*seisK[f]*10^(-3)/f^10

hDispSeisModel3Pend[f_] := dispSeisModel3Pend[f]/l3Pend

suspension thermal noise (without violin mode)

tNoiseParallel3Pend[f_]:=Sqrt[4*(dispXTNoise3Pend[f]^2+dispYTNoise3Pend[f]^2+dispZTNoise3Pend[f]^2)]

tNoiseRotation3Pend[f_]:=Sqrt[4*(dispRollTNoise3Pend[f]^2+dispPitchTNoise3Pend[f]^2+dispYawTNoise3Pend[f]^2)]

dispSTNoise3Pend [f_] :=Sqrt[tNoiseParallel3Pend[f]^2+tNoiseRotation3Pend[f]^2]

hDispSTNoise3Pend [f_] :=Sqrt[tNoiseParallel3Pend[f]^2+tNoiseRotation3Pend[f]^2]/l3Pend

Read out noise

Laser

lambda=1064*10^(-9);(* wavelength (m) *)

p3Pend = 500 W ;(*effective laser power at BS [W]*)

cavity

l3Pend=3000 m;(* length of cavity (m) *)
finesse3Pend=1250;(* finesse of cavity *)
tau3Pend=sTime[l3Pend,finesse3Pend];(* storage time of cavity (sec) *)
fcut3Pend=fCut[l3Pend,finesse3Pend];(* cut-off frequency of cavity (Hz) *)
R23Pend=150;(* curvature of end mirror (m) *)
g13Pend=1;
g23Pend=1-l/R23Pend;
w13Pend=Sqrt[l3Pend*lambda/Pi/Abs[g13Pend]*Sqrt[g13Pend*g23Pend/(1-g13Pend*g23Pend)]];(* beam radius at front mirror (m) *)
w23Pend=Sqrt[l3Pend*lambda/Pi/Abs[g23Pend]*Sqrt[g13Pend*g23Pend/(1-g13Pend*g23Pend)]];(* beam radius at end mirror (m) *)
StringForm["beam radius at front mirror is `` mm",NumberForm[N[w13Pend]*1000,3]]
StringForm["beam radius at end mirror is `` mm",NumberForm[N[w23Pend]*1000,3]]
StringForm["storage time of cavity is `` msec",NumberForm[tau3Pend*1000,3]]
StringForm["cut-off frequency of cavity is `` Hz",NumberForm[fcut3Pend,3]]

shot noise

hShot3Pend[f_] :=hshot[f,p3Pend,tau3Pend]

shot3Pend[f_] := hShot3Pend[f]*l3Pend

radiation pressure noise

hRadia3Pend[f_] :=hradia[f,p3Pend,fcut3Pend,l3Pend,finesse3Pend,mass33Pend]

radia3Pend[f_] :=hRadia3Pend[f]*l3Pend

Mirror thermal noise

Coating

dcoa3Pend=7.5*10^(-6);(* thickness of coating (m) *)

phicoa3Pend=4*10^(-4);(* loss angle of coating*)

noises in cryogenic

thCoat203Pend[f_] := mirrorcoa[f,20 K,dcoa3Pend,phicoa3Pend,w13Pend,w23Pend,saYoung]

thMassStrucure203Pend[f_] := mirrorhomo[f,20 K,saPoisson,1/saQMass20,w13Pend,w23Pend,saYoung]

thElastic203Pend[f_] := Sqrt[2*(thelastic[f,20 K,saAlpha20,saPoisson,saKappa20,saSpHeat20,w13Pend]+thelastic[f,20 K,saAlpha20,saPoisson,saKappa20,saSpHeat20,w23Pend])]

dispThMass203Pend[f_] := Sqrt[thCoat203Pend[f]^2+thMassStrucure203Pend[f]^2+thElastic203Pend[f]^2]

hDispThMass203Pend[f_] := Sqrt[thCoat203Pend[f]^2+thMassStrucure203Pend[f]^2+thElastic203Pend[f]^2]/l3Pend

sum up

disp3Pend[f_] := Sqrt[dispSeis3Pend[f]^2+dispSTNoise3Pend[f]^2+shot3Pend[f]^2+radia3Pend[f]^2+dispThMass203Pend[f]^2]

dispModel3Pend[f_] := Sqrt[dispSeisModel3Pend[f]^2+shot3Pend[f]^2+radia3Pend[f]^2+dispThMass203Pend[f]^2]

hDisp3Pend[f_] := dispModel3Pend[f]/l3Pend

Plots

seminar

plot3Pend0 =LogLogPlot[{dispSTNoise3Pend[f]},
{f,0.1,3},
PlotRange-> All,PlotStyle -> {RGBColor[0,0,1]}]

plot3Pend1 =LogLogPlot[{dispModel3Pend[f],dispSTNoise3Pend[f]},
{f,3,30},
PlotRange-> All,PlotStyle -> {RGBColor[1,0,0],RGBColor[0,0,1]}]

plot3Pend2 =LogLogPlot[{dispModel3Pend[f],dispSTNoise3Pend[f]},
{f,30,300},
PlotRange-> All,PlotStyle -> {RGBColor[1,0,0],RGBColor[0,0,1]}]

Show[plot3Pend1,plot3Pend2,PlotRange -> All]

plot3Pend3 =LogLogPlot[{dispXTNoise3Pend[f],dispYTNoise3Pend[f],dispZTNoise3Pend[f],dispPitchTNoise3Pend[f],dispYawTNoise3Pend[f]},
{f,0.2,3},
PlotRange-> All,PlotStyle -> {RGBColor[0,1,0],RGBColor[0,1,1],RGBColor[1,0,1],RGBColor[1,1,0],RGBColor[0,0.5,1]}]

plot3Pend4 =LogLogPlot[{dispXTNoise3Pend[f],dispYTNoise3Pend[f],dispZTNoise3Pend[f],dispPitchTNoise3Pend[f],dispYawTNoise3Pend[f]},
{f,3,30},
PlotRange-> All,PlotStyle -> {RGBColor[0,1,0],RGBColor[0,1,1],RGBColor[1,0,1],RGBColor[1,1,0],RGBColor[0,0.5,1]}]

plot3Pend5 =LogLogPlot[{dispXTNoise3Pend[f],dispYTNoise3Pend[f],dispZTNoise3Pend[f],dispPitchTNoise3Pend[f],dispYawTNoise3Pend[f]},
{f,30,300},
PlotRange-> All,PlotStyle -> {RGBColor[0,1,0],RGBColor[0,1,1],RGBColor[1,0,1],RGBColor[1,1,0],RGBColor[0,0.5,1]}]

Show[plot3Pend1,plot3Pend2,plot3Pend4,plot3Pend5,PlotRange -> All]

plot3Pend6 =LogLogPlot[{dispZTNoise3Pend[f]},
{f,1,30},
PlotRange-> All,PlotStyle -> {RGBColor[0,1,0]}](*g1 only*)

plot3Pend7 =LogLogPlot[{dispZTNoise3Pend[f]},
{f,30,300},
PlotRange-> All,PlotStyle -> {RGBColor[0,1,0]}](*g1 only*)

plot3Pend8 =LogLogPlot[{dispZTNoise3Pend[f]},
{f,1,30},
PlotRange-> All,PlotStyle -> {RGBColor[1,1,0]}](*g2 only*)

plot3Pend9 =LogLogPlot[{dispZTNoise3Pend[f]},
{f,30,300},
PlotRange-> All,PlotStyle -> {RGBColor[1,1,0]}](*g2 only*)

plot3Pend10 =LogLogPlot[{dispZTNoise3Pend[f]},
{f,1,30},
PlotRange-> All,PlotStyle -> {RGBColor[0,1,1]}](*g3 only*)

plot3Pend11 =LogLogPlot[{dispZTNoise3Pend[f]},
{f,30,300},
PlotRange-> All,PlotStyle -> {RGBColor[0,1,1]}](*g3 only*)

Show[plot3Pend1,plot3Pend2,plot3Pend6,plot3Pend7,plot3Pend8,plot3Pend9,plot3Pend10,plot3Pend11,PlotRange -> All]

plot3Pend12 =LogLogPlot[{dispZTNoise3Pend[f]},
{f,0.03,30},
PlotRange-> All,PlotStyle -> {RGBColor[1,0.5,0]}](*g1 only*)

plot3Pend13 =LogLogPlot[{dispZTNoise3Pend[f]},
{f,30,300},
PlotRange-> All,PlotStyle -> {RGBColor[1,0.5,0]}](*g1 only*)

Show[plot3Pend1,plot3Pend2,plot3Pend6,plot3Pend7,plot3Pend12,plot3Pend13,PlotRange -> All]

plot3Pend14 =LogLogPlot[{dispZTNoise3Pend[f]},
{f,0.03,30},
PlotRange-> All,PlotStyle -> {RGBColor[1,0,0.5]}](*g3 only*)

plot3Pend15 =LogLogPlot[{dispZTNoise3Pend[f]},
{f,30,300},
PlotRange-> All,PlotStyle -> {RGBColor[1,0,0.5]}](*g3 only*)

Show[plot3Pend1,plot3Pend2,plot3Pend10,plot3Pend11,plot3Pend14,plot3Pend15,PlotRange -> All]

plot3Pend16 =LogLogPlot[{dispSTNoise3Pend[f]},
{f,0.1,3},
PlotRange-> All,PlotStyle -> {RGBColor[0,1,0]}]

plot3Pend17 =LogLogPlot[{dispSTNoise3Pend[f]},
{f,3,30},
PlotRange-> All,PlotStyle -> {RGBColor[0,1,0]}]

plot3Pend18 =LogLogPlot[{dispSTNoise3Pend[f]},
{f,30,300},
PlotRange-> All,PlotStyle -> {RGBColor[0,1,0]}]

Show[plot3Pend1,plot3Pend2,plot3Pend0,plot3Pend16,plot3Pend17,plot3Pend18,PlotRange -> All]

LISM (OLD)

Parameters

intersting item

nItemLISM = 4 ;
(*m1 ~ m3 -> 1 ~ 3,
Final mass = 3.*)

coupling & vibration amplification in cryostat

coupleZXLISM = 3/100;(*coupling Z -> X*)
coupleYXLISM = 10/100;(*coupling Y -> X*)

dimensions of mass for triple pendulum

m1

m1DensLISM = alDens;
m1XLISM = 100mm;
m1YLISM = 100 mm;
m1ZLISM = 50 mm;
mCube[m1DensLISM,m1XLISM,m1YLISM,m1ZLISM]

m2

m2DensLISM = alDens;
m2XLISM = 10mm;
m2YLISM = 10 mm;
m2ZLISM = 10 mm;
mCube[m2DensLISM,m2XLISM,m2YLISM,m2ZLISM]

m3

m3DensLISM = alDens;
m3XLISM = 10mm;
m3YLISM = 10 mm;
m3ZLISM = 10 mm;
mCube[m3DensLISM,m3XLISM,m3YLISM,m3ZLISM]

m4

m4DensLISM = saDens/2;
m4RLISM = 100/2mm;
m4LLISM = 60 mm;
mCyl[m4DensLISM,m4RLISM,m4LLISM]

spring for triple pendulum

g1

g1LengthLISM = 0.25m;
g1VFreqLISM = 7 Hz;

g2

g2LengthLISM =0.1m;

g3

g3LengthLISM =0.05m;
g3VFreqLISM = 5Hz;

final suspension

numg4LISM = 4;
diag4LISM = 0.1 mm;
g4LengthLISM = 0.1m;

dissipation for triple pendulum

in spring

g1HPhiLISM = 1/10^5;
g1VPhiLISM =0 1/10^3;

g2HPhiLISM = 1/10^5;
g2VPhiLISM =  0 1/10^3;

g3HPhiLISM = 1/10^4;
g3VPhiLISM = 1/10^2;

g4HPhiLISM = 1/10^5;
g4VPhiLISM = 1/10^3;

temperature for triple pendulum

m1TempLISM = 300 K;
m2TempLISM = 300K;
m3TempLISM = 300K;
m4TempLISM = 300K;

g2TempV3Pend = m2Temp3Pend;

Preparation

mass & moment inertia for LISM pendulum

m1

mass1LISM = mCube[m1DensLISM, m1XLISM,m1YLISM, m1ZLISM];

m2

mass2LISM =4* mCube[m2DensLISM, m2XLISM,m2YLISM, m2ZLISM];

m3

mass3LISM = 4*mCube[m3DensLISM, m3XLISM,m3YLISM, m3ZLISM];

m4

mass4LISM = mCyl[m4DensLISM,m4RLISM,m4LLISM];

suspension wire for LISM pendulum

horizontal

g1HScLISM = scPend[mass1LISM+mass2LISM+mass3LISM+mass4LISM,g1LengthLISM];
g2HScLISM = scPend[mass2LISM+mass3LISM+mass4LISM,g2LengthLISM];
g3HScLISM = scPend[mass3LISM+mass4LISM,g3LengthLISM];
g4HScLISM = scPend[mass4LISM,g4LengthLISM];

vertical

g1VScLISM = scFreq[mass1LISM+mass2LISM+mass3LISM,g1VFreqLISM];
g3VScLISM = scFreq[mass3LISM+mass4LISM,g3VFreqLISM];
g2VScLISM = numg4LISM*scVert[tunYoung,diag4LISM,g2LengthLISM];
g4VScLISM = numg4LISM*scVert[tunYoung,diag4LISM,g4LengthLISM];

g10

g10XLISM = g1HScLISM(1 +I g1HPhiLISM);
g10YLISM = g1HScLISM(1 +I g1HPhiLISM);
g10ZLISM = g1VScLISM(1 +I g1VPhiLISM);

g10XThermalLISM = g1HScLISM(1 +tRoom I g1HPhiLISM);
g10YThermalLISM = g1HScLISM(1 +tRoom I g1HPhiLISM);
g10ZThermalLISM = g1VScLISM(1 +tRoom I g1VPhiLISM);

g12

g12XLISM = g2HScLISM(1 +I g2HPhiLISM);
g12YLISM = g2HScLISM(1 +I g2HPhiLISM);
g12ZLISM = g2VScLISM(1 +I g2VPhiLISM);

g12XThermalLISM = g2HScLISM(1 +m2TempLISM I g2HPhiLISM);
g12YThermalLISM = g2HScLISM(1 +m2TempLISM I g2HPhiLISM);
g12ZThermalLISM = g2VScLISM(1 +g2TempVLISM I g2VPhiLISM);

g21

g21XLISM = g2HScLISM(1 +I g2HPhiLISM);
g21YLISM = g2HScLISM(1 +I g2HPhiLISM);
g21ZLISM = g2VScLISM(1 +I g2VPhiLISM);

g21XThermalLISM = g2HScLISM(1 +m1TempLISM I g2HPhiLISM);
g21YThermalLISM = g2HScLISM(1 +m1TempLISM I g2HPhiLISM);
g21ZThermalLISM = g2VScLISM(1 +g2TempVLISM I g2VPhiLISM);

g23

g23XLISM = g3HScLISM(1 +I g3HPhiLISM);
g23YLISM = g3HScLISM(1 +I g3HPhiLISM);
g23ZLISM = g3VScLISM(1 +I g3VPhiLISM);

g23XThermalLISM = g3HScLISM(1 +m3TempLISM I g3HPhiLISM);
g23YThermalLISM = g3HScLISM(1 +m3TempLISM I g3HPhiLISM);
g23ZThermalLISM = g3VScLISM(1 +m3TempLISM I g3VPhiLISM);

g32

g32XLISM = g3HScLISM(1 +I g3HPhiLISM);
g32YLISM = g3HScLISM(1 +I g3HPhiLISM);
g32ZLISM = g3VScLISM(1 +I g3VPhiLISM);

g32XThermalLISM = g3HScLISM(1 +m2TempLISM I g3HPhiLISM);
g32YThermalLISM = g3HScLISM(1 +m2TempLISM I g3HPhiLISM);
g32ZThermalLISM = g3VScLISM(1 +m2TempLISM I g3VPhiLISM);

g34

g34XLISM = g4HScLISM(1 +I g4HPhiLISM);
g34YLISM = g4HScLISM(1 +I g4HPhiLISM);
g34ZLISM = g4VScLISM(1 +I g4VPhiLISM);

g34XThermalLISM = g4HScLISM(1 +m4TempLISM I g4HPhiLISM);
g34YThermalLISM = g4HScLISM(1 +m4TempLISM I g4HPhiLISM);
g34ZThermalLISM = g4VScLISM(1 +m4TempLISM I g4VPhiLISM);

g43

g43XLISM = g4HScLISM(1 +I g4HPhiLISM);
g43YLISM = g4HScLISM(1 +I g4HPhiLISM);
g43ZLISM = g4VScLISM(1 +I g4VPhiLISM);

g43XThermalLISM = g4HScLISM(1 +m3TempLISM I g4HPhiLISM);
g43YThermalLISM = g4HScLISM(1 +m3TempLISM I g4HPhiLISM);
g43ZThermalLISM = g4VScLISM(1 +m3TempLISM I g4VPhiLISM);

parameter set for LISM pendulum

Z

parZ3LISM = {f,
mass1LISM,mass2LISM,mass3LISM,mass4LISM,
g10ZLISM,g12ZLISM,g21ZLISM,g23ZLISM,g32ZLISM,g34ZLISM,g43ZLISM}

parZ3LISMThermal = {f,
mass1LISM,mass2LISM,mass3LISM,mass4LISM,
g10ZThermalLISM,g12ZThermalLISM,g21ZThermalLISM,g23ZThermalLISM,g32ZThermalLISM,g34ZThermalLISM,g43ZThermalLISM}

calculation for single mirror for triple pendulum

Z

trfZLISM[f_] := trfZYLISM[nItemLISM,f,
mass1LISM,mass2LISM,mass3LISM,mass4LISM,
g10ZLISM,g12ZLISM,g21ZLISM,g23ZLISM,g32ZLISM,g34ZLISM,g43ZLISM]

dispZSeisLISM[f_] := coupleZXLISM*dispZLISM[nItemLISM,f,
mass1LISM,mass2LISM,mass3LISM,mass4LISM,
g10ZLISM,g12ZLISM,g21ZLISM,g23ZLISM,g32ZLISM,g34ZLISM,g43ZLISM]

dispZTNoiseLISM[f_] := coupleZXLISM*tNoiseZLISM[nItemLISM,f,
mass1LISM,mass2LISM,mass3LISM,mass4LISM,
g10ZThermalLISM,g12ZThermalLISM,g21ZThermalLISM,g23ZThermalLISM,g32ZThermalLISM,g34ZThermalLISM,g43ZThermalLISM]

Plots

plotLISM1 =LogLogPlot[{dispZSeisLISM[f],dispZTNoiseLISM[f]},{f,0.1,30}]

plotLISM2 =LogLogPlot[{dispZSeisLISM[f],dispZTNoiseLISM[f]},{f,30,300}]

plotLISM3 =LogLogPlot[{dispZSeisLISM[f],dispZTNoiseLISM[f]},{f,300,1000}]

Show[plotLISM1,plotLISM2,plotLISM3,plotLISM030214,PlotRange -> All]

Single pendulum

Parameters

intersting item

nItemsingle = 1 ;

coupling

coupleZXsingle =3/100;(*coupling Z -> X*)
coupleYXsingle = 10/100;(*coupling Y -> X*)

offset of beam centering

offsetRollsingle = 0 mm;
offsetPitchsingle = 0.1 mm;
offsetYawsingle = 0.1 mm;

dimensions of mass for single pendulum

m1 (CUBE)

(*m1Denssingle = alDens;
m1Xsingle = 100mm;
m1Ysingle = 100 mm;
m1Zsingle = 70 mm;
mCube[m1Denssingle,m1Xsingle,m1Ysingle,m1Zsingle]*)

m1 (Mirror)

m1Denssingle = fsDens;
m1rsingle = 250 mm/2;
m1lsingle = 100 mm;
mCyl[m1Denssingle,m1rsingle,m1lsingle]

spring for single pendulum

g1

(*g1Lengthsingle = lSaPend;
g1Youngsingle = saYoung;
g1Diasingle = diaSaPend;
g1Numsingle = numSaPend;*)

g1Lengthsingle = 460 mm;
g1Youngsingle = pwYoung;
g1Diasingle = 0.3 mm;
g1Numsingle = 2;

position of wire clamp from COM (4 wires + symmetrical distribution) for single pendulum

suspension wires

pg01Xsingle = 0 mm;
pg01Ysingle = 150 mm/2;
pg01Zsingle = +0 mm;
pg01dXsingle = 0.1 mm*10;
pg01dYsingle = 0.1 mm*10;
pg01dZsingle = 0.1 mm*10;

pg10Xsingle = pg01Xsingle;
pg10Ysingle = 250 mm/2 ;
pg10Zsingle = 10 mm;
pg10dXsingle = 0.1 mm*10;
pg10dYsingle = 0.1 mm*10;
pg10dZsingle = 0.1 mm*10;

dissipation for single pendulum

in spring

dDTSingle = (g1Numsingle√(mCyl[m1Denssingle,m1rsingle,m1lsingle] gaccel/g1Numsingle g1Youngsingle (Pi g1Diasingle^4/64))/(2 g1Lengthsingle^2) )/(mCyl[m1Denssingle,m1rsingle,m1lsingle] gaccel/g1Lengthsingle)

g1HPhisingle = 1/(3*10^5);
g1VPhisingle =g1HPhisingle/dDTSingle

1/g1VPhisingle

temperature for single pendulum

g1Tempsingle = 20 K+280 K;

Preparation

coupling matrix

coupleMatsingle=(({{1}, {coupleYXsingle}, {coupleZXsingle}, {offsetRollsingle}, {offsetPitchsingle}, {offsetYawsingle}}));

mass & moment inertia for single pendulum

m1(CUBE)

(*mass1single = mCube[m1Denssingle, m1Xsingle,m1Ysingle, m1Zsingle]; 
iRoll1single = mIRollCube[m1Denssingle, m1Xsingle,m1Ysingle, m1Zsingle];
iPitch1single = mIPitchCube[m1Denssingle, m1Xsingle,m1Ysingle, m1Zsingle];
iYaw1single = mIYawCube[m1Denssingle, m1Xsingle,m1Ysingle, m1Zsingle];*)

m1(mirror)

mass1single = mCyl[m1Denssingle,m1rsingle,m1lsingle]; 
iRoll1single = mILCyl[m1Denssingle,m1rsingle,m1lsingle];
iPitch1single = mIRCyl[m1Denssingle,m1rsingle,m1lsingle];
iYaw1single = mIRCyl[m1Denssingle,m1rsingle,m1lsingle];

suspension wire for single pendulum

horizontal

g1HScsingle = scPend[mass1single,g1Lengthsingle];

vertical

g1VScsingle = g1Numsingle*scVert[g1Youngsingle,g1Diasingle,g1Lengthsingle];

g10

g10Hsingle = g1HScsingle(1 +I g1HPhisingle);
g10Vsingle = g1VScsingle(1 +I g1VPhisingle);

g10HThermalsingle = g1HScsingle(1 +g1Tempsingle I g1HPhisingle);
g10VThermalsingle = g1VScsingle(1 +g1Tempsingle I g1VPhisingle);

t10Rollsingle = ctRoll[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg10Xsingle,pg10Ysingle,pg10Zsingle,g1HScsingle,g1HPhisingle,g1VScsingle,g1VPhisingle];
t10Pitchsingle = ctPitch[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg10Xsingle,pg10Ysingle,pg10Zsingle,g1HScsingle,g1HPhisingle,g1VScsingle,g1VPhisingle];
t10Yawsingle = ctYaw[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg10Xsingle,pg10Ysingle,pg10Zsingle,g1HScsingle,g1HPhisingle,g1VScsingle,g1VPhisingle];

t10RollThermalsingle = ctRoll[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg10Xsingle,pg10Ysingle,pg10Zsingle,g1HScsingle,g1Tempsingle g1HPhisingle,g1VScsingle,g1Tempsingle g1VPhisingle];
t10PitchThermalsingle = ctPitch[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg10Xsingle,pg10Ysingle,pg10Zsingle,g1HScsingle,g1Tempsingle g1HPhisingle,g1VScsingle,g1Tempsingle g1VPhisingle];
t10YawThermalsingle = ctYaw[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg10Xsingle,pg10Ysingle,pg10Zsingle,g1HScsingle,g1Tempsingle g1HPhisingle,g1VScsingle,g1Tempsingle g1VPhisingle];

ct10Rollsingle = ctRoll[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg01Xsingle,pg01Ysingle,pg01Zsingle,g1HScsingle,g1HPhisingle,g1VScsingle,g1VPhisingle];
ct10Pitchsingle = ctPitch[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg01Xsingle,pg01Ysingle,pg01Zsingle,g1HScsingle,g1HPhisingle,g1VScsingle,g1VPhisingle];
ct10Yawsingle = ctYaw[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg01Xsingle,pg01Ysingle,pg01Zsingle,g1HScsingle,g1HPhisingle,g1VScsingle,g1VPhisingle];

ct10RollThermalsingle = ctRoll[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg01Xsingle,pg01Ysingle,pg01Zsingle,g1HScsingle,g1Tempsingle g1HPhisingle,g1VScsingle,g1Tempsingle g1VPhisingle];
ct10PitchThermalsingle = ctPitch[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg01Xsingle,pg01Ysingle,pg01Zsingle,g1HScsingle,g1Tempsingle g1HPhisingle,g1VScsingle,g1Tempsingle g1VPhisingle];
ct10YawThermalsingle = ctYaw[pg01Xsingle,pg01Ysingle,pg10Zsingle+g1Lengthsingle,pg01Xsingle,pg01Ysingle,pg01Zsingle,g1HScsingle,g1Tempsingle g1HPhisingle,g1VScsingle,g1Tempsingle g1VPhisingle];

parameter set for single pendulum

{f,
m,ix,iy,iz,
kh,kv,
tx,ty,tz,
ctx,cty,ctz,
x,y,z,
dx,dy,dz,
x0,y0,z0,
dx0,dy0,z0,
l};

{nItemsingle,f,
mass1single,iRoll1single,iPitch1single,iYaw1single,
g10Hsingle,g10Vsingle,
t10Rollsingle,t10Pitchsingle,t10Yawsingle,
ct10Rollsingle,ct10Pitchsingle,ct10Yawsingle,
pg10Xsingle,pg10Ysingle,pg10Zsingle,pg10dXsingle,pg10dYsingle,pg10dZsingle,
pg01Xsingle,pg01Ysingle,pg01Zsingle,pg01dXsingle,pg01dYsingle,pg01dZsingle,g1Lengthsingle}

{nItemsingle,f,
mass1single,iRoll1single,iPitch1single,iYaw1single,
g10HThermalsingle,g10VThermalsingle,
t10RollThermalsingle,t10PitchThermalsingle,t10YawThermalsingle,
ct10RollThermalsingle,ct10PitchThermalsingle,ct10YawThermalsingle,
pg10Xsingle,pg10Ysingle,pg10Zsingle,pg10dXsingle,pg10dYsingle,pg10dZsingle,
pg01Xsingle,pg01Ysingle,pg01Zsingle,pg01dXsingle,pg01dYsingle,pg01dZsingle,g1Lengthsingle}

calculation for single mirror for single pendulum

trfsingle[ll_,nn_,jj_,f_]:=trfAmpsingle[ll,nn,jj,nItemsingle,f,
mass1single,iRoll1single,iPitch1single,iYaw1single,
g10Hsingle,g10Vsingle,
t10Rollsingle,t10Pitchsingle,t10Yawsingle,
ct10Rollsingle,ct10Pitchsingle,ct10Yawsingle,
pg10Xsingle,pg10Ysingle,pg10Zsingle,pg10dXsingle,pg10dYsingle,pg10dZsingle,
pg01Xsingle,pg01Ysingle,pg01Zsingle,pg01dXsingle,pg01dYsingle,pg01dZsingle,g1Lengthsingle]

noiseSeissingle[nn_,jj_,f_]:=Part[coupleMatsingle,jj].seissingle[nn,jj,nItemsingle,f,
mass1single,iRoll1single,iPitch1single,iYaw1single,
g10Hsingle,g10Vsingle,
t10Rollsingle,t10Pitchsingle,t10Yawsingle,
ct10Rollsingle,ct10Pitchsingle,ct10Yawsingle,
pg10Xsingle,pg10Ysingle,pg10Zsingle,pg10dXsingle,pg10dYsingle,pg10dZsingle,
pg01Xsingle,pg01Ysingle,pg01Zsingle,pg01dXsingle,pg01dYsingle,pg01dZsingle,g1Lengthsingle]

dispTNoisesingle[ll_,nn_,f_]:=

Abs[tNoisesingle[ll,nn,f,
mass1single,iRoll1single,iPitch1single,iYaw1single,
g10HThermalsingle,g10VThermalsingle,
t10RollThermalsingle,t10PitchThermalsingle,t10YawThermalsingle,
ct10RollThermalsingle,ct10PitchThermalsingle,ct10YawThermalsingle,
pg10Xsingle,pg10Ysingle,pg10Zsingle,pg10dXsingle,pg10dYsingle,pg10dZsingle,
pg01Xsingle,pg01Ysingle,pg01Zsingle,pg01dXsingle,pg01dYsingle,pg01dZsingle,g1Lengthsingle]]

(*dispTNoisesingle[nn_,jj_,f_]:=tNoisesingle[nn,jj,nItemsingle,f,
mass1single,iRoll1single,iPitch1single,iYaw1single,
g10HThermalsingle,g10VThermalsingle,
t10RollThermalsingle,t10PitchThermalsingle,t10YawThermalsingle,
ct10RollThermalsingle,ct10PitchThermalsingle,ct10YawThermalsingle,
pg10Xsingle,pg10Ysingle,pg10Zsingle,pg10dXsingle,pg10dYsingle,pg10dZsingle,
pg01Xsingle,pg01Ysingle,pg01Zsingle,pg01dXsingle,pg01dYsingle,pg01dZsingle,g1Lengthsingle]*)

noiseTNoisesingle[ll_,nn_,jj_,f_] := {1}.coupleMatsingle[[jj]]*trfsingle[ll,nn,jj,f]*dispTNoisesingle[ll,nn,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)

seismic noise

noiseSeisSumsingle[f_] := Sqrt[Sum[Sum[noiseSeissingle[nn,jj,f],{jj,1,6}]^2,{nn,1,6}]]

noiseSeisCompsingle[jj_,f_] := Sqrt[Sum[noiseSeissingle[nn,jj,f]^2,{nn,1,6}]] (*sum up of noise in "jj" direction*)

suspension thermal noise (without violin mode)

noiseTNoiseSumsingle[f_] := Sqrt[Sum[Sum[Sum[noiseTNoisesingle[ll,nn,jj,f],{jj,1,6}]^2,{ll,1,6}],{nn,1, nTotalsingle}]]

noiseTNoiseCompsingle[jj_,f_] := Sqrt[Sum[Sum[noiseTNoisesingle[ll,nn,jj,f]^2,{ll,1,6}],{nn,1, nTotalsingle}]] (*sum up of noise in "jj" direction*)

Q & resonant frequency

resSingle=f  /. NSolve[Det[mat6single[f,
mass1single,iRoll1single,iPitch1single,iYaw1single,
g10Hsingle,g10Vsingle,
t10Rollsingle,t10Pitchsingle,t10Yawsingle,
ct10Rollsingle,ct10Pitchsingle,ct10Yawsingle,
pg10Xsingle,pg10Ysingle,pg10Zsingle,pg10dXsingle,pg10dYsingle,pg10dZsingle,
pg01Xsingle,pg01Ysingle,pg01Zsingle,pg01dXsingle,pg01dYsingle,pg01dZsingle,g1Lengthsingle]]==0,f];

Sort[resSingle/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

Plots

plot0 = LogLogPlot[dispCLIOModel[f],{f,10,200}]

plotTN1Single= LogLogPlot[noiseTNoiseSumsingle[f]/2000,{f,0.1,10},PlotStyle -> {RGBColor[0,0,1]}]

plotTN2Single= LogLogPlot[noiseTNoiseSumsingle[f]/2000,{f,10,100},PlotStyle -> {RGBColor[0,0,1]}]

plotTN3Single= LogLogPlot[noiseTNoiseSumsingle[f]/2000,{f,100,1000},PlotStyle -> {RGBColor[0,0,1]},GridLines -> Automatic]

plotTNSingle = Show[plotTN1Single,plotTN2Single,plotTN3Single,PlotRange ->All,GridLines -> Automatic]

Double pendulum

Parameters

intersting item

nItemDouble = 2;

coupling

coupleZXDouble =5/100;(*coupling Z -> X*)
coupleYXDouble = 10/100;(*coupling Y -> X*)

offset of beam centering

offsetRollDouble = 0 mm;
offsetPitchDouble = 0.1 mm;
offsetYawDouble = 0.1 mm;

dimensions of mass for Double pendulum

m1

m1DensDouble = alDens;
m1XDouble = 100mm/1;
m1YDouble = 80 mm/1;
m1ZDouble = 60 mm/1;
mCube[m1DensDouble,m1XDouble,m1YDouble,m1ZDouble]

m2 (Mirror)

m2DensDouble = fsDens;
m2rDouble = 100 mm/2;
m2lDouble = 60 mm;
mCyl[m2DensDouble,m2rDouble,m2lDouble]

m1d

md1DensDouble = susDens;
md1XDouble = 120mm;
md1YDouble = 100 mm;
md1ZDouble = 50 mm;
md1dDouble = 5 mm;
mCage[md1DensDouble,md1XDouble,md1YDouble,md1ZDouble,md1dDouble]

spring for Double pendulum

g1

g1LengthDouble = 260 mm-0 mm;
g1VFreqDouble =  Sqrt[500*4/2.2 kg]/(2 Pi) (*Arai M-thesis p.54*)

g2

(*g1LengthDouble = lSaPend;
g1YoungDouble = saYoung;
g1DiaDouble = diaSaPend;
g1NumDouble = numSaPend;*)

g2LengthDouble = 250 mm-0mm;
g2YoungDouble = tunYoung;
g2DiaDouble = 0.05 mm;
g2NumDouble = 4;

g1d

gd1LengthDouble = 3 cm;
gd1VFreqDouble = 5 Hz;

position of wire clamp from COM (4 wires + symmetrical distribution) for Double pendulum

suspension wires

pg01XDouble = 10 mm;
pg01YDouble = 70 mm/2;
pg01ZDouble = +0 mm;
pg01dXDouble = 0.1 mm*10;
pg01dYDouble = 0.1 mm*10;
pg01dZDouble = +0.1 mm*10;

pg10XDouble = pg01XDouble;
pg10YDouble = pg01YDouble ;
pg10ZDouble = 0.1 mm*1;
pg10dXDouble = 0.1 mm*10;
pg10dYDouble = 0.1 mm*10;
pg10dZDouble = 0.1 mm*10;

pg12XDouble = 10 mm;
pg12YDouble = 70 mm/2+0 mm/2 ;
pg12ZDouble = -0.1 mm*1;
pg12dXDouble = 0.1 mm*10;
pg12dYDouble = 0.1 mm*10;
pg12dZDouble = 0.1 mm*10;

pg21XDouble = 10 mm;
pg21YDouble = 100 mm/2 ;
pg21ZDouble = 0.1 mm*1;
pg21dXDouble = 0.1 mm*10;
pg21dYDouble = 0.1 mm*10;
pg21dZDouble = 0.1 mm*10;

pgd01XDouble = 180 mm/2;
pgd01YDouble = 130 mm/2 ;
pgd01ZDouble = -0.1 mm*1;
pgd01dXDouble = 0.1 mm*10;
pgd01dYDouble = 0.1 mm*10;
pgd01dZDouble = 0.1 mm*10;

pgd10XDouble = pgd01XDouble;
pgd10YDouble = pgd01YDouble ;
pgd10ZDouble = 0.1 mm*1;
pgd10dXDouble = 0.1 mm*10;
pgd10dYDouble = 0.1 mm*10;
pgd10dZDouble = 0.1 mm*10;

dissipation for Double pendulum

dDTDouble = (g2NumDouble√(mCyl[m2DensDouble,m2rDouble,m2lDouble] gaccel/g2NumDouble g2YoungDouble (Pi g2DiaDouble^4/64))/(2 g2LengthDouble^2) )/(mCyl[m2DensDouble,m2rDouble,m2lDouble] gaccel/g2LengthDouble)

in spring

g10HPhiDouble = 1/1.5/10^5/1;
g10VPhiDouble = 1/10^2/1;

g12HPhiDouble = g12VPhiDouble*dDTDouble;
g12VPhiDouble = 1/140;

g21HPhiDouble = g21VPhiDouble*dDTDouble
g21VPhiDouble = 1/140;

gd10HPhiDouble = 1/10^5;
gd10VPhiDouble = 1/10^3;

magnet damping

d1DampFDouble = 5 Hz;
d1DampQDouble = 10;

Preparation

coupling matrix

coupleMatDouble=(({{1}, {coupleYXDouble}, {coupleZXDouble}, {offsetRollDouble}, {offsetPitchDouble}, {offsetYawDouble}}));

mass & moment inertia for Double pendulum

m1(CUBE)

mass1Double = mCube[m1DensDouble, m1XDouble,m1YDouble, m1ZDouble]; 
iRoll1Double = mIRollCube[m1DensDouble, m1XDouble,m1YDouble, m1ZDouble];
iPitch1Double = mIPitchCube[m1DensDouble, m1XDouble,m1YDouble, m1ZDouble];
iYaw1Double = mIYawCube[m1DensDouble, m1XDouble,m1YDouble, m1ZDouble];

m2(mirror)

mass2Double = mCyl[m2DensDouble,m2rDouble,m2lDouble]; 
iRoll2Double = mILCyl[m2DensDouble,m2rDouble,m2lDouble];
iPitch2Double = mIRCyl[m2DensDouble,m2rDouble,m2lDouble];
iYaw2Double = mIRCyl[m2DensDouble,m2rDouble,m2lDouble];

md1(cage)

massd1Double = mCage[md1DensDouble,md1XDouble,md1YDouble,md1ZDouble,md1dDouble]; 
iRolld1Double = mIRollCage[md1DensDouble,md1XDouble,md1YDouble,md1ZDouble,md1dDouble];
iPitchd1Double = mIPitchCage[md1DensDouble,md1XDouble,md1YDouble,md1ZDouble,md1dDouble];
iYawd1Double = mIYawCage[md1DensDouble,md1XDouble,md1YDouble,md1ZDouble,md1dDouble];

suspension wire for Double pendulum

horizontal

g1HScDouble = scPend[mass1Double+mass2Double,g1LengthDouble];
g2HScDouble = scPend[mass2Double,g2LengthDouble];
gd1HScDouble = scPend[massd1Double,gd1LengthDouble];

vertical

g1VScDouble = scFreq[mass1Double+mass2Double,g1VFreqDouble];
g2VScDouble = g2NumDouble*scVert[g2YoungDouble,g2DiaDouble,g2LengthDouble];
gd1VScDouble = scFreq[massd1Double,gd1VFreqDouble];

g10

g10HDouble = g1HScDouble(1 +I g10HPhiDouble);
g10VDouble = g1VScDouble(1 +I g10VPhiDouble);

g10HThermalDouble = g1HScDouble(1 +tRoom I g10HPhiDouble);
g10VThermalDouble = g1VScDouble(1 +tRoom I g10VPhiDouble);

t10RollDouble = ctRoll[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg10XDouble,pg10YDouble,pg10ZDouble,g1HScDouble,g10HPhiDouble,g1VScDouble,g10VPhiDouble];
t10PitchDouble = ctPitch[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg10XDouble,pg10YDouble,pg10ZDouble,g1HScDouble,g10HPhiDouble,g1VScDouble,g10VPhiDouble];
t10YawDouble = ctYaw[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg10XDouble,pg10YDouble,pg10ZDouble,g1HScDouble,g10HPhiDouble,g1VScDouble,g10VPhiDouble];

t10RollThermalDouble = ctRoll[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg10XDouble,pg10YDouble,pg10ZDouble,g1HScDouble,tRoom g10HPhiDouble,g1VScDouble,tRoom g10VPhiDouble];
t10PitchThermalDouble = ctPitch[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg10XDouble,pg10YDouble,pg10ZDouble,g1HScDouble,tRoom g10HPhiDouble,g1VScDouble,tRoom g10VPhiDouble];
t10YawThermalDouble = ctYaw[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg10XDouble,pg10YDouble,pg10ZDouble,g1HScDouble,tRoom g10HPhiDouble,g1VScDouble,tRoom g10VPhiDouble];

ct10RollDouble = ctRoll[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg01XDouble,pg01YDouble,pg01ZDouble,g1HScDouble,g10HPhiDouble,g1VScDouble,g10VPhiDouble];
ct10PitchDouble = ctPitch[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg01XDouble,pg01YDouble,pg01ZDouble,g1HScDouble,g10HPhiDouble,g1VScDouble,g10VPhiDouble];
ct10YawDouble = ctYaw[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg01XDouble,pg01YDouble,pg01ZDouble,g1HScDouble,g10HPhiDouble,g1VScDouble,g10VPhiDouble];

ct10RollThermalDouble = ctRoll[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg01XDouble,pg01YDouble,pg01ZDouble,g1HScDouble,tRoom g10HPhiDouble,g1VScDouble,tRoom g10VPhiDouble];
ct10PitchThermalDouble = ctPitch[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg01XDouble,pg01YDouble,pg01ZDouble,g1HScDouble,tRoom g10HPhiDouble,g1VScDouble,tRoom g10VPhiDouble];
ct10YawThermalDouble = ctYaw[pg01XDouble,pg01YDouble,pg10ZDouble+g1LengthDouble,pg01XDouble,pg01YDouble,pg01ZDouble,g1HScDouble,tRoom g10HPhiDouble,g1VScDouble,tRoom g10VPhiDouble];

g12

g12HDouble = g2HScDouble(1 +I g12HPhiDouble);
g12VDouble = g2VScDouble(1 +I g12VPhiDouble);

g12HThermalDouble = g2HScDouble(1 +tRoom I g12HPhiDouble);
g12VThermalDouble = g2VScDouble(1 +tRoom I g12VPhiDouble);

t12RollDouble = ctRoll[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,g12HPhiDouble,g2VScDouble,g12VPhiDouble];
t12PitchDouble = ctPitch[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,g12HPhiDouble,g2VScDouble,g12VPhiDouble];
t12YawDouble = ctYaw[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,g12HPhiDouble,g2VScDouble,g12VPhiDouble];

t12RollThermalDouble = ctRoll[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,tRoom g12HPhiDouble,g2VScDouble,tRoom g12VPhiDouble];
t12PitchThermalDouble = ctPitch[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,tRoom g12HPhiDouble,g2VScDouble,tRoom g12VPhiDouble];
t12YawThermalDouble = ctYaw[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,tRoom g12HPhiDouble,g2VScDouble,tRoom g12VPhiDouble];

ct12RollDouble = ctRoll[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,g12HPhiDouble,g2VScDouble,g12VPhiDouble];
ct12PitchDouble = ctPitch[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,g12HPhiDouble,g2VScDouble,g12VPhiDouble];
ct12YawDouble = ctYaw[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,g12HPhiDouble,g2VScDouble,g12VPhiDouble];

ct12RollThermalDouble = ctRoll[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,tRoom g12HPhiDouble,g2VScDouble,tRoom g12VPhiDouble];
ct12PitchThermalDouble = ctPitch[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,tRoom g12HPhiDouble,g2VScDouble,tRoom g12VPhiDouble];
ct12YawThermalDouble = ctYaw[pg21XDouble,pg21YDouble,pg12ZDouble-g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,tRoom g12HPhiDouble,g2VScDouble,tRoom g12VPhiDouble];

g21

g21HDouble = g2HScDouble(1 +I g21HPhiDouble);
g21VDouble = g2VScDouble(1 +I g21VPhiDouble);

g21HThermalDouble = g2HScDouble(1 +tRoom I g21HPhiDouble);
g21VThermalDouble = g2VScDouble(1 +tRoom I g21VPhiDouble);

t21RollDouble = ctRoll[pg12XDouble,pg12YDouble,pg21ZDouble+g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,g21HPhiDouble,g2VScDouble,g21VPhiDouble];
t21PitchDouble = ctPitch[pg12XDouble,pg12YDouble,pg21ZDouble+g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,g21HPhiDouble,g2VScDouble,g21VPhiDouble];
t21YawDouble = ctYaw[pg12XDouble,pg12YDouble,pg21ZDouble+g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,g21HPhiDouble,g2VScDouble,g21VPhiDouble];

t21RollThermalDouble = ctRoll[pg12XDouble,pg12YDouble,pg21ZDouble+g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,tRoom g21HPhiDouble,g2VScDouble,tRoom g21VPhiDouble];
t21PitchThermalDouble = ctPitch[pg12XDouble,pg12YDouble,pg21ZDouble+g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,tRoom g21HPhiDouble,g2VScDouble,tRoom g21VPhiDouble];
t21YawThermalDouble = ctYaw[pg12XDouble,pg12YDouble,pg21ZDouble+g2LengthDouble,pg21XDouble,pg21YDouble,pg21ZDouble,g2HScDouble,tRoom g21HPhiDouble,g2VScDouble,tRoom g21VPhiDouble];

ct21RollDouble = ctRoll[pg21XDouble,pg21YDouble,pg21ZDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,g21HPhiDouble,g2VScDouble,g21VPhiDouble];
ct21PitchDouble = ctPitch[pg21XDouble,pg21YDouble,pg21ZDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,g21HPhiDouble,g2VScDouble,g21VPhiDouble];
ct21YawDouble = ctYaw[pg21XDouble,pg21YDouble,pg21ZDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,g21HPhiDouble,g2VScDouble,g21VPhiDouble];

ct21RollThermalDouble = ctRoll[pg12XDouble,pg12YDouble,pg21ZDouble+g2LengthDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,tRoom g21HPhiDouble,g2VScDouble,tRoom g21VPhiDouble];
ct21PitchThermalDouble = ctPitch[pg12XDouble,pg12YDouble,pg21ZDouble+g2LengthDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,tRoom g21HPhiDouble,g2VScDouble,tRoom g21VPhiDouble];
ct21YawThermalDouble = ctYaw[pg12XDouble,pg12YDouble,pg21ZDouble+g2LengthDouble,pg12XDouble,pg12YDouble,pg12ZDouble,g2HScDouble,tRoom g21HPhiDouble,g2VScDouble,tRoom g21VPhiDouble];

gd10

gd10HDouble = gd1HScDouble(1 +I gd10HPhiDouble);
gd10VDouble = gd1VScDouble(1 +I gd10VPhiDouble);

gd10HThermalDouble = gd1HScDouble(1 +tRoom I gd10HPhiDouble);
gd10VThermalDouble = gd1VScDouble(1 +tRoom I gd10VPhiDouble);

td10RollDouble = ctRoll[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,gd1HScDouble,gd10HPhiDouble,gd1VScDouble,gd10VPhiDouble];
td10PitchDouble = ctPitch[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,gd1HScDouble,gd10HPhiDouble,gd1VScDouble,gd10VPhiDouble];
td10YawDouble = ctYaw[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,gd1HScDouble,gd10HPhiDouble,gd1VScDouble,gd10VPhiDouble];

td10RollThermalDouble = ctRoll[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,gd1HScDouble,tRoom gd10HPhiDouble,gd1VScDouble,tRoom gd10VPhiDouble];
td10PitchThermalDouble = ctPitch[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,gd1HScDouble,tRoom gd10HPhiDouble,gd1VScDouble,tRoom gd10VPhiDouble];
td10YawThermalDouble = ctYaw[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,gd1HScDouble,tRoom gd10HPhiDouble,gd1VScDouble,tRoom gd10VPhiDouble];

ctd10RollDouble = ctRoll[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,gd1HScDouble,gd10HPhiDouble,gd1VScDouble,gd10VPhiDouble];
ctd10PitchDouble = ctPitch[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,gd1HScDouble,gd10HPhiDouble,gd1VScDouble,gd10VPhiDouble];
ctd10YawDouble = ctYaw[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,gd1HScDouble,gd10HPhiDouble,gd1VScDouble,gd10VPhiDouble];

ctd10RollThermalDouble = ctRoll[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,gd1HScDouble,tRoom gd10HPhiDouble,gd1VScDouble,tRoom gd10VPhiDouble];
ctd10PitchThermalDouble = ctPitch[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,gd1HScDouble,tRoom gd10HPhiDouble,gd1VScDouble,tRoom gd10VPhiDouble];
ctd10YawThermalDouble = ctYaw[pgd01XDouble,pgd01YDouble,pgd10ZDouble+gd1LengthDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,gd1HScDouble,tRoom gd10HPhiDouble,gd1VScDouble,tRoom gd10VPhiDouble];

damping

d1DampDouble[f_] := Damp[f,d1DampFDouble,d1DampQDouble];

parameter set for Double pendulum

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
md1,ixd1,iyd1,izd1,
kh10,kv10,kh12,kv12,kh21,kv21,khd10,kvd10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,txd10,tyd10,tzd10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctxd10,ctyd10,ctzd10,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,xd01,yd01,zd01,xd10,yd10,zd10,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dxd01,dyd01,zd01,dxd10,dyd10,dzd10,
l1,l2,ld1,
d1};

{nItemDouble,f,
mass1Double,iRoll1Double,iPitch1Double,iYaw1Double,
mass2Double,iRoll2Double,iPitch2Double,iYaw2Double,
massd1Double,iRolld1Double,iPitchd1Double,iYawd1Double,
g10HDouble,g10VDouble,g12HDouble,g12VDouble,g21HDouble,g21VDouble,gd10HDouble,gd10VDouble,
t10RollDouble,t10PitchDouble,t10YawDouble,t12RollDouble,t12PitchDouble,t12YawDouble,t21RollDouble,t21PitchDouble,t21YawDouble,td10RollDouble,td10PitchDouble,td10YawDouble,
ct10RollDouble,ct10PitchDouble,ct10YawDouble,ct12RollDouble,ct12PitchDouble,ct12YawDouble,ct21RollDouble,ct21PitchDouble,ct21YawDouble,ctd10RollDouble,ctd10PitchDouble,ctd10YawDouble,
pg01XDouble,pg01YDouble,pg01ZDouble,
pg10XDouble,pg10YDouble,pg10ZDouble,pg12XDouble,pg12YDouble,pg12ZDouble,pg21XDouble,pg21YDouble,pg21ZDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,
pg01dXDouble,pg01dYDouble,pg01dZDouble,
pg10dXDouble,pg10dYDouble,pg10dZDouble,pg12dXDouble,pg12dYDouble,pg12dZDouble,pg21dXDouble,pg21dYDouble,pg21dZDouble,pgd01dXDouble,pgd01dYDouble,pgd01dZDouble,pgd10dXDouble,pgd10dYDouble,pgd10dZDouble,
g1LengthDouble,g2LengthDouble,gd1LengthDouble,
d1DampDouble[f]}

{nItemDouble,f,
mass1Double,iRoll1Double,iPitch1Double,iYaw1Double,
mass2Double,iRoll2Double,iPitch2Double,iYaw2Double,
massd1Double,iRolld1Double,iPitchd1Double,iYawd1Double,
g10HThermalDouble,g10VThermalDouble,g12HThermalDouble,g12VThermalDouble,g21HThermalDouble,g21VThermalDouble,gd10HThermalDouble,gd10VThermalDouble,
t10RollThermalDouble,t10PitchThermalDouble,t10YawThermalDouble,t12RollThermalDouble,t12PitchThermalDouble,t12YawThermalDouble,t21RollThermalDouble,t21PitchThermalDouble,t21YawThermalDouble,td10RollThermalDouble,td10PitchThermalDouble,td10YawThermalDouble,
ct10RollThermalDouble,ct10PitchThermalDouble,ct10YawThermalDouble,ct12RollThermalDouble,ct12PitchThermalDouble,ct12YawThermalDouble,ct21RollThermalDouble,ct21PitchThermalDouble,ct21YawThermalDouble,ctd10RollThermalDouble,ctd10PitchThermalDouble,ctd10YawThermalDouble,
pg01XDouble,pg01YDouble,pg01ZDouble,
pg10XDouble,pg10YDouble,pg10ZDouble,pg12XDouble,pg12YDouble,pg12ZDouble,pg21XDouble,pg21YDouble,pg21ZDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,
pg01dXDouble,pg01dYDouble,pg01dZDouble,
pg10dXDouble,pg10dYDouble,pg10dZDouble,pg12dXDouble,pg12dYDouble,pg12dZDouble,pg21dXDouble,pg21dYDouble,pg21dZDouble,pgd01dXDouble,pgd01dYDouble,pgd01dZDouble,pgd10dXDouble,pgd10dYDouble,pgd10dZDouble,
g1LengthDouble,g2LengthDouble,gd1LengthDouble,
d1DampDouble[f]}

calculation for Double mirror for Double pendulum

trfDouble[ll_,nn_,jj_,f_]:=trfAmpDouble[ll,nn,jj,nItemDouble,f,
mass1Double,iRoll1Double,iPitch1Double,iYaw1Double,
mass2Double,iRoll2Double,iPitch2Double,iYaw2Double,
massd1Double,iRolld1Double,iPitchd1Double,iYawd1Double,
g10HDouble,g10VDouble,g12HDouble,g12VDouble,g21HDouble,g21VDouble,gd10HDouble,gd10VDouble,
t10RollDouble,t10PitchDouble,t10YawDouble,t12RollDouble,t12PitchDouble,t12YawDouble,t21RollDouble,t21PitchDouble,t21YawDouble,td10RollDouble,td10PitchDouble,td10YawDouble,
ct10RollDouble,ct10PitchDouble,ct10YawDouble,ct12RollDouble,ct12PitchDouble,ct12YawDouble,ct21RollDouble,ct21PitchDouble,ct21YawDouble,ctd10RollDouble,ctd10PitchDouble,ctd10YawDouble,
pg01XDouble,pg01YDouble,pg01ZDouble,
pg10XDouble,pg10YDouble,pg10ZDouble,pg12XDouble,pg12YDouble,pg12ZDouble,pg21XDouble,pg21YDouble,pg21ZDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,
pg01dXDouble,pg01dYDouble,pg01dZDouble,
pg10dXDouble,pg10dYDouble,pg10dZDouble,pg12dXDouble,pg12dYDouble,pg12dZDouble,pg21dXDouble,pg21dYDouble,pg21dZDouble,pgd01dXDouble,pgd01dYDouble,pgd01dZDouble,pgd10dXDouble,pgd10dYDouble,pgd10dZDouble,
g1LengthDouble,g2LengthDouble,gd1LengthDouble,
d1DampDouble[f]]

noiseSeisDouble[nn_,jj_,f_]:=Part[coupleMatDouble,jj].seisDouble[nn,jj,nItemDouble,f,
mass1Double,iRoll1Double,iPitch1Double,iYaw1Double,
mass2Double,iRoll2Double,iPitch2Double,iYaw2Double,
massd1Double,iRolld1Double,iPitchd1Double,iYawd1Double,
g10HDouble,g10VDouble,g12HDouble,g12VDouble,g21HDouble,g21VDouble,gd10HDouble,gd10VDouble,
t10RollDouble,t10PitchDouble,t10YawDouble,t12RollDouble,t12PitchDouble,t12YawDouble,t21RollDouble,t21PitchDouble,t21YawDouble,td10RollDouble,td10PitchDouble,td10YawDouble,
ct10RollDouble,ct10PitchDouble,ct10YawDouble,ct12RollDouble,ct12PitchDouble,ct12YawDouble,ct21RollDouble,ct21PitchDouble,ct21YawDouble,ctd10RollDouble,ctd10PitchDouble,ctd10YawDouble,
pg01XDouble,pg01YDouble,pg01ZDouble,
pg10XDouble,pg10YDouble,pg10ZDouble,pg12XDouble,pg12YDouble,pg12ZDouble,pg21XDouble,pg21YDouble,pg21ZDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,
pg01dXDouble,pg01dYDouble,pg01dZDouble,
pg10dXDouble,pg10dYDouble,pg10dZDouble,pg12dXDouble,pg12dYDouble,pg12dZDouble,pg21dXDouble,pg21dYDouble,pg21dZDouble,pgd01dXDouble,pgd01dYDouble,pgd01dZDouble,pgd10dXDouble,pgd10dYDouble,pgd10dZDouble,
g1LengthDouble,g2LengthDouble,gd1LengthDouble,
d1DampDouble[f]]

dispTNoiseDouble[ll_,nn_,f_]:=
Abs[tNoiseDouble[ll,nn,f,
mass1Double,iRoll1Double,iPitch1Double,iYaw1Double,
mass2Double,iRoll2Double,iPitch2Double,iYaw2Double,
massd1Double,iRolld1Double,iPitchd1Double,iYawd1Double,
g10HThermalDouble,g10VThermalDouble,g12HThermalDouble,g12VThermalDouble,g21HThermalDouble,g21VThermalDouble,gd10HThermalDouble,gd10VThermalDouble,
t10RollThermalDouble,t10PitchThermalDouble,t10YawThermalDouble,t12RollThermalDouble,t12PitchThermalDouble,t12YawThermalDouble,t21RollThermalDouble,t21PitchThermalDouble,t21YawThermalDouble,td10RollThermalDouble,td10PitchThermalDouble,td10YawThermalDouble,
ct10RollThermalDouble,ct10PitchThermalDouble,ct10YawThermalDouble,ct12RollThermalDouble,ct12PitchThermalDouble,ct12YawThermalDouble,ct21RollThermalDouble,ct21PitchThermalDouble,ct21YawThermalDouble,ctd10RollThermalDouble,ctd10PitchThermalDouble,ctd10YawThermalDouble,
pg01XDouble,pg01YDouble,pg01ZDouble,
pg10XDouble,pg10YDouble,pg10ZDouble,pg12XDouble,pg12YDouble,pg12ZDouble,pg21XDouble,pg21YDouble,pg21ZDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,
pg01dXDouble,pg01dYDouble,pg01dZDouble,
pg10dXDouble,pg10dYDouble,pg10dZDouble,pg12dXDouble,pg12dYDouble,pg12dZDouble,pg21dXDouble,pg21dYDouble,pg21dZDouble,pgd01dXDouble,pgd01dYDouble,pgd01dZDouble,pgd10dXDouble,pgd10dYDouble,pgd10dZDouble,
g1LengthDouble,g2LengthDouble,gd1LengthDouble,
d1DampDouble[f]]]

noiseTNoiseDouble[ll_,nn_,jj_,f_] := {1}.coupleMatDouble[[jj]]*trfDouble[ll,nn,jj,f]*dispTNoiseDouble[ll,nn,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)

seismic noise

noiseSeisSumDouble[f_] := Sqrt[Sum[Sum[noiseSeisDouble[nn,jj,f],{jj,1,6}]^2,{nn,1,6}]]

noiseSeisCompDouble[jj_,f_] := Sqrt[Sum[noiseSeisDouble[nn,jj,f]^2,{nn,1,6}]] (*sum up of noise in "jj" direction*)

suspension thermal noise (without violin mode)

noiseTNoiseSumDouble[f_] := Sqrt[Sum[Sum[Sum[noiseTNoiseDouble[ll,nn,jj,f],{jj,1,6}]^2,{ll,1,6}],{nn,1, nTotalDouble}]]

noiseTNoiseCompDouble[jj_,f_] := Sqrt[Sum[Sum[noiseTNoiseDouble[ll,nn,jj,f]^2,{ll,1,6}],{nn,1, nTotalDouble}]] (*sum up of noise in "jj" direction*)

Q & resonant frequency

resDouble=f  /. NSolve[Det[mat6Double[f,
mass1Double,iRoll1Double,iPitch1Double,iYaw1Double,
mass2Double,iRoll2Double,iPitch2Double,iYaw2Double,
massd1Double,iRolld1Double,iPitchd1Double,iYawd1Double,
g10HDouble,g10VDouble,g12HDouble,g12VDouble,g21HDouble,g21VDouble,gd10HDouble,gd10VDouble,
t10RollDouble,t10PitchDouble,t10YawDouble,t12RollDouble,t12PitchDouble,t12YawDouble,t21RollDouble,t21PitchDouble,t21YawDouble,td10RollDouble,td10PitchDouble,td10YawDouble,
ct10RollDouble,ct10PitchDouble,ct10YawDouble,ct12RollDouble,ct12PitchDouble,ct12YawDouble,ct21RollDouble,ct21PitchDouble,ct21YawDouble,ctd10RollDouble,ctd10PitchDouble,ctd10YawDouble,
pg01XDouble,pg01YDouble,pg01ZDouble,
pg10XDouble,pg10YDouble,pg10ZDouble,pg12XDouble,pg12YDouble,pg12ZDouble,pg21XDouble,pg21YDouble,pg21ZDouble,pgd01XDouble,pgd01YDouble,pgd01ZDouble,pgd10XDouble,pgd10YDouble,pgd10ZDouble,
pg01dXDouble,pg01dYDouble,pg01dZDouble,
pg10dXDouble,pg10dYDouble,pg10dZDouble,pg12dXDouble,pg12dYDouble,pg12dZDouble,pg21dXDouble,pg21dYDouble,pg21dZDouble,pgd01dXDouble,pgd01dYDouble,pgd01dZDouble,pgd10dXDouble,pgd10dYDouble,pgd10dZDouble,
g1LengthDouble,g2LengthDouble,gd1LengthDouble,
d1DampDouble[f]]]==0,f]

Sort[resDouble/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

Plots

Seismic & thermal : all components

plot0 = LogLogPlot[dispCLIOModel[f],{f,10,1000}]

plotseis1 = LogLogPlot[2*noiseSeisSumDouble[f],{f,0.1,10},PlotStyle -> {RGBColor[0,1,0]}]

plotseis2= LogLogPlot[2*noiseSeisSumDouble[f],{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

plotseis3 = LogLogPlot[2*noiseSeisSumDouble[f],{f,100,1000},PlotStyle -> {RGBColor[0,1,0]}]

plotseisC5= Show[plotseis1,plotseis2,plotseis3,PlotRange -> All]

plotseisC1= Show[plotseis1,plotseis2,plotseis3,PlotRange -> All]

plotseisC0= Show[plotseis1,plotseis2,plotseis3,PlotRange -> All]

Show[plotseisC1,plotseisC5,plotseisC0,plotLISM030320]

plotTN1= LogLogPlot[2*noiseTNoiseSumDouble[f],{f,0.1,10},PlotStyle -> {RGBColor[0,0,1]}]

plotTN2= LogLogPlot[2*noiseTNoiseSumDouble[f],{f,10,100},PlotStyle -> {RGBColor[0,0,1]}]

plotTN3= LogLogPlot[2*noiseTNoiseSumDouble[f],{f,100,1000},PlotStyle -> {RGBColor[0,0,1]}]

plotTN = Show[plotTN1,plotTN2,plotTN3,PlotRange -> All]

Show[plotTN,plotseisC5,plotLISM030320]

Show[plotTAMA030712,plotTN,PlotRange -> All]

plotTN5 =Show[plotTN3,plotTN2,PlotRange -> All]

Show[plotTN3,plotTAMA030712]

Show[plotTN3,plotLISM030320,GridLines -> Automatic]

seismic: each component

plot1= LogLogPlot[{noiseSeisDouble[1,1,f],noiseSeisDouble[3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[1,0,0.5]}]

plot2= LogLogPlot[{noiseSeisDouble[1,1,f],noiseSeisDouble[3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[1,0,0.5]}]

plot3= LogLogPlot[{noiseSeisDouble[1,1,f],noiseSeisDouble[3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[1,0,0.5]}]

Show[plotseis,plotLISM030320,plot1,plot2,plot3,GridLines -> Automatic]

thermal: each component

plot11=LogLogPlot[{noiseTNoiseDouble[1,1,1,f],noiseTNoiseDouble[5,1,1,f],noiseTNoiseDouble[6,1,3,f], noiseTNoiseDouble[3,1,3,f],noiseTNoiseDouble[4,1,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,1,0],RGBColor[1,0,0.5],RGBColor[0.5,0,1],RGBColor[1,0,1],RGBColor[0.5,1,0.5]}]

plot12=LogLogPlot[{noiseTNoiseDouble[1,1,1,f],noiseTNoiseDouble[5,1,1,f],noiseTNoiseDouble[6,1,3,f], noiseTNoiseDouble[3,1,3,f],noiseTNoiseDouble[4,1,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,1,0],RGBColor[1,0,0.5],RGBColor[0.5,0,1],RGBColor[1,0,1],RGBColor[0.5,1,0.5]}]

plot13=LogLogPlot[{noiseTNoiseDouble[1,1,1,f],noiseTNoiseDouble[5,1,1,f],noiseTNoiseDouble[6,1,3,f], noiseTNoiseDouble[3,1,3,f],noiseTNoiseDouble[4,1,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,1,0],RGBColor[1,0,0.5],RGBColor[0.5,0,1],RGBColor[1,0,1],RGBColor[0.5,1,0.5]}]

plot14=LogLogPlot[{noiseTNoiseDouble[1,2,1,f],noiseTNoiseDouble[5,2,1,f],noiseTNoiseDouble[6,2,3,f], noiseTNoiseDouble[3,2,3,f],noiseTNoiseDouble[4,2,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,1,0],RGBColor[1,0,0.5],RGBColor[0.5,0,1],RGBColor[1,0,1],RGBColor[0.5,1,0.5]}]

plot15=LogLogPlot[{noiseTNoiseDouble[1,2,1,f],noiseTNoiseDouble[5,2,1,f],noiseTNoiseDouble[6,2,3,f], noiseTNoiseDouble[3,2,3,f],noiseTNoiseDouble[4,2,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,1,0],RGBColor[1,0,0.5],RGBColor[0.5,0,1],RGBColor[1,0,1],RGBColor[0.5,1,0.5]}]

plot16=LogLogPlot[{noiseTNoiseDouble[1,2,1,f],noiseTNoiseDouble[5,2,1,f],noiseTNoiseDouble[6,2,3,f], noiseTNoiseDouble[3,2,3,f],noiseTNoiseDouble[4,2,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,1,0],RGBColor[1,0,0.5],RGBColor[0.5,0,1],RGBColor[1,0,1],RGBColor[0.5,1,0.5]}]

Show[plotLISM030320,plotTN,plot11,plot12,plot13,PlotRange -> All]

Show[plot13,plot16,plotLISM030320,plotTN,GridLines -> Automatic]

Show[plotLISM030320,plotTN,plot14,plot15,plot16,PlotRange -> All]

Show[plotLISM030320,plotseis,plotTN,plot11,plot12,plot13,plot14,plot15,plot16,PlotRange -> All]

Plot[{x,2 x,3 x,4 x,5 x},{x,0,10},PlotStyle -> {RGBColor[1,1,0],RGBColor[1,0,0.5],RGBColor[0.5,0,1],RGBColor[1,0,1],RGBColor[0.5,1,0.5]}]

Im[Inverse[(({{-m f^2+kx(1+I phix), cxy}, {cxy, -m f^2+ky(1+I phiy)}}))]]

Im[Inverse[(({{-m f^2+kx(1+I phix), 0}, {0, -m f^2+ky(1+I phiy)}}))]]

thermal: each direction

plot21=LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f], noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[1,0,0.5],RGBColor[0.5,0,1],RGBColor[1,0,1],RGBColor[0.5,1,0.5]}]

plot22=LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f], noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[1,0,0.5],RGBColor[0.5,0,1],RGBColor[1,0,1],RGBColor[0.5,1,0.5]}]

plot23=LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f], noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[1,0,0.5],RGBColor[0.5,0,1],RGBColor[1,0,1],RGBColor[0.5,1,0.5]}]

Show[plotLISM030320,plotseisC5,plotTN,plot21,plot22,plot23,PlotRange -> All]

Plot[{x,2 x,3 x,4 x,5 x},{x,0,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[1,0,0.5],RGBColor[0.5,0,1],RGBColor[1,0,1],RGBColor[0.5,1,0.5]}]

Quad pendulum

Parameters

intersting item

nItemQuad = 4 ;

coupling & vibration amplification in cryostat

coupleZXQuad =5/100;(*coupling Z -> X*)
coupleYXQuad = 10/100;(*coupling Y -> X*)

offset of beam centering

offsetRollQuad = 0 mm;
offsetPitchQuad = 0.1 mm;
offsetYawQuad = 0.1 mm;

dimensions of mass for quad pendulum

m1

m1DensQuad = alDens;
m1XQuad = 100mm;
m1YQuad = 100mm;
m1ZQuad = 70 mm;
mCube[m1DensQuad,m1XQuad,m1YQuad,m1ZQuad]

m2

m2DensQuad = alDens;
m2XQuad = 100mm;
m2YQuad = 100 mm;
m2ZQuad = 70 mm;
mCube[m2DensQuad,m2XQuad,m2YQuad,m2ZQuad]

m3

m3DensQuad = alDens;
m3XQuad = 100mm;
m3YQuad = 100 mm;
m3ZQuad = 70 mm;
mCube[m3DensQuad,m3XQuad,m3YQuad,m3ZQuad]

m4

m4DensQuad = saDens;
m4rQuad = rMass;
m4lQuad = lMass;

m2d

md2DensQuad = susDens;
md2XQuad = 120mm;
md2YQuad = 100 mm;
md2ZQuad = 50 mm;
md2dQuad = 5 mm;
mCage[md2DensQuad,md2XQuad,md2YQuad,md2ZQuad,md2dQuad]

spring for quad pendulum

g1

g1LengthQuad = 1 cm;
g1VFreqQuad = 4 Hz;

g2

g2LengthQuad = 25 cm;
g2VFreqQuad = 4 Hz;

g3

g3LengthQuad = 100 cm;
g3VFreqQuad = 4 Hz;

g4

g4LengthQuad = lSaPend ;

gd2

gd2LengthQuad = 1 cm;
gd2VFreqQuad = 5 Hz;

position of wire clamp from COM (4 wires + symmetrical distribution) for quad pendulum

pg01XQuad = 20 mm;
pg01YQuad = 20 mm;
pg01ZQuad = 0 mm;
pg01dXQuad = 0.1 mm*10;
pg01dYQuad = 0.1 mm*10;
pg01dZQuad = 0.1 mm*10;

pg10XQuad = pg01XQuad;
pg10YQuad = pg01YQuad ;
pg10ZQuad = m1ZQuad/2;
pg10dXQuad = 0.1 mm*10;
pg10dYQuad = 0.1 mm*10 ;
pg10dZQuad = 0.1 mm*10;

pg12XQuad = 20 mm;
pg12YQuad = 20 mm;
pg12ZQuad = -m1ZQuad/2;
pg12dXQuad = 0.1 mm*10;
pg12dYQuad = 0.1 mm*10;
pg12dZQuad = 0.1 mm*10;

pg21XQuad = pg12XQuad;
pg21YQuad = pg12YQuad ;
pg21ZQuad = m2ZQuad/2;
pg21dXQuad = 0.1 mm*10;
pg21dYQuad = 0.1 mm*10 ;
pg21dZQuad = 0.1 mm*10;

pg23XQuad=10 mm;
pg23YQuad=50 mm;
pg23ZQuad=-m2ZQuad/2;
pg23dXQuad=0.1 mm*10;
pg23dYQuad=0.1 mm*10;
pg23dZQuad=0.1 mm*10;

pg32XQuad=pg23XQuad;
pg32YQuad=pg23YQuad;
pg32ZQuad=m3ZQuad/2;
pg32dXQuad=0.1 mm*10;
pg32dYQuad=0.1 mm*10;
pg32dZQuad=0.1 mm*10;

pg34XQuad=10 mm;
pg34YQuad=rMass/2-0 mm;
pg34ZQuad=-0 mm;
pg34dXQuad=0.1 mm*10;
pg34dYQuad=0.1 mm*10;
pg34dZQuad=0.1 mm*10;

pg43XQuad=pg34XQuad;
pg43YQuad=rMass/2;
pg43ZQuad= 0 mm;
pg43dXQuad=0.1 mm*10;
pg43dYQuad=0.1 mm*10;
pg43dZQuad= 0.1 mm*10;

pgd02XQuad = 180 mm/2;
pgd02YQuad = 130 mm/2 ;
pgd02ZQuad = -0 mm*1;
pgd02dXQuad = 0.1 mm*10;
pgd02dYQuad = 0.1 mm*10;
pgd02dZQuad = 0.1 mm*10;

pgd20XQuad = pgd02XQuad;
pgd20YQuad = pgd02YQuad ;
pgd20ZQuad = 0 mm*1;
pgd20dXQuad = 0.1 mm*10;
pgd20dYQuad = 0.1 mm*10;
pgd20dZQuad = 0.1 mm*10;

dissipation

qRoomHQuad = 10^6;
qCryoHQuad = 10^7;
qRoomVQuad = 10^4;
qCryoVQuad  =10^5;

qSaHQuad =  1/(3 10^(-7));
qSaVQuad =  10^6;

qg3VQuad = qCryoVQuad;

g3TempVQuad = m3TempQuad;(*縦防振の板ばねをcryoに入れるときはm3TempQuad,それ以外はm2TempQuad*)

in spring

g10HPhiQuad =  1/qRoomHQuad;
g10VPhiQuad =   1/qRoomVQuad;

g12HPhiQuad =   1/qRoomHQuad;
g12VPhiQuad =  1/qRoomVQuad;

g21HPhiQuad =  1/qRoomHQuad;
g21VPhiQuad =   1/qRoomVQuad;

g23HPhiQuad =   1/qCryoHQuad;
g23VPhiQuad =    1/qg3VQuad;

g32HPhiQuad =   1/qRoomHQuad;
g32VPhiQuad =    1/qg3VQuad;

g34HPhiQuad =  1/qSaHQuad;
g34VPhiQuad =  1/qSaVQuad;

g43HPhiQuad =  1/qSaHQuad;
g43VPhiQuad = 1/qSaVQuad;

gd20HPhiQuad =  1/qRoomHQuad;
gd20VPhiQuad =  1/qRoomVQuad;

magnet damping

d2DampFQuad = 5 Hz;
d2DampQQuad = 10*1;

temperature for triple pendulum

m1TempQuad = 300 K;
m2TempQuad = 300 K;
m3TempQuad = 13 K;
m4TempQuad = 25 K;
md2TempQuad = 300 K;

Preparation

coupling matrix

coupleMatQuad=(({{1}, {coupleYXQuad}, {coupleZXQuad}, {offsetRollQuad}, {offsetPitchQuad}, {offsetYawQuad}}));

mass & moment inertia for Quad pendulum

m1

mass1Quad = mCube[m1DensQuad, m1XQuad,m1YQuad, m1ZQuad]; 
iRoll1Quad = mIRollCube[m1DensQuad, m1XQuad,m1YQuad, m1ZQuad];
iPitch1Quad = mIPitchCube[m1DensQuad, m1XQuad,m1YQuad, m1ZQuad];
iYaw1Quad = mIYawCube[m1DensQuad, m1XQuad,m1YQuad, m1ZQuad];

m2

mass2Quad = mCube[m2DensQuad, m2XQuad,m2YQuad, m2ZQuad]; 
iRoll2Quad = mIRollCube[m2DensQuad, m2XQuad,m2YQuad, m2ZQuad];
iPitch2Quad = mIPitchCube[m2DensQuad, m2XQuad,m2YQuad, m2ZQuad];
iYaw2Quad = mIYawCube[m2DensQuad, m2XQuad,m2YQuad, m2ZQuad];

m3

mass3Quad = mCube[m3DensQuad, m3XQuad,m3YQuad, m3ZQuad]; 
iRoll3Quad = mIRollCube[m3DensQuad, m3XQuad,m3YQuad, m3ZQuad];
iPitch3Quad = mIPitchCube[m3DensQuad, m3XQuad,m3YQuad, m3ZQuad];
iYaw3Quad = mIYawCube[m3DensQuad, m3XQuad,m3YQuad, m3ZQuad];

m4

mass4Quad = mMass; (*see Parameters/Dimensions of final suspension/final mass*)
iRoll4Quad = mILCyl[m4DensQuad, m4rQuad,m4lQuad];
iPitch4Quad = mIRCyl[m4DensQuad, m4rQuad,m4lQuad];
iYaw4Quad = mIRCyl[m4DensQuad, m4rQuad,m4lQuad];

md2(cage)

massd2Quad = mCage[md2DensQuad, md2XQuad,md2YQuad, md2ZQuad,md2dQuad];
iRolld2Quad = mIRollCage[md2DensQuad, md2XQuad,md2YQuad, md2ZQuad,md2dQuad];
iPitchd2Quad = mIPitchCage[md2DensQuad, md2XQuad,md2YQuad, md2ZQuad,md2dQuad];
iYawd2Quad = mIYawCage[md2DensQuad, md2XQuad,md2YQuad, md2ZQuad,md2dQuad];

suspension wire for Quad pendulum

horizontal

g1HScQuad = scPend[mass1Quad+mass2Quad+mass3Quad+mass4Quad,g1LengthQuad];
g2HScQuad = scPend[mass2Quad+mass3Quad+mass4Quad,g2LengthQuad];
g3HScQuad = scPend[mass3Quad+mass4Quad,g3LengthQuad];
g4HScQuad = scPend[mass4Quad,g4LengthQuad];
gd2HScQuad = scPend[massd2Quad,gd2LengthQuad];

vertical

g1VScQuad = scFreq[mass1Quad+mass2Quad+mass3Quad+mass4Quad,g1VFreqQuad];
g2VScQuad = scFreq[mass2Quad+mass3Quad+mass4Quad,g2VFreqQuad];
g3VScQuad = scFreq[mass3Quad+mass4Quad,g3VFreqQuad];
g4VScQuad = numSaPend*scVert[saYoung,diaSaPend,lSaPend];
gd2VScQuad = scFreq[massd2Quad,gd2VFreqQuad];

g10

g10HQuad = g1HScQuad(1 +I g10HPhiQuad);
g10VQuad = g1VScQuad(1 +I g10VPhiQuad);

g10HThermalQuad = g1HScQuad(1 +tRoom I g10HPhiQuad);
g10VThermalQuad = g1VScQuad(1 +tRoom I g10VPhiQuad);

t10RollQuad = ctRoll[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg10XQuad,pg10YQuad,pg10ZQuad,g1HScQuad,g10HPhiQuad,g1VScQuad,g10VPhiQuad];
t10PitchQuad = ctPitch[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg10XQuad,pg10YQuad,pg10ZQuad,g1HScQuad,g10HPhiQuad,g1VScQuad,g10VPhiQuad];
t10YawQuad = ctYaw[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg10XQuad,pg10YQuad,pg10ZQuad,g1HScQuad,g10HPhiQuad,g1VScQuad,g10VPhiQuad];

t10RollThermalQuad = ctRoll[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg10XQuad,pg10YQuad,pg10ZQuad,g1HScQuad,tRoom g10HPhiQuad,g1VScQuad,tRoom g10VPhiQuad];
t10PitchThermalQuad = ctPitch[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg10XQuad,pg10YQuad,pg10ZQuad,g1HScQuad,tRoom g10HPhiQuad,g1VScQuad,tRoom g10VPhiQuad];
t10YawThermalQuad = ctYaw[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg10XQuad,pg10YQuad,pg10ZQuad,g1HScQuad,tRoom g10HPhiQuad,g1VScQuad,tRoom g10VPhiQuad];

ct10RollQuad = ctRoll[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg01XQuad,pg01YQuad,pg01ZQuad,g1HScQuad,g10HPhiQuad,g1VScQuad,g10VPhiQuad];
ct10PitchQuad = ctPitch[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg01XQuad,pg01YQuad,pg01ZQuad,g1HScQuad,g10HPhiQuad,g1VScQuad,g10VPhiQuad];
ct10YawQuad = ctYaw[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg01XQuad,pg01YQuad,pg01ZQuad,g1HScQuad,g10HPhiQuad,g1VScQuad,g10VPhiQuad];

ct10RollThermalQuad = ctRoll[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg01XQuad,pg01YQuad,pg01ZQuad,g1HScQuad,tRoom g10HPhiQuad,g1VScQuad,tRoom g10VPhiQuad];
ct10PitchThermalQuad = ctPitch[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg01XQuad,pg01YQuad,pg01ZQuad,g1HScQuad,tRoom g10HPhiQuad,g1VScQuad,tRoom g10VPhiQuad];
ct10YawThermalQuad = ctYaw[pg01XQuad,pg01YQuad,pg10ZQuad+g1LengthQuad,pg01XQuad,pg01YQuad,pg01ZQuad,g1HScQuad,tRoom g10HPhiQuad,g1VScQuad,tRoom g10VPhiQuad];

g12

g12HQuad = g2HScQuad(1 +I g12HPhiQuad);
g12VQuad = g2VScQuad(1 +I g12VPhiQuad);

g12HThermalQuad = g2HScQuad(1 +tRoom I g12HPhiQuad);
g12VThermalQuad = g2VScQuad(1 +tRoom I g12VPhiQuad);

t12RollQuad = ctRoll[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,g12HPhiQuad,g2VScQuad,g12VPhiQuad];
t12PitchQuad = ctPitch[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,g12HPhiQuad,g2VScQuad,g12VPhiQuad];
t12YawQuad = ctYaw[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,g12HPhiQuad,g2VScQuad,g12VPhiQuad];

t12RollThermalQuad = ctRoll[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,tRoom g12HPhiQuad,g2VScQuad,tRoom g12VPhiQuad];
t12PitchThermalQuad = ctPitch[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,tRoom g12HPhiQuad,g2VScQuad,tRoom g12VPhiQuad];
t12YawThermalQuad = ctYaw[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,tRoom g12HPhiQuad,g2VScQuad,tRoom g12VPhiQuad];

ct12RollQuad = ctRoll[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,g12HPhiQuad,g2VScQuad,g12VPhiQuad];
ct12PitchQuad = ctPitch[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,g12HPhiQuad,g2VScQuad,g12VPhiQuad];
ct12YawQuad = ctYaw[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,g12HPhiQuad,g2VScQuad,g12VPhiQuad];

ct12RollThermalQuad = ctRoll[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,tRoom g12HPhiQuad,g2VScQuad,tRoom g12VPhiQuad];
ct12PitchThermalQuad = ctPitch[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,tRoom g12HPhiQuad,g2VScQuad,tRoom g12VPhiQuad];
ct12YawThermalQuad = ctYaw[pg21XQuad,pg21YQuad,pg12ZQuad-g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,tRoom g12HPhiQuad,g2VScQuad,tRoom g12VPhiQuad];

g21

g21HQuad = g2HScQuad(1 +I g21HPhiQuad);
g21VQuad = g2VScQuad(1 +I g21VPhiQuad);

g21HThermalQuad = g2HScQuad(1 +tRoom I g21HPhiQuad);
g21VThermalQuad = g2VScQuad(1 +tRoom I g21VPhiQuad);

t21RollQuad = ctRoll[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,g21HPhiQuad,g2VScQuad,g21VPhiQuad];
t21PitchQuad = ctPitch[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,g21HPhiQuad,g2VScQuad,g21VPhiQuad];
t21YawQuad = ctYaw[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,g21HPhiQuad,g2VScQuad,g21VPhiQuad];

t21RollThermalQuad = ctRoll[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,tRoom g21HPhiQuad,g2VScQuad,tRoom g21VPhiQuad];
t21PitchThermalQuad = ctPitch[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,tRoom g21HPhiQuad,g2VScQuad,tRoom g21VPhiQuad];
t21YawThermalQuad = ctYaw[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg21XQuad,pg21YQuad,pg21ZQuad,g2HScQuad,tRoom g21HPhiQuad,g2VScQuad,tRoom g21VPhiQuad];

ct21RollQuad = ctRoll[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,g21HPhiQuad,g2VScQuad,g21VPhiQuad];
ct21PitchQuad = ctPitch[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,g21HPhiQuad,g2VScQuad,g21VPhiQuad];
ct21YawQuad = ctYaw[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,g21HPhiQuad,g2VScQuad,g21VPhiQuad];

ct21RollThermalQuad = ctRoll[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,tRoom g21HPhiQuad,g2VScQuad,tRoom g21VPhiQuad];
ct21PitchThermalQuad = ctPitch[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,tRoom g21HPhiQuad,g2VScQuad,tRoom g21VPhiQuad];
ct21YawThermalQuad = ctYaw[pg12XQuad,pg12YQuad,pg21ZQuad+g2LengthQuad,pg12XQuad,pg12YQuad,pg12ZQuad,g2HScQuad,tRoom g21HPhiQuad,g2VScQuad,tRoom g21VPhiQuad];

g23

g23HQuad = g3HScQuad(1 +I g23HPhiQuad);
g23VQuad = g3VScQuad(1 +I g23VPhiQuad);

g23HThermalQuad = g3HScQuad(1 +m3TempQuad I g23HPhiQuad);
g23VThermalQuad = g3VScQuad(1 +g3TempVQuad I g23VPhiQuad);

t23RollQuad = ctRoll[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,g23HPhiQuad,g3VScQuad,g23VPhiQuad];
t23PitchQuad = ctPitch[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,g23HPhiQuad,g3VScQuad,g23VPhiQuad];
t23YawQuad = ctYaw[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,g23HPhiQuad,g3VScQuad,g23VPhiQuad];

t23RollThermalQuad = ctRoll[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,m3TempQuad g23HPhiQuad,g3VScQuad,g3TempVQuad g23VPhiQuad];
t23PitchThermalQuad = ctPitch[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,m3TempQuad g23HPhiQuad,g3VScQuad,g3TempVQuad g23VPhiQuad];
t23YawThermalQuad = ctYaw[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,m3TempQuad g23HPhiQuad,g3VScQuad,g3TempVQuad g23VPhiQuad];

ct23RollQuad = ctRoll[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,g23HPhiQuad,g3VScQuad,g23VPhiQuad];
ct23PitchQuad = ctPitch[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,g23HPhiQuad,g3VScQuad,g23VPhiQuad];
ct23YawQuad = ctYaw[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,g23HPhiQuad,g3VScQuad,g23VPhiQuad];

ct23RollThermalQuad = ctRoll[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,m3TempQuad g23HPhiQuad,g3VScQuad,g3TempVQuad g23VPhiQuad];
ct23PitchThermalQuad = ctPitch[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,m3TempQuad g23HPhiQuad,g3VScQuad,g3TempVQuad g23VPhiQuad];
ct23YawThermalQuad = ctYaw[pg32XQuad,pg32YQuad,pg23ZQuad-g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,m3TempQuad g23HPhiQuad,g3VScQuad,g3TempVQuad g23VPhiQuad];

g32

g32HQuad = g3HScQuad(1 +I g32HPhiQuad);
g32VQuad = g3VScQuad(1 +I g32VPhiQuad);

g32HThermalQuad = g3HScQuad(1 +m2TempQuad I g32HPhiQuad);
g32VThermalQuad = g3VScQuad(1 +g3TempVQuad I g32VPhiQuad);

t32RollQuad = ctRoll[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,g32HPhiQuad,g3VScQuad,g32VPhiQuad];
t32PitchQuad = ctPitch[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,g32HPhiQuad,g3VScQuad,g32VPhiQuad];
t32YawQuad = ctYaw[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,g32HPhiQuad,g3VScQuad,g32VPhiQuad];

t32RollThermalQuad = ctRoll[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,m2TempQuad g32HPhiQuad,g3VScQuad,g3TempVQuad g32VPhiQuad];
t32PitchThermalQuad = ctPitch[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,m2TempQuad g32HPhiQuad,g3VScQuad,g3TempVQuad g32VPhiQuad];
t32YawThermalQuad = ctYaw[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg32XQuad,pg32YQuad,pg32ZQuad,g3HScQuad,m2TempQuad g32HPhiQuad,g3VScQuad,g3TempVQuad g32VPhiQuad];

ct32RollQuad = ctRoll[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,g32HPhiQuad,g3VScQuad,g32VPhiQuad];
ct32PitchQuad = ctPitch[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,g32HPhiQuad,g3VScQuad,g32VPhiQuad];
ct32YawQuad = ctYaw[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,g32HPhiQuad,g3VScQuad,g32VPhiQuad];

ct32RollThermalQuad = ctRoll[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,m2TempQuad g32HPhiQuad,g3VScQuad,g3TempVQuad g32VPhiQuad];
ct32PitchThermalQuad = ctPitch[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,m2TempQuad g32HPhiQuad,g3VScQuad,g3TempVQuad g32VPhiQuad];
ct32YawThermalQuad = ctYaw[pg23XQuad,pg23YQuad,pg32ZQuad+g3LengthQuad,pg23XQuad,pg23YQuad,pg23ZQuad,g3HScQuad,m2TempQuad g32HPhiQuad,g3VScQuad,g3TempVQuad g32VPhiQuad];

g34

g34HQuad = g4HScQuad(1 +I g34HPhiQuad);
g34VQuad = g4VScQuad(1 +I g34VPhiQuad);

g34HThermalQuad = g4HScQuad(1 +m4TempQuad I g34HPhiQuad);
g34VThermalQuad = g4VScQuad(1 +m4TempQuad I g34VPhiQuad);

t34RollQuad = ctRoll[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,g34HPhiQuad,g4VScQuad,g34VPhiQuad];
t34PitchQuad = ctPitch[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,g34HPhiQuad,g4VScQuad,g34VPhiQuad];
t34YawQuad = ctYaw[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,g34HPhiQuad,g4VScQuad,g34VPhiQuad];

t34RollThermalQuad = ctRoll[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,m4TempQuad g34HPhiQuad,g4VScQuad,m4TempQuad g34VPhiQuad];
t34PitchThermalQuad = ctPitch[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,m4TempQuad g34HPhiQuad,g4VScQuad,m4TempQuad g34VPhiQuad];
t34YawThermalQuad = ctYaw[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,m4TempQuad g34HPhiQuad,g4VScQuad,m4TempQuad g34VPhiQuad];

ct34RollQuad = ctRoll[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,g34HPhiQuad,g4VScQuad,g34VPhiQuad];
ct34PitchQuad = ctPitch[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,g34HPhiQuad,g4VScQuad,g34VPhiQuad];
ct34YawQuad = ctYaw[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,g34HPhiQuad,g4VScQuad,g34VPhiQuad];

ct34RollThermalQuad = ctRoll[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,m4TempQuad g34HPhiQuad,g4VScQuad,m4TempQuad g34VPhiQuad];
ct34PitchThermalQuad = ctPitch[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,m4TempQuad g34HPhiQuad,g4VScQuad,m4TempQuad g34VPhiQuad];
ct34YawThermalQuad = ctYaw[pg43XQuad,pg43YQuad,pg34ZQuad-g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,m4TempQuad g34HPhiQuad,g4VScQuad,m4TempQuad g34VPhiQuad];

g43

g43HQuad = g4HScQuad(1 +I g43HPhiQuad);
g43VQuad = g4VScQuad(1 +I g43VPhiQuad);

g43HThermalQuad = g4HScQuad(1 +m3TempQuad I g43HPhiQuad);
g43VThermalQuad = g4VScQuad(1 +m4TempQuad I g43VPhiQuad);

t43RollQuad = ctRoll[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,g43HPhiQuad,g4VScQuad,g43VPhiQuad];
t43PitchQuad = ctPitch[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,g43HPhiQuad,g4VScQuad,g43VPhiQuad];
t43YawQuad = ctYaw[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,g43HPhiQuad,g4VScQuad,g43VPhiQuad];

t43RollThermalQuad = ctRoll[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,m3TempQuad g43HPhiQuad,g4VScQuad,m4TempQuad g43VPhiQuad];
t43PitchThermalQuad = ctPitch[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,m3TempQuad g43HPhiQuad,g4VScQuad,m4TempQuad g43VPhiQuad];
t43YawThermalQuad = ctYaw[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg43XQuad,pg43YQuad,pg43ZQuad,g4HScQuad,m3TempQuad g43HPhiQuad,g4VScQuad,m4TempQuad g43VPhiQuad];

ct43RollQuad = ctRoll[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,g43HPhiQuad,g4VScQuad,g43VPhiQuad];
ct43PitchQuad = ctPitch[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,g43HPhiQuad,g4VScQuad,g43VPhiQuad];
ct43YawQuad = ctYaw[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,g43HPhiQuad,g4VScQuad,g43VPhiQuad];

ct43RollThermalQuad = ctRoll[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,m3TempQuad g43HPhiQuad,g4VScQuad,m4TempQuad g43VPhiQuad];
ct43PitchThermalQuad = ctPitch[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,m3TempQuad g43HPhiQuad,g4VScQuad,m4TempQuad g43VPhiQuad];
ct43YawThermalQuad = ctYaw[pg34XQuad,pg34YQuad,pg43ZQuad+g4LengthQuad,pg34XQuad,pg34YQuad,pg34ZQuad,g4HScQuad,m3TempQuad g43HPhiQuad,g4VScQuad,m4TempQuad g43VPhiQuad];

gd20

gd20HQuad = gd2HScQuad(1 +I gd20HPhiQuad);
gd20VQuad = gd2VScQuad(1 +I gd20VPhiQuad);

gd20HThermalQuad = gd2HScQuad(1 +tRoom I gd20HPhiQuad);
gd20VThermalQuad = gd2VScQuad(1 +tRoom I gd20VPhiQuad);

td20RollQuad = ctRoll[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,gd2HScQuad,gd20HPhiQuad,gd2VScQuad,gd20VPhiQuad];
td20PitchQuad = ctPitch[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,gd2HScQuad,gd20HPhiQuad,gd2VScQuad,gd20VPhiQuad];
td20YawQuad = ctYaw[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,gd2HScQuad,gd20HPhiQuad,gd2VScQuad,gd20VPhiQuad];

td20RollThermalQuad = ctRoll[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,gd2HScQuad,tRoom gd20HPhiQuad,gd2VScQuad,tRoom gd20VPhiQuad];
td20PitchThermalQuad = ctPitch[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,gd2HScQuad,tRoom gd20HPhiQuad,gd2VScQuad,tRoom gd20VPhiQuad];
td20YawThermalQuad = ctYaw[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,gd2HScQuad,tRoom gd20HPhiQuad,gd2VScQuad,tRoom gd20VPhiQuad];

ctd20RollQuad = ctRoll[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd02XQuad,pgd02YQuad,pgd02ZQuad,gd2HScQuad,gd20HPhiQuad,gd2VScQuad,gd20VPhiQuad];
ctd20PitchQuad = ctPitch[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd02XQuad,pgd02YQuad,pgd02ZQuad,gd2HScQuad,gd20HPhiQuad,gd2VScQuad,gd20VPhiQuad];
ctd20YawQuad = ctYaw[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd02XQuad,pgd02YQuad,pgd02ZQuad,gd2HScQuad,gd20HPhiQuad,gd2VScQuad,gd20VPhiQuad];

ctd20RollThermalQuad = ctRoll[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd02XQuad,pgd02YQuad,pgd02ZQuad,gd2HScQuad,tRoom gd20HPhiQuad,gd2VScQuad,tRoom gd20VPhiQuad];
ctd20PitchThermalQuad = ctPitch[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd02XQuad,pgd02YQuad,pgd02ZQuad,gd2HScQuad,tRoom gd20HPhiQuad,gd2VScQuad,tRoom gd20VPhiQuad];
ctd20YawThermalQuad = ctYaw[pgd02XQuad,pgd02YQuad,pgd20ZQuad+gd2LengthQuad,pgd02XQuad,pgd02YQuad,pgd02ZQuad,gd2HScQuad,tRoom gd20HPhiQuad,gd2VScQuad,tRoom gd20VPhiQuad];

damping

d2DampQuad[f_] := Damp[f,d2DampFQuad,d2DampQQuad];

parameter set for Quad pendulum

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
x01,y01,z01,
x10,y10,z10,x12,y12,z12,x21,y21,z21,x23,y23,z23,x32,y32,z32,x34,y34,z34,x43,y43,z43,
xd02,yd02,zd02,
xd20,yd20,zd20,
dx01,dy01,dz01,
dx10,dy10,dz10,dx12,dy12,dz12,dx21,dy21,dz21,dx23,dy23,dz23,dx32,dy32,dz32,dx34,dy34,dz34,dx43,dy43,dz43,
dxd02,dyd02,dzd02,
dxd20,dyd20,dzd20,
l1,l2,l3,l4,ld2,
d2};

{nItemQuad,f,
mass1Quad,iRoll1Quad,iPitch1Quad,iYaw1Quad,mass2Quad,iRoll2Quad,iPitch2Quad,iYaw2Quad,mass3Quad,iRoll3Quad,iPitch3Quad,iYaw3Quad,mass4Quad,iRoll4Quad,iPitch4Quad,iYaw4Quad,massd2Quad,iRolld2Quad,iPitchd2Quad,iYawd2Quad,
g10HQuad,g10VQuad,g12HQuad,g12VQuad,g21HQuad,g21VQuad,g23HQuad,g23VQuad,g32HQuad,g32VQuad,g34HQuad,g34VQuad,g43HQuad,g43VQuad,gd20HQuad,gd20VQuad,
t10RollQuad,t10PitchQuad,t10YawQuad,t12RollQuad,t12PitchQuad,t12YawQuad,t21RollQuad,t21PitchQuad,t21YawQuad,t23RollQuad,t23PitchQuad,t23YawQuad,t32RollQuad,t32PitchQuad,t32YawQuad,t34RollQuad,t34PitchQuad,t34YawQuad,t43RollQuad,t43PitchQuad,t43YawQuad,td20RollQuad,td20PitchQuad,td20YawQuad,
ct10RollQuad,ct10PitchQuad,ct10YawQuad,ct12RollQuad,ct12PitchQuad,ct12YawQuad,ct21RollQuad,ct21PitchQuad,ct21YawQuad,ct23RollQuad,ct23PitchQuad,ct23YawQuad,ct32RollQuad,ct32PitchQuad,ct32YawQuad,ct34RollQuad,ct34PitchQuad,ct34YawQuad,ct43RollQuad,ct43PitchQuad,ct43YawQuad,ctd20RollQuad,ctd20PitchQuad,ctd20YawQuad,
pg01XQuad,pg01YQuad,pg01ZQuad,pg10XQuad,pg10YQuad,pg10ZQuad,pg12XQuad,pg12YQuad,pg12ZQuad,pg21XQuad,pg21YQuad,pg21ZQuad,pg23XQuad,pg23YQuad,pg23ZQuad,pg32XQuad,pg32YQuad,pg32ZQuad,pg34XQuad,pg34YQuad,pg34ZQuad,pg43XQuad,pg43YQuad,pg43ZQuad,
pgd02XQuad,pgd02YQuad,pgd02ZQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,
pg01dXQuad,pg01dYQuad,pg01dZQuad,pg10dXQuad,pg10dYQuad,pg10dZQuad,pg12dXQuad,pg12dYQuad,pg12dZQuad,pg21dXQuad,pg21dYQuad,pg21dZQuad,pg23dXQuad,pg23dYQuad,pg23dZQuad,pg32dXQuad,pg32dYQuad,pg32dZQuad,pg34dXQuad,pg34dYQuad,pg34dZQuad,pg43dXQuad,pg43dYQuad,pg43dZQuad,
pgd02dXQuad,pgd02dYQuad,pgd02dZQuad,pgd20dXQuad,pgd20dYQuad,pgd20dZQuad,
g1LengthQuad,g2LengthQuad,g3LengthQuad,g4LengthQuad,gd2LengthQuad,
d2DampQuad[f]
}

{nItemQuad,f,
mass1Quad,iRoll1Quad,iPitch1Quad,iYaw1Quad,mass2Quad,iRoll2Quad,iPitch2Quad,iYaw2Quad,mass3Quad,iRoll3Quad,iPitch3Quad,iYaw3Quad,mass4Quad,iRoll4Quad,iPitch4Quad,iYaw4Quad,massd2Quad,iRolld2Quad,iPitchd2Quad,iYawd2Quad,
g10HThermalQuad,g10VThermalQuad,g12HThermalQuad,g12VThermalQuad,g21HThermalQuad,g21VThermalQuad,g23HThermalQuad,g23VThermalQuad,g32HThermalQuad,g32VThermalQuad,g34HThermalQuad,g34VThermalQuad,g43HThermalQuad,g43VThermalQuad,gd20HThermalQuad,gd20VThermalQuad,
t10RollThermalQuad,t10PitchThermalQuad,t10YawThermalQuad,t12RollThermalQuad,t12PitchThermalQuad,t12YawThermalQuad,t21RollThermalQuad,t21PitchThermalQuad,t21YawThermalQuad,t23RollThermalQuad,t23PitchThermalQuad,t23YawThermalQuad,t32RollThermalQuad,t32PitchThermalQuad,t32YawThermalQuad,t34RollThermalQuad,t34PitchThermalQuad,t34YawThermalQuad,t43RollThermalQuad,t43PitchThermalQuad,t43YawThermalQuad,td20RollThermalQuad,td20PitchThermalQuad,td20YawThermalQuad,
ct10RollThermalQuad,ct10PitchThermalQuad,ct10YawThermalQuad,ct12RollThermalQuad,ct12PitchThermalQuad,ct12YawThermalQuad,ct21RollThermalQuad,ct21PitchThermalQuad,ct21YawThermalQuad,ct23RollThermalQuad,ct23PitchThermalQuad,ct23YawThermalQuad,ct32RollThermalQuad,ct32PitchThermalQuad,ct32YawThermalQuad,ct34RollThermalQuad,ct34PitchThermalQuad,ct34YawThermalQuad,ct43RollThermalQuad,ct43PitchThermalQuad,ct43YawThermalQuad,ctd20RollThermalQuad,ctd20PitchThermalQuad,ctd20YawThermalQuad,
pg01XQuad,pg01YQuad,pg01ZQuad,pg10XQuad,pg10YQuad,pg10ZQuad,pg12XQuad,pg12YQuad,pg12ZQuad,pg21XQuad,pg21YQuad,pg21ZQuad,pg23XQuad,pg23YQuad,pg23ZQuad,pg32XQuad,pg32YQuad,pg32ZQuad,pg34XQuad,pg34YQuad,pg34ZQuad,pg43XQuad,pg43YQuad,pg43ZQuad,
pgd02XQuad,pgd02YQuad,pgd02ZQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,
pg01dXQuad,pg01dYQuad,pg01dZQuad,pg10dXQuad,pg10dYQuad,pg10dZQuad,pg12dXQuad,pg12dYQuad,pg12dZQuad,pg21dXQuad,pg21dYQuad,pg21dZQuad,pg23dXQuad,pg23dYQuad,pg23dZQuad,pg32dXQuad,pg32dYQuad,pg32dZQuad,pg34dXQuad,pg34dYQuad,pg34dZQuad,pg43dXQuad,pg43dYQuad,pg43dZQuad,
pgd02dXQuad,pgd02dYQuad,pgd02dZQuad,pgd20dXQuad,pgd20dYQuad,pgd20dZQuad,
g1LengthQuad,g2LengthQuad,g3LengthQuad,g4LengthQuad,gd2LengthQuad,
d2DampQuad[f]
}

calculation for Quad pendulum

trfQuad[ll_,nn_,jj_,f_]:=trfAmpQuad[ll,nn,jj,nItemQuad,f,
mass1Quad,iRoll1Quad,iPitch1Quad,iYaw1Quad,mass2Quad,iRoll2Quad,iPitch2Quad,iYaw2Quad,mass3Quad,iRoll3Quad,iPitch3Quad,iYaw3Quad,mass4Quad,iRoll4Quad,iPitch4Quad,iYaw4Quad,massd2Quad,iRolld2Quad,iPitchd2Quad,iYawd2Quad,
g10HQuad,g10VQuad,g12HQuad,g12VQuad,g21HQuad,g21VQuad,g23HQuad,g23VQuad,g32HQuad,g32VQuad,g34HQuad,g34VQuad,g43HQuad,g43VQuad,gd20HQuad,gd20VQuad,
t10RollQuad,t10PitchQuad,t10YawQuad,t12RollQuad,t12PitchQuad,t12YawQuad,t21RollQuad,t21PitchQuad,t21YawQuad,t23RollQuad,t23PitchQuad,t23YawQuad,t32RollQuad,t32PitchQuad,t32YawQuad,t34RollQuad,t34PitchQuad,t34YawQuad,t43RollQuad,t43PitchQuad,t43YawQuad,td20RollQuad,td20PitchQuad,td20YawQuad,
ct10RollQuad,ct10PitchQuad,ct10YawQuad,ct12RollQuad,ct12PitchQuad,ct12YawQuad,ct21RollQuad,ct21PitchQuad,ct21YawQuad,ct23RollQuad,ct23PitchQuad,ct23YawQuad,ct32RollQuad,ct32PitchQuad,ct32YawQuad,ct34RollQuad,ct34PitchQuad,ct34YawQuad,ct43RollQuad,ct43PitchQuad,ct43YawQuad,ctd20RollQuad,ctd20PitchQuad,ctd20YawQuad,
pg01XQuad,pg01YQuad,pg01ZQuad,pg10XQuad,pg10YQuad,pg10ZQuad,pg12XQuad,pg12YQuad,pg12ZQuad,pg21XQuad,pg21YQuad,pg21ZQuad,pg23XQuad,pg23YQuad,pg23ZQuad,pg32XQuad,pg32YQuad,pg32ZQuad,pg34XQuad,pg34YQuad,pg34ZQuad,pg43XQuad,pg43YQuad,pg43ZQuad,
pgd02XQuad,pgd02YQuad,pgd02ZQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,
pg01dXQuad,pg01dYQuad,pg01dZQuad,pg10dXQuad,pg10dYQuad,pg10dZQuad,pg12dXQuad,pg12dYQuad,pg12dZQuad,pg21dXQuad,pg21dYQuad,pg21dZQuad,pg23dXQuad,pg23dYQuad,pg23dZQuad,pg32dXQuad,pg32dYQuad,pg32dZQuad,pg34dXQuad,pg34dYQuad,pg34dZQuad,pg43dXQuad,pg43dYQuad,pg43dZQuad,
pgd02dXQuad,pgd02dYQuad,pgd02dZQuad,pgd20dXQuad,pgd20dYQuad,pgd20dZQuad,
g1LengthQuad,g2LengthQuad,g3LengthQuad,g4LengthQuad,gd2LengthQuad,
d2DampQuad[f]]

noiseSeisQuad[nn_,jj_,f_]:=Part[coupleMatQuad,jj].seisQuad[nn,jj,nItemQuad,f,
mass1Quad,iRoll1Quad,iPitch1Quad,iYaw1Quad,mass2Quad,iRoll2Quad,iPitch2Quad,iYaw2Quad,mass3Quad,iRoll3Quad,iPitch3Quad,iYaw3Quad,mass4Quad,iRoll4Quad,iPitch4Quad,iYaw4Quad,massd2Quad,iRolld2Quad,iPitchd2Quad,iYawd2Quad,
g10HQuad,g10VQuad,g12HQuad,g12VQuad,g21HQuad,g21VQuad,g23HQuad,g23VQuad,g32HQuad,g32VQuad,g34HQuad,g34VQuad,g43HQuad,g43VQuad,gd20HQuad,gd20VQuad,
t10RollQuad,t10PitchQuad,t10YawQuad,t12RollQuad,t12PitchQuad,t12YawQuad,t21RollQuad,t21PitchQuad,t21YawQuad,t23RollQuad,t23PitchQuad,t23YawQuad,t32RollQuad,t32PitchQuad,t32YawQuad,t34RollQuad,t34PitchQuad,t34YawQuad,t43RollQuad,t43PitchQuad,t43YawQuad,td20RollQuad,td20PitchQuad,td20YawQuad,
ct10RollQuad,ct10PitchQuad,ct10YawQuad,ct12RollQuad,ct12PitchQuad,ct12YawQuad,ct21RollQuad,ct21PitchQuad,ct21YawQuad,ct23RollQuad,ct23PitchQuad,ct23YawQuad,ct32RollQuad,ct32PitchQuad,ct32YawQuad,ct34RollQuad,ct34PitchQuad,ct34YawQuad,ct43RollQuad,ct43PitchQuad,ct43YawQuad,ctd20RollQuad,ctd20PitchQuad,ctd20YawQuad,
pg01XQuad,pg01YQuad,pg01ZQuad,pg10XQuad,pg10YQuad,pg10ZQuad,pg12XQuad,pg12YQuad,pg12ZQuad,pg21XQuad,pg21YQuad,pg21ZQuad,pg23XQuad,pg23YQuad,pg23ZQuad,pg32XQuad,pg32YQuad,pg32ZQuad,pg34XQuad,pg34YQuad,pg34ZQuad,pg43XQuad,pg43YQuad,pg43ZQuad,
pgd02XQuad,pgd02YQuad,pgd02ZQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,
pg01dXQuad,pg01dYQuad,pg01dZQuad,pg10dXQuad,pg10dYQuad,pg10dZQuad,pg12dXQuad,pg12dYQuad,pg12dZQuad,pg21dXQuad,pg21dYQuad,pg21dZQuad,pg23dXQuad,pg23dYQuad,pg23dZQuad,pg32dXQuad,pg32dYQuad,pg32dZQuad,pg34dXQuad,pg34dYQuad,pg34dZQuad,pg43dXQuad,pg43dYQuad,pg43dZQuad,
pgd02dXQuad,pgd02dYQuad,pgd02dZQuad,pgd20dXQuad,pgd20dYQuad,pgd20dZQuad,
g1LengthQuad,g2LengthQuad,g3LengthQuad,g4LengthQuad,gd2LengthQuad,
d2DampQuad[f]]

dispTNoiseQuad[ll_,nn_,f_]:=Abs[tNoiseQuad[ll,nn,f,
mass1Quad,iRoll1Quad,iPitch1Quad,iYaw1Quad,mass2Quad,iRoll2Quad,iPitch2Quad,iYaw2Quad,mass3Quad,iRoll3Quad,iPitch3Quad,iYaw3Quad,mass4Quad,iRoll4Quad,iPitch4Quad,iYaw4Quad,massd2Quad,iRolld2Quad,iPitchd2Quad,iYawd2Quad,
g10HThermalQuad,g10VThermalQuad,g12HThermalQuad,g12VThermalQuad,g21HThermalQuad,g21VThermalQuad,g23HThermalQuad,g23VThermalQuad,g32HThermalQuad,g32VThermalQuad,g34HThermalQuad,g34VThermalQuad,g43HThermalQuad,g43VThermalQuad,gd20HThermalQuad,gd20VThermalQuad,
t10RollThermalQuad,t10PitchThermalQuad,t10YawThermalQuad,t12RollThermalQuad,t12PitchThermalQuad,t12YawThermalQuad,t21RollThermalQuad,t21PitchThermalQuad,t21YawThermalQuad,t23RollThermalQuad,t23PitchThermalQuad,t23YawThermalQuad,t32RollThermalQuad,t32PitchThermalQuad,t32YawThermalQuad,t34RollThermalQuad,t34PitchThermalQuad,t34YawThermalQuad,t43RollThermalQuad,t43PitchThermalQuad,t43YawThermalQuad,td20RollThermalQuad,td20PitchThermalQuad,td20YawThermalQuad,
ct10RollThermalQuad,ct10PitchThermalQuad,ct10YawThermalQuad,ct12RollThermalQuad,ct12PitchThermalQuad,ct12YawThermalQuad,ct21RollThermalQuad,ct21PitchThermalQuad,ct21YawThermalQuad,ct23RollThermalQuad,ct23PitchThermalQuad,ct23YawThermalQuad,ct32RollThermalQuad,ct32PitchThermalQuad,ct32YawThermalQuad,ct34RollThermalQuad,ct34PitchThermalQuad,ct34YawThermalQuad,ct43RollThermalQuad,ct43PitchThermalQuad,ct43YawThermalQuad,ctd20RollThermalQuad,ctd20PitchThermalQuad,ctd20YawThermalQuad,
pg01XQuad,pg01YQuad,pg01ZQuad,pg10XQuad,pg10YQuad,pg10ZQuad,pg12XQuad,pg12YQuad,pg12ZQuad,pg21XQuad,pg21YQuad,pg21ZQuad,pg23XQuad,pg23YQuad,pg23ZQuad,pg32XQuad,pg32YQuad,pg32ZQuad,pg34XQuad,pg34YQuad,pg34ZQuad,pg43XQuad,pg43YQuad,pg43ZQuad,
pgd02XQuad,pgd02YQuad,pgd02ZQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,
pg01dXQuad,pg01dYQuad,pg01dZQuad,pg10dXQuad,pg10dYQuad,pg10dZQuad,pg12dXQuad,pg12dYQuad,pg12dZQuad,pg21dXQuad,pg21dYQuad,pg21dZQuad,pg23dXQuad,pg23dYQuad,pg23dZQuad,pg32dXQuad,pg32dYQuad,pg32dZQuad,pg34dXQuad,pg34dYQuad,pg34dZQuad,pg43dXQuad,pg43dYQuad,pg43dZQuad,
pgd02dXQuad,pgd02dYQuad,pgd02dZQuad,pgd20dXQuad,pgd20dYQuad,pgd20dZQuad,
g1LengthQuad,g2LengthQuad,g3LengthQuad,g4LengthQuad,gd2LengthQuad,
d2DampQuad[f]]]

noiseTNoiseQuad[ll_,nn_,jj_,f_] := {1}.coupleMatQuad[[jj]]*trfQuad[ll,nn,jj,f]*dispTNoiseQuad[ll,nn,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)

seismic noise

noiseSeisSumQuad[f_] := Sqrt[Sum[Sum[noiseSeisQuad[nn,jj,f],{jj,1,6}]^2,{nn,1,6}]]

noiseSeisCompQuad[f_] := Sqrt[Sum[noiseSeisQuad[nn,jj,f]^2,{nn,1,6}]]

suspension thermal noise (without violin mode)

noiseTNoiseSumQuad[f_] := Sqrt[Sum[Sum[Sum[noiseTNoiseQuad[ll,nn,jj,f],{jj,1,6}]^2,{ll,1,6}],{nn,1, nTotalQuad}]]

noiseTNoiseCompDouble[jj_,f_] := Sqrt[Sum[Sum[noiseTNoiseQuad[ll,nn,jj,f]^2,{ll,1,6}],{nn,1, nTotalQuad}]] (*sum up of noise in "jj" direction*)

Q & resonant frequency

resQuad=f  /. NSolve[Det[matQuad[f,
mass1Quad,iRoll1Quad,iPitch1Quad,iYaw1Quad,mass2Quad,iRoll2Quad,iPitch2Quad,iYaw2Quad,mass3Quad,iRoll3Quad,iPitch3Quad,iYaw3Quad,mass4Quad,iRoll4Quad,iPitch4Quad,iYaw4Quad,massd2Quad,iRolld2Quad,iPitchd2Quad,iYawd2Quad,
g10HQuad,g10VQuad,g12HQuad,g12VQuad,g21HQuad,g21VQuad,g23HQuad,g23VQuad,g32HQuad,g32VQuad,g34HQuad,g34VQuad,g43HQuad,g43VQuad,gd20HQuad,gd20VQuad,
t10RollQuad,t10PitchQuad,t10YawQuad,t12RollQuad,t12PitchQuad,t12YawQuad,t21RollQuad,t21PitchQuad,t21YawQuad,t23RollQuad,t23PitchQuad,t23YawQuad,t32RollQuad,t32PitchQuad,t32YawQuad,t34RollQuad,t34PitchQuad,t34YawQuad,t43RollQuad,t43PitchQuad,t43YawQuad,td20RollQuad,td20PitchQuad,td20YawQuad,
ct10RollQuad,ct10PitchQuad,ct10YawQuad,ct12RollQuad,ct12PitchQuad,ct12YawQuad,ct21RollQuad,ct21PitchQuad,ct21YawQuad,ct23RollQuad,ct23PitchQuad,ct23YawQuad,ct32RollQuad,ct32PitchQuad,ct32YawQuad,ct34RollQuad,ct34PitchQuad,ct34YawQuad,ct43RollQuad,ct43PitchQuad,ct43YawQuad,ctd20RollQuad,ctd20PitchQuad,ctd20YawQuad,
pg01XQuad,pg01YQuad,pg01ZQuad,pg10XQuad,pg10YQuad,pg10ZQuad,pg12XQuad,pg12YQuad,pg12ZQuad,pg21XQuad,pg21YQuad,pg21ZQuad,pg23XQuad,pg23YQuad,pg23ZQuad,pg32XQuad,pg32YQuad,pg32ZQuad,pg34XQuad,pg34YQuad,pg34ZQuad,pg43XQuad,pg43YQuad,pg43ZQuad,
pgd02XQuad,pgd02YQuad,pgd02ZQuad,pgd20XQuad,pgd20YQuad,pgd20ZQuad,
pg01dXQuad,pg01dYQuad,pg01dZQuad,pg10dXQuad,pg10dYQuad,pg10dZQuad,pg12dXQuad,pg12dYQuad,pg12dZQuad,pg21dXQuad,pg21dYQuad,pg21dZQuad,pg23dXQuad,pg23dYQuad,pg23dZQuad,pg32dXQuad,pg32dYQuad,pg32dZQuad,pg34dXQuad,pg34dYQuad,pg34dZQuad,pg43dXQuad,pg43dYQuad,pg43dZQuad,
pgd02dXQuad,pgd02dYQuad,pgd02dZQuad,pgd20dXQuad,pgd20dYQuad,pgd20dZQuad,
g1LengthQuad,g2LengthQuad,g3LengthQuad,g4LengthQuad,gd2LengthQuad,
d2DampQuad[f]]]==0,f];

Sort[resQuad/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

Plots - better case

all components

plotSeis1Quad = LogLogPlot[2*noiseSeisSumQuad[f],{f,0.1,10},PlotStyle -> RGBColor[0,1,0]]

plotSeis2Quad = LogLogPlot[2*noiseSeisSumQuad[f],{f,10,100},PlotStyle -> RGBColor[0,1,0]]

plotSeis3Quad = LogLogPlot[2*noiseSeisSumQuad[f],{f,100,1000},PlotStyle -> RGBColor[0,1,0]]

plotSeisQuad=Show[plotSeis1Quad,plotSeis2Quad,plotSeis3Quad,PlotRange -> All]

plotTN1Quad =LogLogPlot[2*noiseTNoiseSumQuad[f],{f,0.1,10},PlotStyle -> RGBColor[0,0,1]]

plotTN2Quad =LogLogPlot[2*noiseTNoiseSumQuad[f],{f,10,100},PlotStyle -> RGBColor[0,0,1]]

plotTN3Quad =LogLogPlot[2*noiseTNoiseSumQuad[f],{f,100,1000},PlotStyle -> RGBColor[0,0,1]]

plotTNQuad = Show[plotTN1Quad,plotTN2Quad,plotTN3Quad,PlotRange -> All]

plotShotQuad=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0.5,0]]

Show[plotSeisQuad,plotTNQuad,plotShotQuad,plotCLIOmodel]

Show[plotSeisQuad,plotTNQuad,plotCLIOmodel,plotCLIORoommodel,plotShotQuad,plotLISM030320]

2 noiseTNoiseSumQuad[100]

Show[plotTN2Quad,plotTN3Quad,plotSeis2Quad,plotCLIOmodel,plotShotQuad,plotCLIOMTNRoom,PlotRange -> All ]

all components 2

plotSeis101Quad = LogLogPlot[2*noiseSeisSumQuad[f],{f,0.1,10},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis102Quad = LogLogPlot[2*noiseSeisSumQuad[f],{f,10,100},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis103Quad = LogLogPlot[2*noiseSeisSumQuad[f],{f,100,1000},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeisQuad2=Show[plotSeis101Quad,plotSeis102Quad,plotSeis103Quad,PlotRange -> All]

plotTN101Quad =LogLogPlot[2*noiseTNoiseSumQuad[f],{f,0.1,10},PlotStyle -> RGBColor[0.5,0,1]]

plotTN102Quad =LogLogPlot[2*noiseTNoiseSumQuad[f],{f,10,100},PlotStyle -> RGBColor[0.5,0,1]]

plotTN103Quad =LogLogPlot[2*noiseTNoiseSumQuad[f],{f,100,1000},PlotStyle -> RGBColor[0.5,0,1]]

plotTNQuad2 = Show[plotTN101Quad,plotTN102Quad,plotTN103Quad,PlotRange -> All]

plotShotQuad102=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0,0.5]]

Show[plotTN102Quad,plotTN2Quad,plotCLIO25model]

Show[plotTN102Quad,plotSeis102Quad,plotTN2Quad,plotSeis2Quad,plotCLIOmodel]

Show[plotSeis102Quad,plotSeis2Quad,plotCLIOmodel]

Show[plotTN102Quad,plotTN2Quad,plotCLIOmodel]

Show[plotSeisQuad2,plotTNQuad2,plotCLIOmodel,plotShotQuad102]

Show[plotSeisQuad2,plotTNQuad2,plotCLIOmodel,plotShotQuad102,plotLISM030320]

Show[plotSeisQuad,plotTNQuad,plotSeisQuad2,plotTNQuad2,plotShotQuad102,plotCLIOmodel]

Show[plotSeisQuad,plotSeisQuad2,plotShotQuad102,plotCLIOmodel]

Show[plotTNQuad,plotTNQuad2,plotShotQuad102,plotCLIOmodel]

Show[plotShotQuad,plotShotQuad102,plotCLIOmodel]

seismic noise - each component

plot1= LogLogPlot[{noiseSeisQuad[1,1,f],noiseSeisQuad[3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot2=LogLogPlot[{noiseSeisQuad[1,1,f],noiseSeisQuad[3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot3=LogLogPlot[{noiseSeisQuad[1,1,f],noiseSeisQuad[3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

Show[plotSeisQuad,plot1,plot2,plot3,PlotRange -> All]

thermal noise - each component

plot11= LogLogPlot[{noiseTNoiseQuad[1,4,1,f],noiseTNoiseQuad[5,4,1,f],noiseTNoiseQuad[6,4,1,f],noiseTNoiseQuad[3,4,3,f],noiseTNoiseQuad[4,4,3,f],noiseTNoiseQuad[5,4,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot12= LogLogPlot[{noiseTNoiseQuad[1,4,1,f],noiseTNoiseQuad[5,4,1,f],noiseTNoiseQuad[6,4,1,f],noiseTNoiseQuad[3,4,3,f],noiseTNoiseQuad[4,4,3,f],noiseTNoiseQuad[5,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot13= LogLogPlot[{noiseTNoiseQuad[1,4,1,f],noiseTNoiseQuad[5,4,1,f],noiseTNoiseQuad[6,4,1,f],noiseTNoiseQuad[3,4,3,f],noiseTNoiseQuad[4,4,3,f],noiseTNoiseQuad[5,4,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNQuad,plot11,plot12,plot13,plotCLIOmodel]

Show[plot12,plotTNQuad,plotCLIOmodel]

plot21= LogLogPlot[{noiseTNoiseQuad[1,3,1,f],noiseTNoiseQuad[5,3,1,f],noiseTNoiseQuad[6,3,1,f],noiseTNoiseQuad[3,3,3,f],noiseTNoiseQuad[4,3,3,f],noiseTNoiseQuad[5,3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot22= LogLogPlot[{noiseTNoiseQuad[1,3,1,f],noiseTNoiseQuad[5,3,1,f],noiseTNoiseQuad[6,3,1,f],noiseTNoiseQuad[3,3,3,f],noiseTNoiseQuad[4,3,3,f],noiseTNoiseQuad[5,3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot23= LogLogPlot[{noiseTNoiseQuad[1,3,1,f],noiseTNoiseQuad[5,3,1,f],noiseTNoiseQuad[6,3,1,f],noiseTNoiseQuad[3,3,3,f],noiseTNoiseQuad[4,3,3,f],noiseTNoiseQuad[5,3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNQuad,plot21,plot22,plot23,plotCLIOmodel]

Show[plot22,plotTNQuad,plotCLIOmodel]

Plot[{f,2 f,3 f,4 f,5 f,6 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot24= LogLogPlot[{noiseTNoiseQuad[3,3,3,f],noiseTNoiseQuad[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

plot25= LogLogPlot[{noiseTNoiseQuad[3,3,3,f],noiseTNoiseQuad[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

Show[plot24,plot24bc,plotCLIOmodel]

Show[plot25,plot24bc,plotCLIOmodel]

thermal noise - each direction

plot31= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot32= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot33= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

Show[plotTNQuad,plot31,plot32,plot33,plotCLIOmodel,PlotRange -> All]

plot34 =Show[plot32,plot33,PlotRange -> All]

Show[plot34,plotCLIOmodel,plotTN2Quad,plotTN3Quad]

Plot[{f,2 f,3 f,4 f,5 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

thermal noise - each dissipation g4

plot41= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.8]}]

plot42= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.8]}]

plot43= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.8]}]

Show[plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

Show[plotTNbcQuad,plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

thermal noise - each dissipation g3

plot51= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0.8]}]

plot52= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0.8]}]

plot53= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0.8]}]

plot54= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

Show[plotTNQuad,plot51,plot52,plot53,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plotTNQuad]

Show[plot54,plot52]

thermal noise - each dissipation magnet damping

plot61= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0]}]

plot62= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0]}]

plot63= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0]}]

Show[plotTNQuad,plot61,plot62,plot63,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plot62,plotTNQuad]

Plots - bad case

all components

plotCLIOmodel= LogLogPlot[dispCLIOModel[f],{f,10,1000}]

plotSeis1bcQuad = LogLogPlot[2*noiseSeisSumQuad[f],{f,0.1,10},PlotStyle -> RGBColor[0,1,0]]

plotSeis2bcQuad = LogLogPlot[2*noiseSeisSumQuad[f],{f,10,100},PlotStyle -> RGBColor[0,1,0]]

plotSeis3bcQuad = LogLogPlot[2*noiseSeisSumQuad[f],{f,100,1000},PlotStyle -> RGBColor[0,1,0]]

plotSeisbcQuad=Show[plotSeis1bcQuad,plotSeis2bcQuad,plotSeis3bcQuad,PlotRange -> All]

plotTN1bcQuad =LogLogPlot[2*noiseTNoiseSumQuad[f],{f,0.1,10},PlotStyle -> RGBColor[0,0,1]]

plotTN2bcQuad =LogLogPlot[2*noiseTNoiseSumQuad[f],{f,10,100},PlotStyle -> RGBColor[0,0,1]]

plotTN3bcQuad =LogLogPlot[2*noiseTNoiseSumQuad[f],{f,100,1000},PlotStyle -> RGBColor[0,0,1]]

plotTNbcQuad = Show[plotTN1bcQuad,plotTN2bcQuad,plotTN3bcQuad,PlotRange -> All]

Show[plotSeisbcQuad,plotTNbcQuad,plotCLIOmodel]

Show[plotSeisbcQuad,plotTNvcQuad,plotCLIOmodel,plotLISM030320]

Show[plotTN2bcQuad,plotTN3bcQuad,plotSeis2bcQuad,plotSeis3bcQuad,plotCLIOmodel,PlotRange -> All,GridLines -> Automatic ]

seismic noise - each component

plot1bc= LogLogPlot[{noiseSeisQuad[1,1,f],noiseSeisQuad[3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot2bc=LogLogPlot[{noiseSeisQuad[1,1,f],noiseSeisQuad[3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot3bc=LogLogPlot[{noiseSeisQuad[1,1,f],noiseSeisQuad[3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

Show[plotSeisQuad,plot1bc,plot2bc,plot3bc,PlotRange -> All]

thermal noise - each component

plot11bc= LogLogPlot[{noiseTNoiseQuad[1,4,1,f],noiseTNoiseQuad[5,4,1,f],noiseTNoiseQuad[6,4,1,f],noiseTNoiseQuad[3,4,3,f],noiseTNoiseQuad[4,4,3,f],noiseTNoiseQuad[5,4,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot12bc= LogLogPlot[{noiseTNoiseQuad[1,4,1,f],noiseTNoiseQuad[5,4,1,f],noiseTNoiseQuad[6,4,1,f],noiseTNoiseQuad[3,4,3,f],noiseTNoiseQuad[4,4,3,f],noiseTNoiseQuad[5,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot13bc= LogLogPlot[{noiseTNoiseQuad[1,4,1,f],noiseTNoiseQuad[5,4,1,f],noiseTNoiseQuad[6,4,1,f],noiseTNoiseQuad[3,4,3,f],noiseTNoiseQuad[4,4,3,f],noiseTNoiseQuad[5,4,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNbcQuad,plot11bc,plot12bc,plot13bc,plotCLIOmodel]

Show[plot12bc,plotTNbcQuad,plotCLIOmodel]

plot21bc= LogLogPlot[{noiseTNoiseQuad[1,3,1,f],noiseTNoiseQuad[5,3,1,f],noiseTNoiseQuad[6,3,1,f],noiseTNoiseQuad[3,3,3,f],noiseTNoiseQuad[4,3,3,f],noiseTNoiseQuad[5,3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot22bc= LogLogPlot[{noiseTNoiseQuad[1,3,1,f],noiseTNoiseQuad[5,3,1,f],noiseTNoiseQuad[6,3,1,f],noiseTNoiseQuad[3,3,3,f],noiseTNoiseQuad[4,3,3,f],noiseTNoiseQuad[5,3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot23bc= LogLogPlot[{noiseTNoiseQuad[1,3,1,f],noiseTNoiseQuad[5,3,1,f],noiseTNoiseQuad[6,3,1,f],noiseTNoiseQuad[3,3,3,f],noiseTNoiseQuad[4,3,3,f],noiseTNoiseQuad[5,3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNbcQuad,plot21bc,plot22bc,plot23bc,plotCLIOmodel]

Show[plot22bc,plotTNbcQuad,plotCLIOmodel]

Plot[{f,2 f,3 f,4 f,5 f,6 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot24bc= LogLogPlot[{noiseTNoiseQuad[3,3,3,f],noiseTNoiseQuad[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[0.5,0.5,1]}]

Show[plot24bc,plotTNbcQuad,plotCLIOmodel]

thermal noise - each direction

plot31bc= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot32bc= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot33bc= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

Show[plotTNbcQuad,plot31bc,plot32bc,plot33bc,plotCLIOmodel,PlotRange -> All]

plot34bc=Show[plot32bc,plot33bc,PlotRange -> All]

Show[plot34bc,plotCLIOmodel,plotTN2bcQuad,plotTN3bcQuad]

Plot[{f,2 f,3 f,4 f,5 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

coil[x_,y_,a_] := ((Sqrt[(x+a)^2+(y+a)^2])/((x+a) (y+a)))-((Sqrt[(x+a)^2+(y-a)^2])/((x+a) (y-a)))-((Sqrt[(x-a)^2+(y+a)^2])/((x-a) (y+a)))+((Sqrt[(x-a)^2+(y-a)^2])/((x-a) (y-a)))

Plot3D[coil[x,y,1.5],{x,-1,1},{y,-1,1}]

Plot[coil[x,0,1.5],{x,-0.0001,0.0001}]

thermal noise - each dissipation g4

plot41bc= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5]}]

plot42bc= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5]}]

plot43bc= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5]}]

Show[plotTNbcQuad,plot41bc,plot42bc,plot43bc,plotCLIOmodel,PlotRange -> All]

thermal noise - each dissipation g3

plot51bc= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0.5]}]

plot52bc= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0.5]}]

plot53bc= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0.5]}]

Show[plotTNbcQuad,plot51bc,plot52bc,plot53bc,plotCLIOmodel,PlotRange -> All]

Show[plot52bc,plot42bc,plot62bc,PlotRange -> All]

thermal noise - each dissipation magnet damping

plot61bc= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,1,0]}]

plot62bc= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,1,0]}]

plot63bc= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,1,0]}]

Show[plotTNbcQuad,plot61bc,plot62bc,plot63bc,plotCLIOmodel,PlotRange -> All]

Quad pendulum simplified (2004/01)

Parameters

intersting item

nItemQuadS = 4 ;

coupling & vibration amplification in cryostat

coupleZXQuadS =5/100;(*coupling Z -> X*)
coupleYXQuadS = 10/100;(*coupling Y -> X*)

offset of beam centering

offsetRollQuadS = 0 mm;
offsetPitchQuadS = 0.1 mm;
offsetYawQuadS = 0.1 mm;

dimensions of mass for quad pendulum

m1

m1DensQuadS = alDens;
m1XQuadS = 100mm;
m1YQuadS = 100mm;
m1ZQuadS = 70 mm;
mCube[m1DensQuadS,m1XQuadS,m1YQuadS,m1ZQuadS]

m2

m2DensQuadS = alDens;
m2XQuadS = 100mm;
m2YQuadS = 100 mm;
m2ZQuadS = 70 mm;
mCube[m2DensQuadS,m2XQuadS,m2YQuadS,m2ZQuadS]

m3

m3DensQuadS =susDens;
m3XQuadS = 70mm;
m3YQuadS = 70 mm;
m3ZQuadS = 50 mm;
mCube[m3DensQuadS,m3XQuadS,m3YQuadS,m3ZQuadS]

m4

m4DensQuadS = saDens;
m4rQuadS = rMass;
m4lQuadS = lMass;

m2d

md2DensQuadS = susDens;
md2XQuadS = 120mm;
md2YQuadS = 100 mm;
md2ZQuadS = 50 mm;
md2dQuadS = 5 mm;
mCage[md2DensQuadS,md2XQuadS,md2YQuadS,md2ZQuadS,md2dQuadS]

spring for quad pendulum

g1

g1LengthQuadS = 1 cm;
g1VFreqQuadS = 4 Hz;

g2

g2LengthQuadS = 25 cm;
g2VFreqQuadS = 4 Hz;

g3

g3LengthQuadS = 100 cm;
g3VFreqQuadS = 4 Hz;

g4

g4LengthQuadS = lSaPend ;

gd2

gd2LengthQuadS = 1 cm;
gd2VFreqQuadS = 5 Hz;

position of wire clamp from COM (4 wires + symmetrical distribution) for quad pendulum

pg01XQuadS = 20 mm;
pg01YQuadS = 50 mm;
pg01ZQuadS = 0 mm;
pg01dXQuadS = 0.1 mm*10;
pg01dYQuadS = 0.1 mm*10;
pg01dZQuadS = 0.1 mm*10;

pg10XQuadS = pg01XQuadS;
pg10YQuadS = pg01YQuadS ;
pg10ZQuadS = m1ZQuadS/2;
pg10dXQuadS = 0.1 mm*10;
pg10dYQuadS = 0.1 mm*10 ;
pg10dZQuadS = 0.1 mm*10;

pg12XQuadS = 20 mm;
pg12YQuadS = 50 mm;
pg12ZQuadS = -m1ZQuadS/2;
pg12dXQuadS = 0.1 mm*10;
pg12dYQuadS = 0.1 mm*10;
pg12dZQuadS = 0.1 mm*10;

pg21XQuadS = pg12XQuadS;
pg21YQuadS = pg12YQuadS ;
pg21ZQuadS = m2ZQuadS/2;
pg21dXQuadS = 0.1 mm*10;
pg21dYQuadS = 0.1 mm*10 ;
pg21dZQuadS = 0.1 mm*10;

pg23XQuadS=10 mm;
pg23YQuadS=50 mm;
pg23ZQuadS=-m2ZQuadS/2;
pg23dXQuadS=0.1 mm*10;
pg23dYQuadS=0.1 mm*10;
pg23dZQuadS=0.1 mm*10;

pg32XQuadS=pg23XQuadS;
pg32YQuadS=pg23YQuadS;
pg32ZQuadS=m3ZQuadS/2;
pg32dXQuadS=0.1 mm*10;
pg32dYQuadS=0.1 mm*10;
pg32dZQuadS=0.1 mm*10;

pg34XQuadS=10 mm;
pg34YQuadS=rMass/2-0 mm;
pg34ZQuadS=-0 mm;
pg34dXQuadS=0.1 mm*10;
pg34dYQuadS=0.1 mm*10;
pg34dZQuadS=0.1 mm*10;

pg43XQuadS=pg34XQuadS;
pg43YQuadS=rMass/2;
pg43ZQuadS= 0 mm;
pg43dXQuadS=0.1 mm*10;
pg43dYQuadS=0.1 mm*10;
pg43dZQuadS= 0.1 mm*10;

pgd02XQuadS = 180 mm/2;
pgd02YQuadS = 130 mm/2 ;
pgd02ZQuadS = -0 mm*1;
pgd02dXQuadS = 0.1 mm*10;
pgd02dYQuadS = 0.1 mm*10;
pgd02dZQuadS = 0.1 mm*10;

pgd20XQuadS = pgd02XQuadS;
pgd20YQuadS = pgd02YQuadS ;
pgd20ZQuadS = 0 mm*1;
pgd20dXQuadS = 0.1 mm*10;
pgd20dYQuadS = 0.1 mm*10;
pgd20dZQuadS = 0.1 mm*10;

dissipation

qRoomHQuadS = 10^6;
qCryoHQuadS = 10^7;
qRoomVQuadS = 10^4;
qCryoVQuadS  =10^5;

qSaHQuadS =  1/(3 10^(-7));
qSaVQuadS =  10^6;

qg3VQuadS = qCryoVQuadS;

g3TempVQuadS = m3TempQuadS;(*縦防振の板ばねをcryoに入れるときはm3TempQuadS,それ以外はm2TempQuadS*)

in spring

g10HPhiQuadS =  1/qRoomHQuadS;
g10VPhiQuadS =   1/qRoomVQuadS;

g12HPhiQuadS =   1/qRoomHQuadS;
g12VPhiQuadS =  1/qRoomVQuadS;

g21HPhiQuadS =  1/qRoomHQuadS;
g21VPhiQuadS =   1/qRoomVQuadS;

g23HPhiQuadS =   1/qCryoHQuadS;
g23VPhiQuadS =    1/qg3VQuadS;

g32HPhiQuadS =   1/qRoomHQuadS;
g32VPhiQuadS =    1/qg3VQuadS;

g34HPhiQuadS =  1/qSaHQuadS;
g34VPhiQuadS =  1/qSaVQuadS;

g43HPhiQuadS =  1/qSaHQuadS;
g43VPhiQuadS = 1/qSaVQuadS;

gd20HPhiQuadS =  1/qRoomHQuadS;
gd20VPhiQuadS =  1/qRoomVQuadS;

magnet damping

d2DampFQuadS = 5 Hz;
d2DampQQuadS = 10*1;

temperature for triple pendulum

m1TempQuadS = 300 K;
m2TempQuadS = 300 K;
m3TempQuadS = 13 K;
m4TempQuadS = 25 K;
md2TempQuadS = 300 K;

Preparation

coupling matrix

coupleMatQuadS=(({{1}, {coupleYXQuadS}, {coupleZXQuadS}, {offsetRollQuadS}, {offsetPitchQuadS}, {offsetYawQuadS}}));

mass & moment inertia for QuadS pendulum

m1

mass1QuadS = mCube[m1DensQuadS, m1XQuadS,m1YQuadS, m1ZQuadS]; 
iRoll1QuadS = mIRollCube[m1DensQuadS, m1XQuadS,m1YQuadS, m1ZQuadS];
iPitch1QuadS = mIPitchCube[m1DensQuadS, m1XQuadS,m1YQuadS, m1ZQuadS];
iYaw1QuadS = mIYawCube[m1DensQuadS, m1XQuadS,m1YQuadS, m1ZQuadS];

m2

mass2QuadS = mCube[m2DensQuadS, m2XQuadS,m2YQuadS, m2ZQuadS]; 
iRoll2QuadS = mIRollCube[m2DensQuadS, m2XQuadS,m2YQuadS, m2ZQuadS];
iPitch2QuadS = mIPitchCube[m2DensQuadS, m2XQuadS,m2YQuadS, m2ZQuadS];
iYaw2QuadS = mIYawCube[m2DensQuadS, m2XQuadS,m2YQuadS, m2ZQuadS];

m3

mass3QuadS = mCube[m3DensQuadS, m3XQuadS,m3YQuadS, m3ZQuadS]; 
iRoll3QuadS = mIRollCube[m3DensQuadS, m3XQuadS,m3YQuadS, m3ZQuadS];
iPitch3QuadS = mIPitchCube[m3DensQuadS, m3XQuadS,m3YQuadS, m3ZQuadS];
iYaw3QuadS = mIYawCube[m3DensQuadS, m3XQuadS,m3YQuadS, m3ZQuadS];

m4

mass4QuadS = mMass; (*see Parameters/Dimensions of final suspension/final mass*)
iRoll4QuadS = mILCyl[m4DensQuadS, m4rQuadS,m4lQuadS];
iPitch4QuadS = mIRCyl[m4DensQuadS, m4rQuadS,m4lQuadS];
iYaw4QuadS = mIRCyl[m4DensQuadS, m4rQuadS,m4lQuadS];

md2(cage)

massd2QuadS = mCage[md2DensQuadS, md2XQuadS,md2YQuadS, md2ZQuadS,md2dQuadS];
iRolld2QuadS = mIRollCage[md2DensQuadS, md2XQuadS,md2YQuadS, md2ZQuadS,md2dQuadS];
iPitchd2QuadS = mIPitchCage[md2DensQuadS, md2XQuadS,md2YQuadS, md2ZQuadS,md2dQuadS];
iYawd2QuadS = mIYawCage[md2DensQuadS, md2XQuadS,md2YQuadS, md2ZQuadS,md2dQuadS];

suspension wire for QuadS pendulum

horizontal

g1HScQuadS = scPend[mass1QuadS+mass2QuadS+mass3QuadS+mass4QuadS,g1LengthQuadS];
g2HScQuadS = scPend[mass2QuadS+mass3QuadS+mass4QuadS,g2LengthQuadS];
g3HScQuadS = scPend[mass3QuadS+mass4QuadS,g3LengthQuadS];
g4HScQuadS = scPend[mass4QuadS,g4LengthQuadS];
gd2HScQuadS = scPend[massd2QuadS,gd2LengthQuadS];

vertical

g1VScQuadS = scFreq[mass1QuadS+mass2QuadS+mass3QuadS+mass4QuadS,g1VFreqQuadS];
g2VScQuadS = scFreq[mass2QuadS+mass3QuadS+mass4QuadS,g2VFreqQuadS];
g3VScQuadS = scFreq[mass3QuadS+mass4QuadS,g3VFreqQuadS];
g4VScQuadS = numSaPend*scVert[saYoung,diaSaPend,lSaPend];
gd2VScQuadS = scFreq[massd2QuadS,gd2VFreqQuadS];

g10

g10HQuadS = g1HScQuadS(1 +I g10HPhiQuadS);
g10VQuadS = g1VScQuadS(1 +I g10VPhiQuadS);

g10HThermalQuadS = g1HScQuadS(1 +tRoom I g10HPhiQuadS);
g10VThermalQuadS = g1VScQuadS(1 +tRoom I g10VPhiQuadS);

t10RollQuadS = ctRoll[pg10XQuadS,pg10YQuadS,pg10ZQuadS,pg10XQuadS,pg10YQuadS,pg10ZQuadS,g1HScQuadS,g10HPhiQuadS,g1VScQuadS,g10VPhiQuadS];
t10PitchQuadS = ctPitch[pg10XQuadS,pg10YQuadS,pg10ZQuadS,pg10XQuadS,pg10YQuadS,pg10ZQuadS,g1HScQuadS,g10HPhiQuadS,g1VScQuadS,g10VPhiQuadS];
t10YawQuadS = ctYaw[pg10XQuadS,pg10YQuadS,pg10ZQuadS,pg10XQuadS,pg10YQuadS,pg10ZQuadS,g1HScQuadS,g10HPhiQuadS,g1VScQuadS,g10VPhiQuadS];

t10RollThermalQuadS = ctRoll[pg10XQuadS,pg10YQuadS,pg10ZQuadS,pg10XQuadS,pg10YQuadS,pg10ZQuadS,g1HScQuadS,tRoom g10HPhiQuadS,g1VScQuadS,tRoom g10VPhiQuadS];
t10PitchThermalQuadS = ctPitch[pg10XQuadS,pg10YQuadS,pg10ZQuadS,pg10XQuadS,pg10YQuadS,pg10ZQuadS,g1HScQuadS,tRoom g10HPhiQuadS,g1VScQuadS,tRoom g10VPhiQuadS];
t10YawThermalQuadS = ctYaw[pg10XQuadS,pg10YQuadS,pg10ZQuadS,pg10XQuadS,pg10YQuadS,pg10ZQuadS,g1HScQuadS,tRoom g10HPhiQuadS,g1VScQuadS,tRoom g10VPhiQuadS];

ct10RollQuadS = ctRoll[pg01XQuadS,pg01YQuadS,pg10ZQuadS+g1LengthQuadS,pg01XQuadS,pg01YQuadS,pg01ZQuadS,g1HScQuadS,g10HPhiQuadS,g1VScQuadS,g10VPhiQuadS];
ct10PitchQuadS = ctPitch[pg01XQuadS,pg01YQuadS,pg10ZQuadS+g1LengthQuadS,pg01XQuadS,pg01YQuadS,pg01ZQuadS,g1HScQuadS,g10HPhiQuadS,g1VScQuadS,g10VPhiQuadS];
ct10YawQuadS = ctYaw[pg01XQuadS,pg01YQuadS,pg10ZQuadS+g1LengthQuadS,pg01XQuadS,pg01YQuadS,pg01ZQuadS,g1HScQuadS,g10HPhiQuadS,g1VScQuadS,g10VPhiQuadS];

ct10RollThermalQuadS = ctRoll[pg01XQuadS,pg01YQuadS,pg10ZQuadS+g1LengthQuadS,pg01XQuadS,pg01YQuadS,pg01ZQuadS,g1HScQuadS,tRoom g10HPhiQuadS,g1VScQuadS,tRoom g10VPhiQuadS];
ct10PitchThermalQuadS = ctPitch[pg01XQuadS,pg01YQuadS,pg10ZQuadS+g1LengthQuadS,pg01XQuadS,pg01YQuadS,pg01ZQuadS,g1HScQuadS,tRoom g10HPhiQuadS,g1VScQuadS,tRoom g10VPhiQuadS];
ct10YawThermalQuadS = ctYaw[pg01XQuadS,pg01YQuadS,pg10ZQuadS+g1LengthQuadS,pg01XQuadS,pg01YQuadS,pg01ZQuadS,g1HScQuadS,tRoom g10HPhiQuadS,g1VScQuadS,tRoom g10VPhiQuadS];

g12

g12HQuadS = g2HScQuadS(1 +I g12HPhiQuadS);
g12VQuadS = g2VScQuadS(1 +I g12VPhiQuadS);

g12HThermalQuadS = g2HScQuadS(1 +tRoom I g12HPhiQuadS);
g12VThermalQuadS = g2VScQuadS(1 +tRoom I g12VPhiQuadS);

t12RollQuadS = ctRoll[pg12XQuadS,pg12YQuadS,pg12ZQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,g12HPhiQuadS,g2VScQuadS,g12VPhiQuadS];
t12PitchQuadS = ctPitch[pg12XQuadS,pg12YQuadS,pg12ZQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,g12HPhiQuadS,g2VScQuadS,g12VPhiQuadS];
t12YawQuadS = ctYaw[pg12XQuadS,pg12YQuadS,pg12ZQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,g12HPhiQuadS,g2VScQuadS,g12VPhiQuadS];

t12RollThermalQuadS = ctRoll[pg12XQuadS,pg12YQuadS,pg12ZQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,tRoom g12HPhiQuadS,g2VScQuadS,tRoom g12VPhiQuadS];
t12PitchThermalQuadS = ctPitch[pg12XQuadS,pg12YQuadS,pg12ZQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,tRoom g12HPhiQuadS,g2VScQuadS,tRoom g12VPhiQuadS];
t12YawThermalQuadS = ctYaw[pg12XQuadS,pg12YQuadS,pg12ZQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,tRoom g12HPhiQuadS,g2VScQuadS,tRoom g12VPhiQuadS];

ct12RollQuadS = ctRoll[pg21XQuadS,pg21YQuadS,pg12ZQuadS-g2LengthQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,g12HPhiQuadS,g2VScQuadS,g12VPhiQuadS];
ct12PitchQuadS = ctPitch[pg21XQuadS,pg21YQuadS,pg12ZQuadS-g2LengthQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,g12HPhiQuadS,g2VScQuadS,g12VPhiQuadS];
ct12YawQuadS = ctYaw[pg21XQuadS,pg21YQuadS,pg12ZQuadS-g2LengthQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,g12HPhiQuadS,g2VScQuadS,g12VPhiQuadS];

ct12RollThermalQuadS = ctRoll[pg21XQuadS,pg21YQuadS,pg12ZQuadS-g2LengthQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,tRoom g12HPhiQuadS,g2VScQuadS,tRoom g12VPhiQuadS];
ct12PitchThermalQuadS = ctPitch[pg21XQuadS,pg21YQuadS,pg12ZQuadS-g2LengthQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,tRoom g12HPhiQuadS,g2VScQuadS,tRoom g12VPhiQuadS];
ct12YawThermalQuadS = ctYaw[pg21XQuadS,pg21YQuadS,pg12ZQuadS-g2LengthQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,tRoom g12HPhiQuadS,g2VScQuadS,tRoom g12VPhiQuadS];

g21

g21HQuadS = g2HScQuadS(1 +I g21HPhiQuadS);
g21VQuadS = g2VScQuadS(1 +I g21VPhiQuadS);

g21HThermalQuadS = g2HScQuadS(1 +tRoom I g21HPhiQuadS);
g21VThermalQuadS = g2VScQuadS(1 +tRoom I g21VPhiQuadS);

t21RollQuadS = ctRoll[pg21XQuadS,pg21YQuadS,pg21ZQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,g21HPhiQuadS,g2VScQuadS,g21VPhiQuadS];
t21PitchQuadS = ctPitch[pg21XQuadS,pg21YQuadS,pg21ZQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,g21HPhiQuadS,g2VScQuadS,g21VPhiQuadS];
t21YawQuadS = ctYaw[pg21XQuadS,pg21YQuadS,pg21ZQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,g21HPhiQuadS,g2VScQuadS,g21VPhiQuadS];

t21RollThermalQuadS = ctRoll[pg21XQuadS,pg21YQuadS,pg21ZQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,tRoom g21HPhiQuadS,g2VScQuadS,tRoom g21VPhiQuadS];
t21PitchThermalQuadS = ctPitch[pg21XQuadS,pg21YQuadS,pg21ZQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,tRoom g21HPhiQuadS,g2VScQuadS,tRoom g21VPhiQuadS];
t21YawThermalQuadS = ctYaw[pg21XQuadS,pg21YQuadS,pg21ZQuadS,pg21XQuadS,pg21YQuadS,pg21ZQuadS,g2HScQuadS,tRoom g21HPhiQuadS,g2VScQuadS,tRoom g21VPhiQuadS];

ct21RollQuadS = ctRoll[pg12XQuadS,pg12YQuadS,pg21ZQuadS+g2LengthQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,g21HPhiQuadS,g2VScQuadS,g21VPhiQuadS];
ct21PitchQuadS = ctPitch[pg12XQuadS,pg12YQuadS,pg21ZQuadS+g2LengthQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,g21HPhiQuadS,g2VScQuadS,g21VPhiQuadS];
ct21YawQuadS = ctYaw[pg12XQuadS,pg12YQuadS,pg21ZQuadS+g2LengthQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,g21HPhiQuadS,g2VScQuadS,g21VPhiQuadS];

ct21RollThermalQuadS = ctRoll[pg12XQuadS,pg12YQuadS,pg21ZQuadS+g2LengthQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,tRoom g21HPhiQuadS,g2VScQuadS,tRoom g21VPhiQuadS];
ct21PitchThermalQuadS = ctPitch[pg12XQuadS,pg12YQuadS,pg21ZQuadS+g2LengthQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,tRoom g21HPhiQuadS,g2VScQuadS,tRoom g21VPhiQuadS];
ct21YawThermalQuadS = ctYaw[pg12XQuadS,pg12YQuadS,pg21ZQuadS+g2LengthQuadS,pg12XQuadS,pg12YQuadS,pg12ZQuadS,g2HScQuadS,tRoom g21HPhiQuadS,g2VScQuadS,tRoom g21VPhiQuadS];

g23

g23HQuadS = g3HScQuadS(1 +I g23HPhiQuadS);
g23VQuadS = g3VScQuadS(1 +I g23VPhiQuadS);

g23HThermalQuadS = g3HScQuadS(1 +m3TempQuadS I g23HPhiQuadS);
g23VThermalQuadS = g3VScQuadS(1 +g3TempVQuadS I g23VPhiQuadS);

t23RollQuadS = ctRoll[pg23XQuadS,pg23YQuadS,pg23ZQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,g23HPhiQuadS,g3VScQuadS,g23VPhiQuadS];
t23PitchQuadS = ctPitch[pg23XQuadS,pg23YQuadS,pg23ZQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,g23HPhiQuadS,g3VScQuadS,g23VPhiQuadS];
t23YawQuadS = ctYaw[pg23XQuadS,pg23YQuadS,pg23ZQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,g23HPhiQuadS,g3VScQuadS,g23VPhiQuadS];

t23RollThermalQuadS = ctRoll[pg23XQuadS,pg23YQuadS,pg23ZQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,m3TempQuadS g23HPhiQuadS,g3VScQuadS,g3TempVQuadS g23VPhiQuadS];
t23PitchThermalQuadS = ctPitch[pg23XQuadS,pg23YQuadS,pg23ZQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,m3TempQuadS g23HPhiQuadS,g3VScQuadS,g3TempVQuadS g23VPhiQuadS];
t23YawThermalQuadS = ctYaw[pg23XQuadS,pg23YQuadS,pg23ZQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,m3TempQuadS g23HPhiQuadS,g3VScQuadS,g3TempVQuadS g23VPhiQuadS];

ct23RollQuadS = ctRoll[pg32XQuadS,pg32YQuadS,pg23ZQuadS-g3LengthQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,g23HPhiQuadS,g3VScQuadS,g23VPhiQuadS];
ct23PitchQuadS = ctPitch[pg32XQuadS,pg32YQuadS,pg23ZQuadS-g3LengthQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,g23HPhiQuadS,g3VScQuadS,g23VPhiQuadS];
ct23YawQuadS = ctYaw[pg32XQuadS,pg32YQuadS,pg23ZQuadS-g3LengthQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,g23HPhiQuadS,g3VScQuadS,g23VPhiQuadS];

ct23RollThermalQuadS = ctRoll[pg32XQuadS,pg32YQuadS,pg23ZQuadS-g3LengthQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,m3TempQuadS g23HPhiQuadS,g3VScQuadS,g3TempVQuadS g23VPhiQuadS];
ct23PitchThermalQuadS = ctPitch[pg32XQuadS,pg32YQuadS,pg23ZQuadS-g3LengthQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,m3TempQuadS g23HPhiQuadS,g3VScQuadS,g3TempVQuadS g23VPhiQuadS];
ct23YawThermalQuadS = ctYaw[pg32XQuadS,pg32YQuadS,pg23ZQuadS-g3LengthQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,m3TempQuadS g23HPhiQuadS,g3VScQuadS,g3TempVQuadS g23VPhiQuadS];

g32

g32HQuadS = g3HScQuadS(1 +I g32HPhiQuadS);
g32VQuadS = g3VScQuadS(1 +I g32VPhiQuadS);

g32HThermalQuadS = g3HScQuadS(1 +m2TempQuadS I g32HPhiQuadS);
g32VThermalQuadS = g3VScQuadS(1 +g3TempVQuadS I g32VPhiQuadS);

t32RollQuadS = ctRoll[pg32XQuadS,pg32YQuadS,pg32ZQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,g32HPhiQuadS,g3VScQuadS,g32VPhiQuadS];
t32PitchQuadS = ctPitch[pg32XQuadS,pg32YQuadS,pg32ZQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,g32HPhiQuadS,g3VScQuadS,g32VPhiQuadS];
t32YawQuadS = ctYaw[pg32XQuadS,pg32YQuadS,pg32ZQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,g32HPhiQuadS,g3VScQuadS,g32VPhiQuadS];

t32RollThermalQuadS = ctRoll[pg32XQuadS,pg32YQuadS,pg32ZQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,m2TempQuadS g32HPhiQuadS,g3VScQuadS,g3TempVQuadS g32VPhiQuadS];
t32PitchThermalQuadS = ctPitch[pg32XQuadS,pg32YQuadS,pg32ZQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,m2TempQuadS g32HPhiQuadS,g3VScQuadS,g3TempVQuadS g32VPhiQuadS];
t32YawThermalQuadS = ctYaw[pg32XQuadS,pg32YQuadS,pg32ZQuadS,pg32XQuadS,pg32YQuadS,pg32ZQuadS,g3HScQuadS,m2TempQuadS g32HPhiQuadS,g3VScQuadS,g3TempVQuadS g32VPhiQuadS];

ct32RollQuadS = ctRoll[pg23XQuadS,pg23YQuadS,pg32ZQuadS+g3LengthQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,g32HPhiQuadS,g3VScQuadS,g32VPhiQuadS];
ct32PitchQuadS = ctPitch[pg23XQuadS,pg23YQuadS,pg32ZQuadS+g3LengthQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,g32HPhiQuadS,g3VScQuadS,g32VPhiQuadS];
ct32YawQuadS = ctYaw[pg23XQuadS,pg23YQuadS,pg32ZQuadS+g3LengthQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,g32HPhiQuadS,g3VScQuadS,g32VPhiQuadS];

ct32RollThermalQuadS = ctRoll[pg23XQuadS,pg23YQuadS,pg32ZQuadS+g3LengthQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,m2TempQuadS g32HPhiQuadS,g3VScQuadS,g3TempVQuadS g32VPhiQuadS];
ct32PitchThermalQuadS = ctPitch[pg23XQuadS,pg23YQuadS,pg32ZQuadS+g3LengthQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,m2TempQuadS g32HPhiQuadS,g3VScQuadS,g3TempVQuadS g32VPhiQuadS];
ct32YawThermalQuadS = ctYaw[pg23XQuadS,pg23YQuadS,pg32ZQuadS+g3LengthQuadS,pg23XQuadS,pg23YQuadS,pg23ZQuadS,g3HScQuadS,m2TempQuadS g32HPhiQuadS,g3VScQuadS,g3TempVQuadS g32VPhiQuadS];

g34

g34HQuadS = g4HScQuadS(1 +I g34HPhiQuadS);
g34VQuadS = g4VScQuadS(1 +I g34VPhiQuadS);

g34HThermalQuadS = g4HScQuadS(1 +m4TempQuadS I g34HPhiQuadS);
g34VThermalQuadS = g4VScQuadS(1 +m4TempQuadS I g34VPhiQuadS);

t34RollQuadS = ctRoll[pg34XQuadS,pg34YQuadS,pg34ZQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,g34HPhiQuadS,g4VScQuadS,g34VPhiQuadS];
t34PitchQuadS = ctPitch[pg34XQuadS,pg34YQuadS,pg34ZQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,g34HPhiQuadS,g4VScQuadS,g34VPhiQuadS];
t34YawQuadS = ctYaw[pg34XQuadS,pg34YQuadS,pg34ZQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,g34HPhiQuadS,g4VScQuadS,g34VPhiQuadS];

t34RollThermalQuadS = ctRoll[pg34XQuadS,pg34YQuadS,pg34ZQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,m4TempQuadS g34HPhiQuadS,g4VScQuadS,m4TempQuadS g34VPhiQuadS];
t34PitchThermalQuadS = ctPitch[pg34XQuadS,pg34YQuadS,pg34ZQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,m4TempQuadS g34HPhiQuadS,g4VScQuadS,m4TempQuadS g34VPhiQuadS];
t34YawThermalQuadS = ctYaw[pg34XQuadS,pg34YQuadS,pg34ZQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,m4TempQuadS g34HPhiQuadS,g4VScQuadS,m4TempQuadS g34VPhiQuadS];

ct34RollQuadS = ctRoll[pg43XQuadS,pg43YQuadS,pg34ZQuadS-g4LengthQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,g34HPhiQuadS,g4VScQuadS,g34VPhiQuadS];
ct34PitchQuadS = ctPitch[pg43XQuadS,pg43YQuadS,pg34ZQuadS-g4LengthQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,g34HPhiQuadS,g4VScQuadS,g34VPhiQuadS];
ct34YawQuadS = ctYaw[pg43XQuadS,pg43YQuadS,pg34ZQuadS-g4LengthQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,g34HPhiQuadS,g4VScQuadS,g34VPhiQuadS];

ct34RollThermalQuadS = ctRoll[pg43XQuadS,pg43YQuadS,pg34ZQuadS-g4LengthQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,m4TempQuadS g34HPhiQuadS,g4VScQuadS,m4TempQuadS g34VPhiQuadS];
ct34PitchThermalQuadS = ctPitch[pg43XQuadS,pg43YQuadS,pg34ZQuadS-g4LengthQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,m4TempQuadS g34HPhiQuadS,g4VScQuadS,m4TempQuadS g34VPhiQuadS];
ct34YawThermalQuadS = ctYaw[pg43XQuadS,pg43YQuadS,pg34ZQuadS-g4LengthQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,m4TempQuadS g34HPhiQuadS,g4VScQuadS,m4TempQuadS g34VPhiQuadS];

g43

g43HQuadS = g4HScQuadS(1 +I g43HPhiQuadS);
g43VQuadS = g4VScQuadS(1 +I g43VPhiQuadS);

g43HThermalQuadS = g4HScQuadS(1 +m3TempQuadS I g43HPhiQuadS);
g43VThermalQuadS = g4VScQuadS(1 +m4TempQuadS I g43VPhiQuadS);

t43RollQuadS = ctRoll[pg43XQuadS,pg43YQuadS,pg43ZQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,g43HPhiQuadS,g4VScQuadS,g43VPhiQuadS];
t43PitchQuadS = ctPitch[pg43XQuadS,pg43YQuadS,pg43ZQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,g43HPhiQuadS,g4VScQuadS,g43VPhiQuadS];
t43YawQuadS = ctYaw[pg43XQuadS,pg43YQuadS,pg43ZQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,g43HPhiQuadS,g4VScQuadS,g43VPhiQuadS];

t43RollThermalQuadS = ctRoll[pg43XQuadS,pg43YQuadS,pg43ZQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,m3TempQuadS g43HPhiQuadS,g4VScQuadS,m4TempQuadS g43VPhiQuadS];
t43PitchThermalQuadS = ctPitch[pg43XQuadS,pg43YQuadS,pg43ZQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,m3TempQuadS g43HPhiQuadS,g4VScQuadS,m4TempQuadS g43VPhiQuadS];
t43YawThermalQuadS = ctYaw[pg43XQuadS,pg43YQuadS,pg43ZQuadS,pg43XQuadS,pg43YQuadS,pg43ZQuadS,g4HScQuadS,m3TempQuadS g43HPhiQuadS,g4VScQuadS,m4TempQuadS g43VPhiQuadS];

ct43RollQuadS = ctRoll[pg34XQuadS,pg34YQuadS,pg43ZQuadS+g4LengthQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,g43HPhiQuadS,g4VScQuadS,g43VPhiQuadS];
ct43PitchQuadS = ctPitch[pg34XQuadS,pg34YQuadS,pg43ZQuadS+g4LengthQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,g43HPhiQuadS,g4VScQuadS,g43VPhiQuadS];
ct43YawQuadS = ctYaw[pg34XQuadS,pg34YQuadS,pg43ZQuadS+g4LengthQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,g43HPhiQuadS,g4VScQuadS,g43VPhiQuadS];

ct43RollThermalQuadS = ctRoll[pg34XQuadS,pg34YQuadS,pg43ZQuadS+g4LengthQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,m3TempQuadS g43HPhiQuadS,g4VScQuadS,m4TempQuadS g43VPhiQuadS];
ct43PitchThermalQuadS = ctPitch[pg34XQuadS,pg34YQuadS,pg43ZQuadS+g4LengthQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,m3TempQuadS g43HPhiQuadS,g4VScQuadS,m4TempQuadS g43VPhiQuadS];
ct43YawThermalQuadS = ctYaw[pg34XQuadS,pg34YQuadS,pg43ZQuadS+g4LengthQuadS,pg34XQuadS,pg34YQuadS,pg34ZQuadS,g4HScQuadS,m3TempQuadS g43HPhiQuadS,g4VScQuadS,m4TempQuadS g43VPhiQuadS];

gd20

gd20HQuadS = gd2HScQuadS(1 +I gd20HPhiQuadS);
gd20VQuadS = gd2VScQuadS(1 +I gd20VPhiQuadS);

gd20HThermalQuadS = gd2HScQuadS(1 +tRoom I gd20HPhiQuadS);
gd20VThermalQuadS = gd2VScQuadS(1 +tRoom I gd20VPhiQuadS);

td20RollQuadS = ctRoll[pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,gd2HScQuadS,gd20HPhiQuadS,gd2VScQuadS,gd20VPhiQuadS];
td20PitchQuadS = ctPitch[pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,gd2HScQuadS,gd20HPhiQuadS,gd2VScQuadS,gd20VPhiQuadS];
td20YawQuadS = ctYaw[pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,gd2HScQuadS,gd20HPhiQuadS,gd2VScQuadS,gd20VPhiQuadS];

td20RollThermalQuadS = ctRoll[pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,gd2HScQuadS,tRoom gd20HPhiQuadS,gd2VScQuadS,tRoom gd20VPhiQuadS];
td20PitchThermalQuadS = ctPitch[pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,gd2HScQuadS,tRoom gd20HPhiQuadS,gd2VScQuadS,tRoom gd20VPhiQuadS];
td20YawThermalQuadS = ctYaw[pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,pgd20XQuadS,pgd20YQuadS,pgd20ZQuadS,gd2HScQuadS,tRoom gd20HPhiQuadS,gd2VScQuadS,tRoom gd20VPhiQuadS];

ctd20RollQuadS = ctRoll[pgd02XQuadS,pgd02YQuadS,pgd20ZQuadS+gd2LengthQuadS,pgd02XQuadS,pgd02YQuadS,pgd02ZQuadS,gd2HScQuadS,gd20HPhiQuadS,gd2VScQuadS,gd20VPhiQuadS];
ctd20PitchQuadS = ctPitch[pgd02XQuadS,pgd02YQuadS,pgd20ZQuadS+gd2LengthQuadS,pgd02XQuadS,pgd02YQuadS,pgd02ZQuadS,gd2HScQuadS,gd20HPhiQuadS,gd2VScQuadS,gd20VPhiQuadS];
ctd20YawQuadS = ctYaw[pgd02XQuadS,pgd02YQuadS,pgd20ZQuadS+gd2LengthQuadS,pgd02XQuadS,pgd02YQuadS,pgd02ZQuadS,gd2HScQuadS,gd20HPhiQuadS,gd2VScQuadS,gd20VPhiQuadS];

ctd20RollThermalQuadS = ctRoll[pgd02XQuadS,pgd02YQuadS,pgd20ZQuadS+gd2LengthQuadS,pgd02XQuadS,pgd02YQuadS,pgd02ZQuadS,gd2HScQuadS,tRoom gd20HPhiQuadS,gd2VScQuadS,tRoom gd20VPhiQuadS];
ctd20PitchThermalQuadS = ctPitch[pgd02XQuadS,pgd02YQuadS,pgd20ZQuadS+gd2LengthQuadS,pgd02XQuadS,pgd02YQuadS,pgd02ZQuadS,gd2HScQuadS,tRoom gd20HPhiQuadS,gd2VScQuadS,tRoom gd20VPhiQuadS];
ctd20YawThermalQuadS = ctYaw[pgd02XQuadS,pgd02YQuadS,pgd20ZQuadS+gd2LengthQuadS,pgd02XQuadS,pgd02YQuadS,pgd02ZQuadS,gd2HScQuadS,tRoom gd20HPhiQuadS,gd2VScQuadS,tRoom gd20VPhiQuadS];

damping

d2DampQuadS[f_] := Damp[f,d2DampFQuadS,d2DampQQuadS];

parameter set for QuadS pendulum

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd20,kvd20,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
d2};

{nItemQuadS,f,
mass1QuadS,iRoll1QuadS,iPitch1QuadS,iYaw1QuadS,mass2QuadS,iRoll2QuadS,iPitch2QuadS,iYaw2QuadS,mass3QuadS,iRoll3QuadS,iPitch3QuadS,iYaw3QuadS,mass4QuadS,iRoll4QuadS,iPitch4QuadS,iYaw4QuadS,massd2QuadS,iRolld2QuadS,iPitchd2QuadS,iYawd2QuadS,
g10HQuadS,g10VQuadS,g12HQuadS,g12VQuadS,g21HQuadS,g21VQuadS,g23HQuadS,g23VQuadS,g32HQuadS,g32VQuadS,g34HQuadS,g34VQuadS,g43HQuadS,g43VQuadS,gd20HQuadS,gd20VQuadS,
t10RollQuadS,t10PitchQuadS,t10YawQuadS,t12RollQuadS,t12PitchQuadS,t12YawQuadS,t21RollQuadS,t21PitchQuadS,t21YawQuadS,t23RollQuadS,t23PitchQuadS,t23YawQuadS,t32RollQuadS,t32PitchQuadS,t32YawQuadS,t34RollQuadS,t34PitchQuadS,t34YawQuadS,t43RollQuadS,t43PitchQuadS,t43YawQuadS,td20RollQuadS,td20PitchQuadS,td20YawQuadS,
ct10RollQuadS,ct10PitchQuadS,ct10YawQuadS,ct12RollQuadS,ct12PitchQuadS,ct12YawQuadS,ct21RollQuadS,ct21PitchQuadS,ct21YawQuadS,ct23RollQuadS,ct23PitchQuadS,ct23YawQuadS,ct32RollQuadS,ct32PitchQuadS,ct32YawQuadS,ct34RollQuadS,ct34PitchQuadS,ct34YawQuadS,ct43RollQuadS,ct43PitchQuadS,ct43YawQuadS,ctd20RollQuadS,ctd20PitchQuadS,ctd20YawQuadS,
pg01ZQuadS,pg10ZQuadS,pg12ZQuadS,pg21ZQuadS,pg23ZQuadS,pg32ZQuadS,pg34ZQuadS,pg43ZQuadS,
pgd02ZQuadS,pgd20ZQuadS,
d2DampQuadS[f]
}

{nItemQuadS,f,
mass1QuadS,iRoll1QuadS,iPitch1QuadS,iYaw1QuadS,mass2QuadS,iRoll2QuadS,iPitch2QuadS,iYaw2QuadS,mass3QuadS,iRoll3QuadS,iPitch3QuadS,iYaw3QuadS,mass4QuadS,iRoll4QuadS,iPitch4QuadS,iYaw4QuadS,massd2QuadS,iRolld2QuadS,iPitchd2QuadS,iYawd2QuadS,
g10HThermalQuadS,g10VThermalQuadS,g12HThermalQuadS,g12VThermalQuadS,g21HThermalQuadS,g21VThermalQuadS,g23HThermalQuadS,g23VThermalQuadS,g32HThermalQuadS,g32VThermalQuadS,g34HThermalQuadS,g34VThermalQuadS,g43HThermalQuadS,g43VThermalQuadS,gd20HThermalQuadS,gd20VThermalQuadS,
t10RollThermalQuadS,t10PitchThermalQuadS,t10YawThermalQuadS,t12RollThermalQuadS,t12PitchThermalQuadS,t12YawThermalQuadS,t21RollThermalQuadS,t21PitchThermalQuadS,t21YawThermalQuadS,t23RollThermalQuadS,t23PitchThermalQuadS,t23YawThermalQuadS,t32RollThermalQuadS,t32PitchThermalQuadS,t32YawThermalQuadS,t34RollThermalQuadS,t34PitchThermalQuadS,t34YawThermalQuadS,t43RollThermalQuadS,t43PitchThermalQuadS,t43YawThermalQuadS,td20RollThermalQuadS,td20PitchThermalQuadS,td20YawThermalQuadS,
ct10RollThermalQuadS,ct10PitchThermalQuadS,ct10YawThermalQuadS,ct12RollThermalQuadS,ct12PitchThermalQuadS,ct12YawThermalQuadS,ct21RollThermalQuadS,ct21PitchThermalQuadS,ct21YawThermalQuadS,ct23RollThermalQuadS,ct23PitchThermalQuadS,ct23YawThermalQuadS,ct32RollThermalQuadS,ct32PitchThermalQuadS,ct32YawThermalQuadS,ct34RollThermalQuadS,ct34PitchThermalQuadS,ct34YawThermalQuadS,ct43RollThermalQuadS,ct43PitchThermalQuadS,ct43YawThermalQuadS,ctd20RollThermalQuadS,ctd20PitchThermalQuadS,ctd20YawThermalQuadS,
pg01ZQuadS,pg10ZQuadS,pg12ZQuadS,pg21ZQuadS,pg23ZQuadS,pg32ZQuadS,pg34ZQuadS,pg43ZQuadS,
pgd02ZQuadS,pgd20ZQuadS,
d2DampQuadS[f]
}

calculation for QuadS pendulum

trfQuadS[ll_,nn_,jj_,f_]:=trfAmpQuadS[ll,nn,jj,nItemQuadS,f,
mass1QuadS,iRoll1QuadS,iPitch1QuadS,iYaw1QuadS,mass2QuadS,iRoll2QuadS,iPitch2QuadS,iYaw2QuadS,mass3QuadS,iRoll3QuadS,iPitch3QuadS,iYaw3QuadS,mass4QuadS,iRoll4QuadS,iPitch4QuadS,iYaw4QuadS,massd2QuadS,iRolld2QuadS,iPitchd2QuadS,iYawd2QuadS,
g10HQuadS,g10VQuadS,g12HQuadS,g12VQuadS,g21HQuadS,g21VQuadS,g23HQuadS,g23VQuadS,g32HQuadS,g32VQuadS,g34HQuadS,g34VQuadS,g43HQuadS,g43VQuadS,gd20HQuadS,gd20VQuadS,
t10RollQuadS,t10PitchQuadS,t10YawQuadS,t12RollQuadS,t12PitchQuadS,t12YawQuadS,t21RollQuadS,t21PitchQuadS,t21YawQuadS,t23RollQuadS,t23PitchQuadS,t23YawQuadS,t32RollQuadS,t32PitchQuadS,t32YawQuadS,t34RollQuadS,t34PitchQuadS,t34YawQuadS,t43RollQuadS,t43PitchQuadS,t43YawQuadS,td20RollQuadS,td20PitchQuadS,td20YawQuadS,
ct10RollQuadS,ct10PitchQuadS,ct10YawQuadS,ct12RollQuadS,ct12PitchQuadS,ct12YawQuadS,ct21RollQuadS,ct21PitchQuadS,ct21YawQuadS,ct23RollQuadS,ct23PitchQuadS,ct23YawQuadS,ct32RollQuadS,ct32PitchQuadS,ct32YawQuadS,ct34RollQuadS,ct34PitchQuadS,ct34YawQuadS,ct43RollQuadS,ct43PitchQuadS,ct43YawQuadS,ctd20RollQuadS,ctd20PitchQuadS,ctd20YawQuadS,
pg01ZQuadS,pg10ZQuadS,pg12ZQuadS,pg21ZQuadS,pg23ZQuadS,pg32ZQuadS,pg34ZQuadS,pg43ZQuadS,
pgd02ZQuadS,pgd20ZQuadS,
d2DampQuadS[f]
]

noiseSeisQuadS[nn_,jj_,f_]:=Part[coupleMatQuadS,jj].seisQuadS[nn,jj,nItemQuadS,f,
mass1QuadS,iRoll1QuadS,iPitch1QuadS,iYaw1QuadS,mass2QuadS,iRoll2QuadS,iPitch2QuadS,iYaw2QuadS,mass3QuadS,iRoll3QuadS,iPitch3QuadS,iYaw3QuadS,mass4QuadS,iRoll4QuadS,iPitch4QuadS,iYaw4QuadS,massd2QuadS,iRolld2QuadS,iPitchd2QuadS,iYawd2QuadS,
g10HQuadS,g10VQuadS,g12HQuadS,g12VQuadS,g21HQuadS,g21VQuadS,g23HQuadS,g23VQuadS,g32HQuadS,g32VQuadS,g34HQuadS,g34VQuadS,g43HQuadS,g43VQuadS,gd20HQuadS,gd20VQuadS,
t10RollQuadS,t10PitchQuadS,t10YawQuadS,t12RollQuadS,t12PitchQuadS,t12YawQuadS,t21RollQuadS,t21PitchQuadS,t21YawQuadS,t23RollQuadS,t23PitchQuadS,t23YawQuadS,t32RollQuadS,t32PitchQuadS,t32YawQuadS,t34RollQuadS,t34PitchQuadS,t34YawQuadS,t43RollQuadS,t43PitchQuadS,t43YawQuadS,td20RollQuadS,td20PitchQuadS,td20YawQuadS,
ct10RollQuadS,ct10PitchQuadS,ct10YawQuadS,ct12RollQuadS,ct12PitchQuadS,ct12YawQuadS,ct21RollQuadS,ct21PitchQuadS,ct21YawQuadS,ct23RollQuadS,ct23PitchQuadS,ct23YawQuadS,ct32RollQuadS,ct32PitchQuadS,ct32YawQuadS,ct34RollQuadS,ct34PitchQuadS,ct34YawQuadS,ct43RollQuadS,ct43PitchQuadS,ct43YawQuadS,ctd20RollQuadS,ctd20PitchQuadS,ctd20YawQuadS,
pg01ZQuadS,pg10ZQuadS,pg12ZQuadS,pg21ZQuadS,pg23ZQuadS,pg32ZQuadS,pg34ZQuadS,pg43ZQuadS,
pgd02ZQuadS,pgd20ZQuadS,
d2DampQuadS[f]
]

dispTNoiseQuadS[ll_,nn_,f_]:=tNoiseQuadS[ll,nn,f,
mass1QuadS,iRoll1QuadS,iPitch1QuadS,iYaw1QuadS,mass2QuadS,iRoll2QuadS,iPitch2QuadS,iYaw2QuadS,mass3QuadS,iRoll3QuadS,iPitch3QuadS,iYaw3QuadS,mass4QuadS,iRoll4QuadS,iPitch4QuadS,iYaw4QuadS,massd2QuadS,iRolld2QuadS,iPitchd2QuadS,iYawd2QuadS,
g10HThermalQuadS,g10VThermalQuadS,g12HThermalQuadS,g12VThermalQuadS,g21HThermalQuadS,g21VThermalQuadS,g23HThermalQuadS,g23VThermalQuadS,g32HThermalQuadS,g32VThermalQuadS,g34HThermalQuadS,g34VThermalQuadS,g43HThermalQuadS,g43VThermalQuadS,gd20HThermalQuadS,gd20VThermalQuadS,
t10RollThermalQuadS,t10PitchThermalQuadS,t10YawThermalQuadS,t12RollThermalQuadS,t12PitchThermalQuadS,t12YawThermalQuadS,t21RollThermalQuadS,t21PitchThermalQuadS,t21YawThermalQuadS,t23RollThermalQuadS,t23PitchThermalQuadS,t23YawThermalQuadS,t32RollThermalQuadS,t32PitchThermalQuadS,t32YawThermalQuadS,t34RollThermalQuadS,t34PitchThermalQuadS,t34YawThermalQuadS,t43RollThermalQuadS,t43PitchThermalQuadS,t43YawThermalQuadS,td20RollThermalQuadS,td20PitchThermalQuadS,td20YawThermalQuadS,
ct10RollThermalQuadS,ct10PitchThermalQuadS,ct10YawThermalQuadS,ct12RollThermalQuadS,ct12PitchThermalQuadS,ct12YawThermalQuadS,ct21RollThermalQuadS,ct21PitchThermalQuadS,ct21YawThermalQuadS,ct23RollThermalQuadS,ct23PitchThermalQuadS,ct23YawThermalQuadS,ct32RollThermalQuadS,ct32PitchThermalQuadS,ct32YawThermalQuadS,ct34RollThermalQuadS,ct34PitchThermalQuadS,ct34YawThermalQuadS,ct43RollThermalQuadS,ct43PitchThermalQuadS,ct43YawThermalQuadS,ctd20RollThermalQuadS,ctd20PitchThermalQuadS,ctd20YawThermalQuadS,
pg01ZQuadS,pg10ZQuadS,pg12ZQuadS,pg21ZQuadS,pg23ZQuadS,pg32ZQuadS,pg34ZQuadS,pg43ZQuadS,
pgd02ZQuadS,pgd20ZQuadS,
d2DampQuadS[f]
]

noiseTNoiseQuadS[ll_,nn_,jj_,f_] := {1}.coupleMatQuadS[[jj]]*trfQuadS[ll,nn,jj,f]*dispTNoiseQuadS[ll,nn,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)

seismic noise

noiseSeisSumQuadS[f_] := Sqrt[Sum[Sum[noiseSeisQuadS[nn,jj,f],{jj,1,6}]^2,{nn,1,6}]]

noiseSeisCompQuadS[jj_,f_] := Sqrt[Sum[noiseSeisQuadS[nn,jj,f]^2,{nn,1,6}]]

suspension thermal noise (without violin mode)

noiseTNoiseSumQuadS[f_] := Sqrt[Sum[Sum[Sum[noiseTNoiseQuadS[ll,nn,jj,f],{jj,1,6}]^2,{ll,1,6}],{nn,1, nTotalQuadS}]]

noiseTNoiseCompDouble[jj_,f_] := Sqrt[Sum[Sum[noiseTNoiseQuadS[ll,nn,jj,f]^2,{ll,1,6}],{nn,1, nTotalQuadS}]] (*sum up of noise in "jj" direction*)

effect of small clamp between vertical spring and wire

matsclamp[sk_,lk_,sm_,lm_,f_]:=(({{-sm (2 Pi f)^2+sk+lk, -lk}, {-lk, -lm (2 Pi f)^2+lk}}))

UtNoisematsclamp[sk_,lk_,sm_,lm_,f_]:=Part[Sqrt[-((4 kb 300)/(2 Pi f))Im[Inverse[matsclamp[sk,lk,sm,lm,f]]]],1,1]*Abs[Part[Inverse[matsclamp[sk,lk,sm,lm,f]],1,2]]/Abs[Part[Inverse[matsclamp[sk,lk,sm,lm,f]],1,1]]

tNoisematsclamp[sk_,lk_,sm_,lm_,f_]:=Part[Sqrt[-((4 kb 300)/(2 Pi f))Im[Inverse[matsclamp[sk,lk,sm,lm,f]]]],2,2]

sumtNoisematsclamp[sk_,lk_,sm_,lm_,f_]:=Sqrt[tNoisematsclamp[sk,lk,sm,lm,f]^2+UtNoisematsclamp[sk,lk,sm,lm,f]^2]

matsclamp2[sk_,lk_,sm_,lm_,f_]:=(({{-sm (2 Pi f)^2+sk+lk, -sk}, {-sk, -lm (2 Pi f)^2+sk}}))

UtNoisematsclamp2[sk_,lk_,sm_,lm_,f_]:=Part[Sqrt[-((4 kb 300)/(2 Pi f))Im[Inverse[matsclamp2[sk,lk,sm,lm,f]]]],1,1]*Abs[Part[Inverse[matsclamp2[sk,lk,sm,lm,f]],1,2]]/Abs[Part[Inverse[matsclamp2[sk,lk,sm,lm,f]],1,1]]

tNoisematsclamp2[sk_,lk_,sm_,lm_,f_]:=Part[Sqrt[-((4 kb 300)/(2 Pi f))Im[Inverse[matsclamp2[sk,lk,sm,lm,f]]]],2,2]

sumtNoisematsclamp2[sk_,lk_,sm_,lm_,f_]:=Sqrt[tNoisematsclamp2[sk,lk,sm,lm,f]^2+UtNoisematsclamp2[sk,lk,sm,lm,f]^2]

trf2mass[sk_,lk_,sm_,lm_,f_]:=Abs[1/((1/sk)((((-sm (2 Pi f)^2+sk+lk) (-lm (2 Pi f)^2+lk ))/lk)-lk))];

{mass1QuadS/100,mass1QuadS,g32VQuadS,g43VQuadS,100}

trf2mass[g32VQuadS,g43VQuadS,mass1QuadS/100,mass1QuadS,100]

LogLogPlot[{sumtNoisematsclamp[g32VQuadS,g4VScQuadS(1+I 10^(-1)),mass1QuadS/1,mass1QuadS,f],sumtNoisematsclamp2[g32VQuadS,g4VScQuadS(1+I 10^(-1)),mass1QuadS/1,mass1QuadS,f]},{f,0.1,300},PlotStyle ->{ RGBColor[0,1,0],RGBColor[0,0,1]}]

LogLogPlot[{sumtNoisematsclamp[g32VQuadS,g4VScQuadS(1+I 10^(-1)),mass1QuadS/10,mass1QuadS,f],sumtNoisematsclamp2[g32VQuadS,g4VScQuadS(1+I 10^(-1)),mass1QuadS/10,mass1QuadS,f]},{f,0.1,300},PlotStyle ->{ RGBColor[0,1,0],RGBColor[0,0,1]}]

LogLogPlot[{sumtNoisematsclamp[g32VQuadS,g4VScQuadS(1+I 10^(-1)),mass1QuadS/100,mass1QuadS,f],sumtNoisematsclamp2[g32VQuadS,g4VScQuadS(1+I 10^(-1)),mass1QuadS/100,mass1QuadS,f]},{f,0.3,500},PlotStyle ->{ RGBColor[0,1,0],RGBColor[0,0,1]}]

LogLogPlot[{sumtNoisematsclamp[g32VQuadS,g4VScQuadS(1+I 10^(-3)),mass1QuadS/f,mass1QuadS,f],sumtNoisematsclamp2[g32VQuadS,g4VScQuadS(1+I 10^(-3)),mass1QuadS/f,mass1QuadS,100],UtNoisematsclamp2[g32VQuadS,g4VScQuadS(1+I 10^(-3)),mass1QuadS/f,mass1QuadS,100],tNoisematsclamp2[g32VQuadS,g4VScQuadS(1+I 10^(-3)),mass1QuadS/f,mass1QuadS,100]},{f,0.1,100},PlotStyle ->{ RGBColor[0,1,0],RGBColor[0,0,1],RGBColor[1,0,0]}]

LogLogPlot[trf2mass[g32VQuadS,g43VQuadS,mass1QuadS/1,mass1QuadS,f],{f,0.3,300}]

LogLogPlot[trf2mass[g32VQuadS,g43VQuadS,mass1QuadS/10,mass1QuadS,f],{f,0.3,300}]

LogLogPlot[trf2mass[g32VQuadS,g43VQuadS,mass1QuadS/100,mass1QuadS,f],{f,0.3,300}]

LogLogPlot[trf2mass[g32VQuadS,g43VQuadS,mass1QuadS/f,mass1QuadS,100],{f,1,100}]

Q & resonant frequency

resQuadS=f  /. NSolve[Det[matQuadS[f,
mass1QuadS,iRoll1QuadS,iPitch1QuadS,iYaw1QuadS,mass2QuadS,iRoll2QuadS,iPitch2QuadS,iYaw2QuadS,mass3QuadS,iRoll3QuadS,iPitch3QuadS,iYaw3QuadS,mass4QuadS,iRoll4QuadS,iPitch4QuadS,iYaw4QuadS,massd2QuadS,iRolld2QuadS,iPitchd2QuadS,iYawd2QuadS,
g10HQuadS,g10VQuadS,g12HQuadS,g12VQuadS,g21HQuadS,g21VQuadS,g23HQuadS,g23VQuadS,g32HQuadS,g32VQuadS,g34HQuadS,g34VQuadS,g43HQuadS,g43VQuadS,gd20HQuadS,gd20VQuadS,
t10RollQuadS,t10PitchQuadS,t10YawQuadS,t12RollQuadS,t12PitchQuadS,t12YawQuadS,t21RollQuadS,t21PitchQuadS,t21YawQuadS,t23RollQuadS,t23PitchQuadS,t23YawQuadS,t32RollQuadS,t32PitchQuadS,t32YawQuadS,t34RollQuadS,t34PitchQuadS,t34YawQuadS,t43RollQuadS,t43PitchQuadS,t43YawQuadS,td20RollQuadS,td20PitchQuadS,td20YawQuadS,
ct10RollQuadS,ct10PitchQuadS,ct10YawQuadS,ct12RollQuadS,ct12PitchQuadS,ct12YawQuadS,ct21RollQuadS,ct21PitchQuadS,ct21YawQuadS,ct23RollQuadS,ct23PitchQuadS,ct23YawQuadS,ct32RollQuadS,ct32PitchQuadS,ct32YawQuadS,ct34RollQuadS,ct34PitchQuadS,ct34YawQuadS,ct43RollQuadS,ct43PitchQuadS,ct43YawQuadS,ctd20RollQuadS,ctd20PitchQuadS,ctd20YawQuadS,
pg01ZQuadS,pg10ZQuadS,pg12ZQuadS,pg21ZQuadS,pg23ZQuadS,pg32ZQuadS,pg34ZQuadS,pg43ZQuadS,
pgd02ZQuadS,pgd20ZQuadS,
d2DampQuadS[f]]]==0,f];

Sort[resQuadS/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

Plots

all components

plotSeis1QuadS = LogLogPlot[2*noiseSeisSumQuadS[f],{f,0.1,10},PlotStyle -> RGBColor[0,1,0]]

plotSeis2QuadS = LogLogPlot[2*noiseSeisSumQuadS[f],{f,10,100},PlotStyle -> RGBColor[0,1,0]]

plotSeis3QuadS = LogLogPlot[2*noiseSeisSumQuadS[f],{f,100,1000},PlotStyle -> RGBColor[0,1,0]]

plotSeisQuadS=Show[plotSeis1QuadS,plotSeis2QuadS,plotSeis3QuadS,PlotRange -> All]

plotTN1QuadS =LogLogPlot[2*noiseTNoiseSumQuadS[f],{f,0.1,10},PlotStyle -> RGBColor[0,0,1]]

plotTN2QuadS =LogLogPlot[2*noiseTNoiseSumQuadS[f],{f,10,100},PlotStyle -> RGBColor[0,0,1]]

plotTN3QuadS =LogLogPlot[2*noiseTNoiseSumQuadS[f],{f,100,1000},PlotStyle -> RGBColor[0,0,1]]

plotTNQuadS = Show[plotTN1QuadS,plotTN2QuadS,plotTN3QuadS,PlotRange -> All]

plotShotQuadS=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0.5,0]]

Show[plotSeisQuadS,plotTNQuadS,plotShotQuadS,plotCLIOmodel]

Show[plotSeisQuadS,plotTNQuadS,plotCLIOmodel,plotCLIORoommodel,plotShotQuadS,plotLISM030320]

2 noiseTNoiseSumQuadS[100]

Show[plotTN2QuadS,plotTN3QuadS,plotSeis2QuadS,plotCLIOmodel,plotShotQuadS,plotCLIOMTNRoom,PlotRange -> All ]

all components 2

plotSeis101QuadS = LogLogPlot[2*noiseSeisSumQuadS[f],{f,0.1,10},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis102QuadS = LogLogPlot[2*noiseSeisSumQuadS[f],{f,10,100},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis103QuadS = LogLogPlot[2*noiseSeisSumQuadS[f],{f,100,1000},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeisQuadS2=Show[plotSeis101QuadS,plotSeis102QuadS,plotSeis103QuadS,PlotRange -> All]

plotTN101QuadS =LogLogPlot[2*noiseTNoiseSumQuadS[f],{f,0.1,10},PlotStyle -> RGBColor[0.5,0,1]]

plotTN102QuadS =LogLogPlot[2*noiseTNoiseSumQuadS[f],{f,10,100},PlotStyle -> RGBColor[0.5,0,1]]

plotTN103QuadS =LogLogPlot[2*noiseTNoiseSumQuadS[f],{f,100,1000},PlotStyle -> RGBColor[0.5,0,1]]

plotTNQuadS2 = Show[plotTN101QuadS,plotTN102QuadS,plotTN103QuadS,PlotRange -> All]

plotShotQuadS102=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0,0.5]]

Show[plotTN102QuadS,plotTN2QuadS,plotCLIO25model]

Show[plotTN102QuadS,plotSeis102QuadS,plotTN2QuadS,plotSeis2QuadS,plotCLIOmodel]

Show[plotSeis102QuadS,plotSeis2QuadS,plotCLIOmodel]

Show[plotTN102QuadS,plotTN2QuadS,plotCLIOmodel]

Show[plotSeisQuadS2,plotTNQuadS2,plotCLIOmodel,plotShotQuadS102]

Show[plotSeisQuadS2,plotTNQuadS2,plotCLIOmodel,plotShotQuadS102,plotLISM030320]

Show[plotSeisQuadS,plotTNQuadS,plotSeisQuadS2,plotTNQuadS2,plotShotQuadS102,plotCLIOmodel]

Show[plotSeisQuadS,plotSeisQuadS2,plotShotQuadS102,plotCLIOmodel]

Show[plotTNQuadS,plotTNQuadS2,plotShotQuadS102,plotCLIOmodel]

Show[plotShotQuadS,plotShotQuadS102,plotCLIOmodel]

seismic noise - each component

plot1= LogLogPlot[{noiseSeisQuadS[1,1,f],noiseSeisQuadS[3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot2=LogLogPlot[{noiseSeisQuadS[1,1,f],noiseSeisQuadS[3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot3=LogLogPlot[{noiseSeisQuadS[1,1,f],noiseSeisQuadS[3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

Show[plotSeisQuadS,plot1,plot2,plot3,PlotRange -> All]

thermal noise - each component

plot11= LogLogPlot[{noiseTNoiseQuadS[1,4,1,f],noiseTNoiseQuadS[5,4,1,f],noiseTNoiseQuadS[6,4,1,f],noiseTNoiseQuadS[3,4,3,f],noiseTNoiseQuadS[4,4,3,f],noiseTNoiseQuadS[5,4,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot12= LogLogPlot[{noiseTNoiseQuadS[1,4,1,f],noiseTNoiseQuadS[5,4,1,f],noiseTNoiseQuadS[6,4,1,f],noiseTNoiseQuadS[3,4,3,f],noiseTNoiseQuadS[4,4,3,f],noiseTNoiseQuadS[5,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot13= LogLogPlot[{noiseTNoiseQuadS[1,4,1,f],noiseTNoiseQuadS[5,4,1,f],noiseTNoiseQuadS[6,4,1,f],noiseTNoiseQuadS[3,4,3,f],noiseTNoiseQuadS[4,4,3,f],noiseTNoiseQuadS[5,4,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNQuadS,plot11,plot12,plot13,plotCLIOmodel]

Show[plot12,plotTNQuadS,plotCLIOmodel]

plot21= LogLogPlot[{noiseTNoiseQuadS[1,3,1,f],noiseTNoiseQuadS[5,3,1,f],noiseTNoiseQuadS[6,3,1,f],noiseTNoiseQuadS[3,3,3,f],noiseTNoiseQuadS[4,3,3,f],noiseTNoiseQuadS[5,3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot22= LogLogPlot[{noiseTNoiseQuadS[1,3,1,f],noiseTNoiseQuadS[5,3,1,f],noiseTNoiseQuadS[6,3,1,f],noiseTNoiseQuadS[3,3,3,f],noiseTNoiseQuadS[4,3,3,f],noiseTNoiseQuadS[5,3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot23= LogLogPlot[{noiseTNoiseQuadS[1,3,1,f],noiseTNoiseQuadS[5,3,1,f],noiseTNoiseQuadS[6,3,1,f],noiseTNoiseQuadS[3,3,3,f],noiseTNoiseQuadS[4,3,3,f],noiseTNoiseQuadS[5,3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNQuadS,plot21,plot22,plot23,plotCLIOmodel]

Show[plot22,plotTNQuadS,plotCLIOmodel]

Plot[{f,2 f,3 f,4 f,5 f,6 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot24= LogLogPlot[{noiseTNoiseQuadS[3,3,3,f],noiseTNoiseQuadS[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

plot25= LogLogPlot[{noiseTNoiseQuadS[3,3,3,f],noiseTNoiseQuadS[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

Show[plot24,plot24bc,plotCLIOmodel]

Show[plot25,plot24bc,plotCLIOmodel]

thermal noise - each direction

plot31= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot32= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot33= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

Show[plotTNQuadS,plot31,plot32,plot33,plotCLIOmodel,PlotRange -> All]

plot34 =Show[plot32,plot33,PlotRange -> All]

Show[plot34,plotCLIOmodel,plotTN2QuadS,plotTN3QuadS]

Plot[{f,2 f,3 f,4 f,5 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

thermal noise - each dissipation g4

plot41= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.8]}]

plot42= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.8]}]

plot43= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.8]}]

Show[plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

Show[plotTNbcQuadS,plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

thermal noise - each dissipation g3

plot51= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0.8]}]

plot52= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0.8]}]

plot53= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0.8]}]

plot54= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

Show[plotTNQuadS,plot51,plot52,plot53,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plotTNQuadS]

Show[plot54,plot52]

thermal noise - each dissipation magnet damping

plot61= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0]}]

plot62= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0]}]

plot63= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0]}]

Show[plotTNQuadS,plot61,plot62,plot63,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plot62,plotTNQuadS]

Quad pendulum simplified + heat link(2004/01)

Parameters

intersting item

nItemQuadSa = 4 ;

coupling & vibration amplification in cryostat

coupleZXQuadSa =5/100;(*coupling Z -> X*)
coupleYXQuadSa = 10/100;(*coupling Y -> X*)

offset of beam centering

offsetRollQuadSa = 0 mm;
offsetPitchQuadSa = 0.1 mm;
offsetYawQuadSa = 0.1 mm;

vibration amplification factor in cryostat

vibAmpQuadSa = 100;

dimensions of mass for quad pendulum

m1

m1DensQuadSa = alDens;
m1XQuadSa = 100mm;
m1YQuadSa = 100mm;
m1ZQuadSa = 70 mm;
mCube[m1DensQuadSa,m1XQuadSa,m1YQuadSa,m1ZQuadSa]

m2

m2DensQuadSa = alDens;
m2XQuadSa = 100mm;
m2YQuadSa = 100 mm;
m2ZQuadSa = 70 mm;
mCube[m2DensQuadSa,m2XQuadSa,m2YQuadSa,m2ZQuadSa]

m3

m3DensQuadSa = alDens;
m3XQuadSa = 100mm;
m3YQuadSa = 100 mm;
m3ZQuadSa = 70 mm;
mCube[m3DensQuadSa,m3XQuadSa,m3YQuadSa,m3ZQuadSa]

m4

m4DensQuadSa = saDens;
m4rQuadSa = rMass;
m4lQuadSa = lMass;

m2d

md2DensQuadSa = susDens;
md2XQuadSa = 120mm;
md2YQuadSa = 100 mm;
md2ZQuadSa = 50 mm;
md2dQuadSa = 5 mm;
mCage[md2DensQuadSa,md2XQuadSa,md2YQuadSa,md2ZQuadSa,md2dQuadSa]

spring for quad pendulum

g1

g1LengthQuadSa = 1 cm;
g1VFreqQuadSa = 4 Hz;

g2

g2LengthQuadSa = 25 cm;
g2VFreqQuadSa = 4 Hz;

g3

g3LengthQuadSa = 100 cm;
g3VFreqQuadSa = 4 Hz;

g4

g4LengthQuadSa = lSaPend ;

gd2

gd2LengthQuadSa = 1 cm;
gd2VFreqQuadSa = 5 Hz;

kA

kAUYoungQuadSa = alYoung;
kAUShearQuadSa = alShear;
kAURadQuadSa = Pi;
kAUDiaQuadSa = 0.2*10^(-3)m;
kAURadiusQuadSa = 15 cm;
kANumQuadSa = 1;

heat check

kUslQuadSa := 1/(((lU[kAURadQuadSa,kAURadiusQuadSa])/(kANumQuadSa*aC[kAUDiaQuadSa])))

hAl2[tUMass,tISCryo,3000,kUslQuadSa](*heat transfered by heat link [W]*)

hAl2[tUMass,tISCryo,3000,kUslQuadSa]/heatSusMax(*show safety margin*)

position of wire clamp from COM (4 wires + symmetrical distribution) for quad pendulum

pg01XQuadSa = 20 mm;
pg01YQuadSa = 20 mm;
pg01ZQuadSa = 0 mm;
pg01dXQuadSa = 0.1 mm*10;
pg01dYQuadSa = 0.1 mm*10;
pg01dZQuadSa = 0.1 mm*10;

pg10XQuadSa = pg01XQuadSa;
pg10YQuadSa = pg01YQuadSa ;
pg10ZQuadSa = m1ZQuadSa/2;
pg10dXQuadSa = 0.1 mm*10;
pg10dYQuadSa = 0.1 mm*10 ;
pg10dZQuadSa = 0.1 mm*10;

pg12XQuadSa = 20 mm;
pg12YQuadSa = 20 mm;
pg12ZQuadSa = -m1ZQuadSa/2;
pg12dXQuadSa = 0.1 mm*10;
pg12dYQuadSa = 0.1 mm*10;
pg12dZQuadSa = 0.1 mm*10;

pg21XQuadSa = pg12XQuadSa;
pg21YQuadSa = pg12YQuadSa ;
pg21ZQuadSa = m2ZQuadSa/2;
pg21dXQuadSa = 0.1 mm*10;
pg21dYQuadSa = 0.1 mm*10 ;
pg21dZQuadSa = 0.1 mm*10;

pg23XQuadSa=10 mm;
pg23YQuadSa=50 mm;
pg23ZQuadSa=-m2ZQuadSa/2;
pg23dXQuadSa=0.1 mm*10;
pg23dYQuadSa=0.1 mm*10;
pg23dZQuadSa=0.1 mm*10;

pg32XQuadSa=pg23XQuadSa;
pg32YQuadSa=pg23YQuadSa;
pg32ZQuadSa=m3ZQuadSa/2;
pg32dXQuadSa=0.1 mm*10;
pg32dYQuadSa=0.1 mm*10;
pg32dZQuadSa=0.1 mm*10;

pg34XQuadSa=10 mm;
pg34YQuadSa=rMass/2-0 mm;
pg34ZQuadSa=-0 mm;
pg34dXQuadSa=0.1 mm*10;
pg34dYQuadSa=0.1 mm*10;
pg34dZQuadSa=0.1 mm*10;

pg43XQuadSa=pg34XQuadSa;
pg43YQuadSa=rMass/2;
pg43ZQuadSa= 0 mm;
pg43dXQuadSa=0.1 mm*10;
pg43dYQuadSa=0.1 mm*10;
pg43dZQuadSa= 0.1 mm*10;

pgd02XQuadSa = 180 mm/2;
pgd02YQuadSa = 130 mm/2 ;
pgd02ZQuadSa = -0 mm*1;
pgd02dXQuadSa = 0.1 mm*10;
pgd02dYQuadSa = 0.1 mm*10;
pgd02dZQuadSa = 0.1 mm*10;

pgd20XQuadSa = pgd02XQuadSa;
pgd20YQuadSa = pgd02YQuadSa ;
pgd20ZQuadSa = 0 mm*1;
pgd20dXQuadSa = 0.1 mm*10;
pgd20dYQuadSa = 0.1 mm*10;
pgd20dZQuadSa = 0.1 mm*10;

pk01XQuadSa =70 mm;(*from COM of m3*)
pk01YQuadSa = 1 mm /2;(*from COM of m3*)
pk01ZQuadSa = 100 mm;(*from COM of m3*)
pk10XQuadSa =  - m3XQuadSa/2;
pk10YQuadSa = 1 mm /2;
pk10ZQuadSa = 1 mm /2;

dissipation

qRoomHQuadSa = 10^6;
qCryoHQuadSa = 10^7;
qRoomVQuadSa = 10^4;
qCryoVQuadSa  =10^5;
qUAlQuadSa =  10^3;

qSaHQuadSa =  1/(3 10^(-7));
qSaVQuadSa =  10^6;

qg3VQuadSa = qCryoVQuadSa;

g3TempVQuadSa = m3TempQuadSa;(*縦防振の板ばねをcryoに入れるときはm3TempQuadSa,それ以外はm2TempQuadSa*)

in spring

g10HPhiQuadSa =  1/qRoomHQuadSa;
g10VPhiQuadSa =   1/qRoomVQuadSa;

g12HPhiQuadSa =   1/qRoomHQuadSa;
g12VPhiQuadSa =  1/qRoomVQuadSa;

g21HPhiQuadSa =  1/qRoomHQuadSa;
g21VPhiQuadSa =   1/qRoomVQuadSa;

g23HPhiQuadSa =   1/qCryoHQuadSa;
g23VPhiQuadSa =    1/qg3VQuadSa;

g32HPhiQuadSa =   1/qRoomHQuadSa;
g32VPhiQuadSa =    1/qg3VQuadSa;

g34HPhiQuadSa =  1/qSaHQuadSa;
g34VPhiQuadSa =  1/qSaVQuadSa;

g43HPhiQuadSa =  1/qSaHQuadSa;
g43VPhiQuadSa = 1/qSaVQuadSa;

gd20HPhiQuadSa =  1/qRoomHQuadSa;
gd20VPhiQuadSa =  1/qRoomVQuadSa;

kAPhiQuadSa =   1/qUAlQuadSa;

magnet damping

d2DampFQuadSa = 5 Hz;
d2DampQQuadSa = 10*1;

temperature for triple pendulum

m1TempQuadSa = 300 K;
m2TempQuadSa = 300 K;
m3TempQuadSa = 13 K;
m4TempQuadSa = 25 K;
md2TempQuadSa = 300 K;

tISCryoQuadSa = 8 K;

Preparation

coupling matrix

coupleMatQuadSa=(({{1}, {coupleYXQuadSa}, {coupleZXQuadSa}, {offsetRollQuadSa}, {offsetPitchQuadSa}, {offsetYawQuadSa}}));

mass & moment inertia for QuadSa pendulum

m1

mass1QuadSa = mCube[m1DensQuadSa, m1XQuadSa,m1YQuadSa, m1ZQuadSa]; 
iRoll1QuadSa = mIRollCube[m1DensQuadSa, m1XQuadSa,m1YQuadSa, m1ZQuadSa];
iPitch1QuadSa = mIPitchCube[m1DensQuadSa, m1XQuadSa,m1YQuadSa, m1ZQuadSa];
iYaw1QuadSa = mIYawCube[m1DensQuadSa, m1XQuadSa,m1YQuadSa, m1ZQuadSa];

m2

mass2QuadSa = mCube[m2DensQuadSa, m2XQuadSa,m2YQuadSa, m2ZQuadSa]; 
iRoll2QuadSa = mIRollCube[m2DensQuadSa, m2XQuadSa,m2YQuadSa, m2ZQuadSa];
iPitch2QuadSa = mIPitchCube[m2DensQuadSa, m2XQuadSa,m2YQuadSa, m2ZQuadSa];
iYaw2QuadSa = mIYawCube[m2DensQuadSa, m2XQuadSa,m2YQuadSa, m2ZQuadSa];

m3

mass3QuadSa = mCube[m3DensQuadSa, m3XQuadSa,m3YQuadSa, m3ZQuadSa]; 
iRoll3QuadSa = mIRollCube[m3DensQuadSa, m3XQuadSa,m3YQuadSa, m3ZQuadSa];
iPitch3QuadSa = mIPitchCube[m3DensQuadSa, m3XQuadSa,m3YQuadSa, m3ZQuadSa];
iYaw3QuadSa = mIYawCube[m3DensQuadSa, m3XQuadSa,m3YQuadSa, m3ZQuadSa];

m4

mass4QuadSa = mMass; (*see Parameters/Dimensions of final suspension/final mass*)
iRoll4QuadSa = mILCyl[m4DensQuadSa, m4rQuadSa,m4lQuadSa];
iPitch4QuadSa = mIRCyl[m4DensQuadSa, m4rQuadSa,m4lQuadSa];
iYaw4QuadSa = mIRCyl[m4DensQuadSa, m4rQuadSa,m4lQuadSa];

md2(cage)

massd2QuadSa = mCage[md2DensQuadSa, md2XQuadSa,md2YQuadSa, md2ZQuadSa,md2dQuadSa];
iRolld2QuadSa = mIRollCage[md2DensQuadSa, md2XQuadSa,md2YQuadSa, md2ZQuadSa,md2dQuadSa];
iPitchd2QuadSa = mIPitchCage[md2DensQuadSa, md2XQuadSa,md2YQuadSa, md2ZQuadSa,md2dQuadSa];
iYawd2QuadSa = mIYawCage[md2DensQuadSa, md2XQuadSa,md2YQuadSa, md2ZQuadSa,md2dQuadSa];

suspension wire for QuadSa pendulum

horizontal

g1HScQuadSa = scPend[mass1QuadSa+mass2QuadSa+mass3QuadSa+mass4QuadSa,g1LengthQuadSa];
g2HScQuadSa = scPend[mass2QuadSa+mass3QuadSa+mass4QuadSa,g2LengthQuadSa];
g3HScQuadSa = scPend[mass3QuadSa+mass4QuadSa,g3LengthQuadSa];
g4HScQuadSa = scPend[mass4QuadSa,g4LengthQuadSa];
gd2HScQuadSa = scPend[massd2QuadSa,gd2LengthQuadSa];

vertical

g1VScQuadSa = scFreq[mass1QuadSa+mass2QuadSa+mass3QuadSa+mass4QuadSa,g1VFreqQuadSa];
g2VScQuadSa = scFreq[mass2QuadSa+mass3QuadSa+mass4QuadSa,g2VFreqQuadSa];
g3VScQuadSa = scFreq[mass3QuadSa+mass4QuadSa,g3VFreqQuadSa];
g4VScQuadSa = numSaPend*scVert[saYoung,diaSaPend,lSaPend];
gd2VScQuadSa = scFreq[massd2QuadSa,gd2VFreqQuadSa];

g10

g10HQuadSa = g1HScQuadSa(1 +I g10HPhiQuadSa);
g10VQuadSa = g1VScQuadSa(1 +I g10VPhiQuadSa);

g10HThermalQuadSa = g1HScQuadSa(1 +tRoom I g10HPhiQuadSa);
g10VThermalQuadSa = g1VScQuadSa(1 +tRoom I g10VPhiQuadSa);

t10RollQuadSa = ctRoll[pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,g1HScQuadSa,g10HPhiQuadSa,g1VScQuadSa,g10VPhiQuadSa];
t10PitchQuadSa = ctPitch[pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,g1HScQuadSa,g10HPhiQuadSa,g1VScQuadSa,g10VPhiQuadSa];
t10YawQuadSa = ctYaw[pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,g1HScQuadSa,g10HPhiQuadSa,g1VScQuadSa,g10VPhiQuadSa];

t10RollThermalQuadSa = ctRoll[pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,g1HScQuadSa,tRoom g10HPhiQuadSa,g1VScQuadSa,tRoom g10VPhiQuadSa];
t10PitchThermalQuadSa = ctPitch[pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,g1HScQuadSa,tRoom g10HPhiQuadSa,g1VScQuadSa,tRoom g10VPhiQuadSa];
t10YawThermalQuadSa = ctYaw[pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,pg10XQuadSa,pg10YQuadSa,pg10ZQuadSa,g1HScQuadSa,tRoom g10HPhiQuadSa,g1VScQuadSa,tRoom g10VPhiQuadSa];

ct10RollQuadSa = ctRoll[pg01XQuadSa,pg01YQuadSa,pg10ZQuadSa+g1LengthQuadSa,pg01XQuadSa,pg01YQuadSa,pg01ZQuadSa,g1HScQuadSa,g10HPhiQuadSa,g1VScQuadSa,g10VPhiQuadSa];
ct10PitchQuadSa = ctPitch[pg01XQuadSa,pg01YQuadSa,pg10ZQuadSa+g1LengthQuadSa,pg01XQuadSa,pg01YQuadSa,pg01ZQuadSa,g1HScQuadSa,g10HPhiQuadSa,g1VScQuadSa,g10VPhiQuadSa];
ct10YawQuadSa = ctYaw[pg01XQuadSa,pg01YQuadSa,pg10ZQuadSa+g1LengthQuadSa,pg01XQuadSa,pg01YQuadSa,pg01ZQuadSa,g1HScQuadSa,g10HPhiQuadSa,g1VScQuadSa,g10VPhiQuadSa];

ct10RollThermalQuadSa = ctRoll[pg01XQuadSa,pg01YQuadSa,pg10ZQuadSa+g1LengthQuadSa,pg01XQuadSa,pg01YQuadSa,pg01ZQuadSa,g1HScQuadSa,tRoom g10HPhiQuadSa,g1VScQuadSa,tRoom g10VPhiQuadSa];
ct10PitchThermalQuadSa = ctPitch[pg01XQuadSa,pg01YQuadSa,pg10ZQuadSa+g1LengthQuadSa,pg01XQuadSa,pg01YQuadSa,pg01ZQuadSa,g1HScQuadSa,tRoom g10HPhiQuadSa,g1VScQuadSa,tRoom g10VPhiQuadSa];
ct10YawThermalQuadSa = ctYaw[pg01XQuadSa,pg01YQuadSa,pg10ZQuadSa+g1LengthQuadSa,pg01XQuadSa,pg01YQuadSa,pg01ZQuadSa,g1HScQuadSa,tRoom g10HPhiQuadSa,g1VScQuadSa,tRoom g10VPhiQuadSa];

g12

g12HQuadSa = g2HScQuadSa(1 +I g12HPhiQuadSa);
g12VQuadSa = g2VScQuadSa(1 +I g12VPhiQuadSa);

g12HThermalQuadSa = g2HScQuadSa(1 +tRoom I g12HPhiQuadSa);
g12VThermalQuadSa = g2VScQuadSa(1 +tRoom I g12VPhiQuadSa);

t12RollQuadSa = ctRoll[pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,g12HPhiQuadSa,g2VScQuadSa,g12VPhiQuadSa];
t12PitchQuadSa = ctPitch[pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,g12HPhiQuadSa,g2VScQuadSa,g12VPhiQuadSa];
t12YawQuadSa = ctYaw[pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,g12HPhiQuadSa,g2VScQuadSa,g12VPhiQuadSa];

t12RollThermalQuadSa = ctRoll[pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,tRoom g12HPhiQuadSa,g2VScQuadSa,tRoom g12VPhiQuadSa];
t12PitchThermalQuadSa = ctPitch[pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,tRoom g12HPhiQuadSa,g2VScQuadSa,tRoom g12VPhiQuadSa];
t12YawThermalQuadSa = ctYaw[pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,tRoom g12HPhiQuadSa,g2VScQuadSa,tRoom g12VPhiQuadSa];

ct12RollQuadSa = ctRoll[pg21XQuadSa,pg21YQuadSa,pg12ZQuadSa-g2LengthQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,g12HPhiQuadSa,g2VScQuadSa,g12VPhiQuadSa];
ct12PitchQuadSa = ctPitch[pg21XQuadSa,pg21YQuadSa,pg12ZQuadSa-g2LengthQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,g12HPhiQuadSa,g2VScQuadSa,g12VPhiQuadSa];
ct12YawQuadSa = ctYaw[pg21XQuadSa,pg21YQuadSa,pg12ZQuadSa-g2LengthQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,g12HPhiQuadSa,g2VScQuadSa,g12VPhiQuadSa];

ct12RollThermalQuadSa = ctRoll[pg21XQuadSa,pg21YQuadSa,pg12ZQuadSa-g2LengthQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,tRoom g12HPhiQuadSa,g2VScQuadSa,tRoom g12VPhiQuadSa];
ct12PitchThermalQuadSa = ctPitch[pg21XQuadSa,pg21YQuadSa,pg12ZQuadSa-g2LengthQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,tRoom g12HPhiQuadSa,g2VScQuadSa,tRoom g12VPhiQuadSa];
ct12YawThermalQuadSa = ctYaw[pg21XQuadSa,pg21YQuadSa,pg12ZQuadSa-g2LengthQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,tRoom g12HPhiQuadSa,g2VScQuadSa,tRoom g12VPhiQuadSa];

g21

g21HQuadSa = g2HScQuadSa(1 +I g21HPhiQuadSa);
g21VQuadSa = g2VScQuadSa(1 +I g21VPhiQuadSa);

g21HThermalQuadSa = g2HScQuadSa(1 +tRoom I g21HPhiQuadSa);
g21VThermalQuadSa = g2VScQuadSa(1 +tRoom I g21VPhiQuadSa);

t21RollQuadSa = ctRoll[pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,g21HPhiQuadSa,g2VScQuadSa,g21VPhiQuadSa];
t21PitchQuadSa = ctPitch[pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,g21HPhiQuadSa,g2VScQuadSa,g21VPhiQuadSa];
t21YawQuadSa = ctYaw[pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,g21HPhiQuadSa,g2VScQuadSa,g21VPhiQuadSa];

t21RollThermalQuadSa = ctRoll[pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,tRoom g21HPhiQuadSa,g2VScQuadSa,tRoom g21VPhiQuadSa];
t21PitchThermalQuadSa = ctPitch[pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,tRoom g21HPhiQuadSa,g2VScQuadSa,tRoom g21VPhiQuadSa];
t21YawThermalQuadSa = ctYaw[pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,pg21XQuadSa,pg21YQuadSa,pg21ZQuadSa,g2HScQuadSa,tRoom g21HPhiQuadSa,g2VScQuadSa,tRoom g21VPhiQuadSa];

ct21RollQuadSa = ctRoll[pg12XQuadSa,pg12YQuadSa,pg21ZQuadSa+g2LengthQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,g21HPhiQuadSa,g2VScQuadSa,g21VPhiQuadSa];
ct21PitchQuadSa = ctPitch[pg12XQuadSa,pg12YQuadSa,pg21ZQuadSa+g2LengthQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,g21HPhiQuadSa,g2VScQuadSa,g21VPhiQuadSa];
ct21YawQuadSa = ctYaw[pg12XQuadSa,pg12YQuadSa,pg21ZQuadSa+g2LengthQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,g21HPhiQuadSa,g2VScQuadSa,g21VPhiQuadSa];

ct21RollThermalQuadSa = ctRoll[pg12XQuadSa,pg12YQuadSa,pg21ZQuadSa+g2LengthQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,tRoom g21HPhiQuadSa,g2VScQuadSa,tRoom g21VPhiQuadSa];
ct21PitchThermalQuadSa = ctPitch[pg12XQuadSa,pg12YQuadSa,pg21ZQuadSa+g2LengthQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,tRoom g21HPhiQuadSa,g2VScQuadSa,tRoom g21VPhiQuadSa];
ct21YawThermalQuadSa = ctYaw[pg12XQuadSa,pg12YQuadSa,pg21ZQuadSa+g2LengthQuadSa,pg12XQuadSa,pg12YQuadSa,pg12ZQuadSa,g2HScQuadSa,tRoom g21HPhiQuadSa,g2VScQuadSa,tRoom g21VPhiQuadSa];

g23

g23HQuadSa = g3HScQuadSa(1 +I g23HPhiQuadSa);
g23VQuadSa = g3VScQuadSa(1 +I g23VPhiQuadSa);

g23HThermalQuadSa = g3HScQuadSa(1 +m3TempQuadSa I g23HPhiQuadSa);
g23VThermalQuadSa = g3VScQuadSa(1 +g3TempVQuadSa I g23VPhiQuadSa);

t23RollQuadSa = ctRoll[pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,g23HPhiQuadSa,g3VScQuadSa,g23VPhiQuadSa];
t23PitchQuadSa = ctPitch[pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,g23HPhiQuadSa,g3VScQuadSa,g23VPhiQuadSa];
t23YawQuadSa = ctYaw[pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,g23HPhiQuadSa,g3VScQuadSa,g23VPhiQuadSa];

t23RollThermalQuadSa = ctRoll[pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,m3TempQuadSa g23HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g23VPhiQuadSa];
t23PitchThermalQuadSa = ctPitch[pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,m3TempQuadSa g23HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g23VPhiQuadSa];
t23YawThermalQuadSa = ctYaw[pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,m3TempQuadSa g23HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g23VPhiQuadSa];

ct23RollQuadSa = ctRoll[pg32XQuadSa,pg32YQuadSa,pg23ZQuadSa-g3LengthQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,g23HPhiQuadSa,g3VScQuadSa,g23VPhiQuadSa];
ct23PitchQuadSa = ctPitch[pg32XQuadSa,pg32YQuadSa,pg23ZQuadSa-g3LengthQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,g23HPhiQuadSa,g3VScQuadSa,g23VPhiQuadSa];
ct23YawQuadSa = ctYaw[pg32XQuadSa,pg32YQuadSa,pg23ZQuadSa-g3LengthQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,g23HPhiQuadSa,g3VScQuadSa,g23VPhiQuadSa];

ct23RollThermalQuadSa = ctRoll[pg32XQuadSa,pg32YQuadSa,pg23ZQuadSa-g3LengthQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,m3TempQuadSa g23HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g23VPhiQuadSa];
ct23PitchThermalQuadSa = ctPitch[pg32XQuadSa,pg32YQuadSa,pg23ZQuadSa-g3LengthQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,m3TempQuadSa g23HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g23VPhiQuadSa];
ct23YawThermalQuadSa = ctYaw[pg32XQuadSa,pg32YQuadSa,pg23ZQuadSa-g3LengthQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,m3TempQuadSa g23HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g23VPhiQuadSa];

g32

g32HQuadSa = g3HScQuadSa(1 +I g32HPhiQuadSa);
g32VQuadSa = g3VScQuadSa(1 +I g32VPhiQuadSa);

g32HThermalQuadSa = g3HScQuadSa(1 +m2TempQuadSa I g32HPhiQuadSa);
g32VThermalQuadSa = g3VScQuadSa(1 +g3TempVQuadSa I g32VPhiQuadSa);

t32RollQuadSa = ctRoll[pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,g32HPhiQuadSa,g3VScQuadSa,g32VPhiQuadSa];
t32PitchQuadSa = ctPitch[pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,g32HPhiQuadSa,g3VScQuadSa,g32VPhiQuadSa];
t32YawQuadSa = ctYaw[pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,g32HPhiQuadSa,g3VScQuadSa,g32VPhiQuadSa];

t32RollThermalQuadSa = ctRoll[pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,m2TempQuadSa g32HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g32VPhiQuadSa];
t32PitchThermalQuadSa = ctPitch[pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,m2TempQuadSa g32HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g32VPhiQuadSa];
t32YawThermalQuadSa = ctYaw[pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,pg32XQuadSa,pg32YQuadSa,pg32ZQuadSa,g3HScQuadSa,m2TempQuadSa g32HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g32VPhiQuadSa];

ct32RollQuadSa = ctRoll[pg23XQuadSa,pg23YQuadSa,pg32ZQuadSa+g3LengthQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,g32HPhiQuadSa,g3VScQuadSa,g32VPhiQuadSa];
ct32PitchQuadSa = ctPitch[pg23XQuadSa,pg23YQuadSa,pg32ZQuadSa+g3LengthQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,g32HPhiQuadSa,g3VScQuadSa,g32VPhiQuadSa];
ct32YawQuadSa = ctYaw[pg23XQuadSa,pg23YQuadSa,pg32ZQuadSa+g3LengthQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,g32HPhiQuadSa,g3VScQuadSa,g32VPhiQuadSa];

ct32RollThermalQuadSa = ctRoll[pg23XQuadSa,pg23YQuadSa,pg32ZQuadSa+g3LengthQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,m2TempQuadSa g32HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g32VPhiQuadSa];
ct32PitchThermalQuadSa = ctPitch[pg23XQuadSa,pg23YQuadSa,pg32ZQuadSa+g3LengthQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,m2TempQuadSa g32HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g32VPhiQuadSa];
ct32YawThermalQuadSa = ctYaw[pg23XQuadSa,pg23YQuadSa,pg32ZQuadSa+g3LengthQuadSa,pg23XQuadSa,pg23YQuadSa,pg23ZQuadSa,g3HScQuadSa,m2TempQuadSa g32HPhiQuadSa,g3VScQuadSa,g3TempVQuadSa g32VPhiQuadSa];

g34

g34HQuadSa = g4HScQuadSa(1 +I g34HPhiQuadSa);
g34VQuadSa = g4VScQuadSa(1 +I g34VPhiQuadSa);

g34HThermalQuadSa = g4HScQuadSa(1 +m4TempQuadSa I g34HPhiQuadSa);
g34VThermalQuadSa = g4VScQuadSa(1 +m4TempQuadSa I g34VPhiQuadSa);

t34RollQuadSa = ctRoll[pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,g34HPhiQuadSa,g4VScQuadSa,g34VPhiQuadSa];
t34PitchQuadSa = ctPitch[pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,g34HPhiQuadSa,g4VScQuadSa,g34VPhiQuadSa];
t34YawQuadSa = ctYaw[pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,g34HPhiQuadSa,g4VScQuadSa,g34VPhiQuadSa];

t34RollThermalQuadSa = ctRoll[pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,m4TempQuadSa g34HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g34VPhiQuadSa];
t34PitchThermalQuadSa = ctPitch[pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,m4TempQuadSa g34HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g34VPhiQuadSa];
t34YawThermalQuadSa = ctYaw[pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,m4TempQuadSa g34HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g34VPhiQuadSa];

ct34RollQuadSa = ctRoll[pg43XQuadSa,pg43YQuadSa,pg34ZQuadSa-g4LengthQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,g34HPhiQuadSa,g4VScQuadSa,g34VPhiQuadSa];
ct34PitchQuadSa = ctPitch[pg43XQuadSa,pg43YQuadSa,pg34ZQuadSa-g4LengthQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,g34HPhiQuadSa,g4VScQuadSa,g34VPhiQuadSa];
ct34YawQuadSa = ctYaw[pg43XQuadSa,pg43YQuadSa,pg34ZQuadSa-g4LengthQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,g34HPhiQuadSa,g4VScQuadSa,g34VPhiQuadSa];

ct34RollThermalQuadSa = ctRoll[pg43XQuadSa,pg43YQuadSa,pg34ZQuadSa-g4LengthQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,m4TempQuadSa g34HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g34VPhiQuadSa];
ct34PitchThermalQuadSa = ctPitch[pg43XQuadSa,pg43YQuadSa,pg34ZQuadSa-g4LengthQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,m4TempQuadSa g34HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g34VPhiQuadSa];
ct34YawThermalQuadSa = ctYaw[pg43XQuadSa,pg43YQuadSa,pg34ZQuadSa-g4LengthQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,m4TempQuadSa g34HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g34VPhiQuadSa];

g43

g43HQuadSa = g4HScQuadSa(1 +I g43HPhiQuadSa);
g43VQuadSa = g4VScQuadSa(1 +I g43VPhiQuadSa);

g43HThermalQuadSa = g4HScQuadSa(1 +m3TempQuadSa I g43HPhiQuadSa);
g43VThermalQuadSa = g4VScQuadSa(1 +m4TempQuadSa I g43VPhiQuadSa);

t43RollQuadSa = ctRoll[pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,g43HPhiQuadSa,g4VScQuadSa,g43VPhiQuadSa];
t43PitchQuadSa = ctPitch[pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,g43HPhiQuadSa,g4VScQuadSa,g43VPhiQuadSa];
t43YawQuadSa = ctYaw[pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,g43HPhiQuadSa,g4VScQuadSa,g43VPhiQuadSa];

t43RollThermalQuadSa = ctRoll[pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,m3TempQuadSa g43HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g43VPhiQuadSa];
t43PitchThermalQuadSa = ctPitch[pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,m3TempQuadSa g43HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g43VPhiQuadSa];
t43YawThermalQuadSa = ctYaw[pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,pg43XQuadSa,pg43YQuadSa,pg43ZQuadSa,g4HScQuadSa,m3TempQuadSa g43HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g43VPhiQuadSa];

ct43RollQuadSa = ctRoll[pg34XQuadSa,pg34YQuadSa,pg43ZQuadSa+g4LengthQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,g43HPhiQuadSa,g4VScQuadSa,g43VPhiQuadSa];
ct43PitchQuadSa = ctPitch[pg34XQuadSa,pg34YQuadSa,pg43ZQuadSa+g4LengthQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,g43HPhiQuadSa,g4VScQuadSa,g43VPhiQuadSa];
ct43YawQuadSa = ctYaw[pg34XQuadSa,pg34YQuadSa,pg43ZQuadSa+g4LengthQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,g43HPhiQuadSa,g4VScQuadSa,g43VPhiQuadSa];

ct43RollThermalQuadSa = ctRoll[pg34XQuadSa,pg34YQuadSa,pg43ZQuadSa+g4LengthQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,m3TempQuadSa g43HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g43VPhiQuadSa];
ct43PitchThermalQuadSa = ctPitch[pg34XQuadSa,pg34YQuadSa,pg43ZQuadSa+g4LengthQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,m3TempQuadSa g43HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g43VPhiQuadSa];
ct43YawThermalQuadSa = ctYaw[pg34XQuadSa,pg34YQuadSa,pg43ZQuadSa+g4LengthQuadSa,pg34XQuadSa,pg34YQuadSa,pg34ZQuadSa,g4HScQuadSa,m3TempQuadSa g43HPhiQuadSa,g4VScQuadSa,m4TempQuadSa g43VPhiQuadSa];

gd20

gd20HQuadSa = gd2HScQuadSa(1 +I gd20HPhiQuadSa);
gd20VQuadSa = gd2VScQuadSa(1 +I gd20VPhiQuadSa);

gd20HThermalQuadSa = gd2HScQuadSa(1 +tRoom I gd20HPhiQuadSa);
gd20VThermalQuadSa = gd2VScQuadSa(1 +tRoom I gd20VPhiQuadSa);

td20RollQuadSa = ctRoll[pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,gd2HScQuadSa,gd20HPhiQuadSa,gd2VScQuadSa,gd20VPhiQuadSa];
td20PitchQuadSa = ctPitch[pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,gd2HScQuadSa,gd20HPhiQuadSa,gd2VScQuadSa,gd20VPhiQuadSa];
td20YawQuadSa = ctYaw[pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,gd2HScQuadSa,gd20HPhiQuadSa,gd2VScQuadSa,gd20VPhiQuadSa];

td20RollThermalQuadSa = ctRoll[pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,gd2HScQuadSa,tRoom gd20HPhiQuadSa,gd2VScQuadSa,tRoom gd20VPhiQuadSa];
td20PitchThermalQuadSa = ctPitch[pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,gd2HScQuadSa,tRoom gd20HPhiQuadSa,gd2VScQuadSa,tRoom gd20VPhiQuadSa];
td20YawThermalQuadSa = ctYaw[pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,pgd20XQuadSa,pgd20YQuadSa,pgd20ZQuadSa,gd2HScQuadSa,tRoom gd20HPhiQuadSa,gd2VScQuadSa,tRoom gd20VPhiQuadSa];

ctd20RollQuadSa = ctRoll[pgd02XQuadSa,pgd02YQuadSa,pgd20ZQuadSa+gd2LengthQuadSa,pgd02XQuadSa,pgd02YQuadSa,pgd02ZQuadSa,gd2HScQuadSa,gd20HPhiQuadSa,gd2VScQuadSa,gd20VPhiQuadSa];
ctd20PitchQuadSa = ctPitch[pgd02XQuadSa,pgd02YQuadSa,pgd20ZQuadSa+gd2LengthQuadSa,pgd02XQuadSa,pgd02YQuadSa,pgd02ZQuadSa,gd2HScQuadSa,gd20HPhiQuadSa,gd2VScQuadSa,gd20VPhiQuadSa];
ctd20YawQuadSa = ctYaw[pgd02XQuadSa,pgd02YQuadSa,pgd20ZQuadSa+gd2LengthQuadSa,pgd02XQuadSa,pgd02YQuadSa,pgd02ZQuadSa,gd2HScQuadSa,gd20HPhiQuadSa,gd2VScQuadSa,gd20VPhiQuadSa];

ctd20RollThermalQuadSa = ctRoll[pgd02XQuadSa,pgd02YQuadSa,pgd20ZQuadSa+gd2LengthQuadSa,pgd02XQuadSa,pgd02YQuadSa,pgd02ZQuadSa,gd2HScQuadSa,tRoom gd20HPhiQuadSa,gd2VScQuadSa,tRoom gd20VPhiQuadSa];
ctd20PitchThermalQuadSa = ctPitch[pgd02XQuadSa,pgd02YQuadSa,pgd20ZQuadSa+gd2LengthQuadSa,pgd02XQuadSa,pgd02YQuadSa,pgd02ZQuadSa,gd2HScQuadSa,tRoom gd20HPhiQuadSa,gd2VScQuadSa,tRoom gd20VPhiQuadSa];
ctd20YawThermalQuadSa = ctYaw[pgd02XQuadSa,pgd02YQuadSa,pgd20ZQuadSa+gd2LengthQuadSa,pgd02XQuadSa,pgd02YQuadSa,pgd02ZQuadSa,gd2HScQuadSa,tRoom gd20HPhiQuadSa,gd2VScQuadSa,tRoom gd20VPhiQuadSa];

heat link

kA

kAXscQuadSa = kANumQuadSa*scUX[kAUYoungQuadSa,kAURadQuadSa,kAUDiaQuadSa,kAURadiusQuadSa];
kAYscQuadSa = kANumQuadSa*scUY[kAUShearQuadSa,kAUDiaQuadSa,kAURadiusQuadSa];
kAZscQuadSa = kANumQuadSa*scUZ[kAUYoungQuadSa,kAURadQuadSa,kAUDiaQuadSa,kAURadiusQuadSa];

k10

k10XQuadSa = kAXscQuadSa(1+ I kAPhiQuadSa);
k10YQuadSa = kAYscQuadSa(1+ I kAPhiQuadSa);
k10ZQuadSa = kAZscQuadSa(1+ I kAPhiQuadSa);

k10XThermalQuadSa = kAXscQuadSa(1+ tISCryoQuadSa I kAPhiQuadSa);
k10YThermalQuadSa = kAYscQuadSa(1+ tISCryoQuadSa I kAPhiQuadSa);
k10ZThermalQuadSa = kAZscQuadSa(1+ tISCryoQuadSa I kAPhiQuadSa);

tk10RollQuadSa = ctURoll[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa];
tk10PitchQuadSa = ctUPitch[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa];
tk10YawQuadSa = ctUYaw[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa];

tk10RollThermalQuadSa = ctURoll[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa tISCryoQuadSa kAPhiQuadSa];
tk10PitchThermalQuadSa = ctUPitch[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa tISCryoQuadSa kAPhiQuadSa];
tk10YawThermalQuadSa = ctUYaw[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa tISCryoQuadSa kAPhiQuadSa];

ctk10RollQuadSa = ctURoll[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa];
ctk10PitchQuadSa = ctUPitch[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa];
ctk10YawQuadSa = ctUYaw[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa];

ctk10RollThermalQuadSa = ctURoll[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa tISCryoQuadSa kAPhiQuadSa];
ctk10PitchThermalQuadSa = ctUPitch[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa tISCryoQuadSa kAPhiQuadSa];
ctk10YawThermalQuadSa = ctUYaw[pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,kAPhiQuadSa tISCryoQuadSa kAPhiQuadSa];

damping

d2DampQuadSa[f_] := Damp[f,d2DampFQuadSa,d2DampQQuadSa];

parameter set for QuadSa pendulum

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
kxu10,kyu10,kzu10,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,
txu10,tyu10,tzu10,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,
ctxd20,ctyd20,ctzd20,ctxu10,ctyu10,ctzu10,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,
xu01,yu01,zu01,xu10,yu10,zu10,
d2};

{nItemQuadSa,f,
mass1QuadSa,iRoll1QuadSa,iPitch1QuadSa,iYaw1QuadSa,mass2QuadSa,iRoll2QuadSa,iPitch2QuadSa,iYaw2QuadSa,mass3QuadSa,iRoll3QuadSa,iPitch3QuadSa,iYaw3QuadSa,mass4QuadSa,iRoll4QuadSa,iPitch4QuadSa,iYaw4QuadSa,massd2QuadSa,iRolld2QuadSa,iPitchd2QuadSa,iYawd2QuadSa,
g10HQuadSa,g10VQuadSa,g12HQuadSa,g12VQuadSa,g21HQuadSa,g21VQuadSa,g23HQuadSa,g23VQuadSa,g32HQuadSa,g32VQuadSa,g34HQuadSa,g34VQuadSa,g43HQuadSa,g43VQuadSa,gd20HQuadSa,gd20VQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,
t10RollQuadSa,t10PitchQuadSa,t10YawQuadSa,t12RollQuadSa,t12PitchQuadSa,t12YawQuadSa,t21RollQuadSa,t21PitchQuadSa,t21YawQuadSa,t23RollQuadSa,t23PitchQuadSa,t23YawQuadSa,t32RollQuadSa,t32PitchQuadSa,t32YawQuadSa,t34RollQuadSa,t34PitchQuadSa,t34YawQuadSa,t43RollQuadSa,t43PitchQuadSa,t43YawQuadSa,td20RollQuadSa,td20PitchQuadSa,td20YawQuadSa,tk10RollQuadSa,tk10PitchQuadSa,tk10YawQuadSa,
ct10RollQuadSa,ct10PitchQuadSa,ct10YawQuadSa,ct12RollQuadSa,ct12PitchQuadSa,ct12YawQuadSa,ct21RollQuadSa,ct21PitchQuadSa,ct21YawQuadSa,ct23RollQuadSa,ct23PitchQuadSa,ct23YawQuadSa,ct32RollQuadSa,ct32PitchQuadSa,ct32YawQuadSa,ct34RollQuadSa,ct34PitchQuadSa,ct34YawQuadSa,ct43RollQuadSa,ct43PitchQuadSa,ct43YawQuadSa,ctd20RollQuadSa,ctd20PitchQuadSa,ctd20YawQuadSa,ctk10RollQuadSa,ctk10PitchQuadSa,ctk10YawQuadSa,
pg01ZQuadSa,pg10ZQuadSa,pg12ZQuadSa,pg21ZQuadSa,pg23ZQuadSa,pg32ZQuadSa,pg34ZQuadSa,pg43ZQuadSa,
pgd02ZQuadSa,pgd20ZQuadSa,
pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,

d2DampQuadSa[f]
}

{f,
mass1QuadSa,iRoll1QuadSa,iPitch1QuadSa,iYaw1QuadSa,mass2QuadSa,iRoll2QuadSa,iPitch2QuadSa,iYaw2QuadSa,mass3QuadSa,iRoll3QuadSa,iPitch3QuadSa,iYaw3QuadSa,mass4QuadSa,iRoll4QuadSa,iPitch4QuadSa,iYaw4QuadSa,massd2QuadSa,iRolld2QuadSa,iPitchd2QuadSa,iYawd2QuadSa,
g10HThermalQuadSa,g10VThermalQuadSa,g12HThermalQuadSa,g12VThermalQuadSa,g21HThermalQuadSa,g21VThermalQuadSa,g23HThermalQuadSa,g23VThermalQuadSa,g32HThermalQuadSa,g32VThermalQuadSa,g34HThermalQuadSa,g34VThermalQuadSa,g43HThermalQuadSa,g43VThermalQuadSa,gd20HThermalQuadSa,gd20VThermalQuadSa,k10XThermalQuadSa,k10YThermalQuadSa,k10ZThermalQuadSa,
t10RollThermalQuadSa,t10PitchThermalQuadSa,t10YawThermalQuadSa,t12RollThermalQuadSa,t12PitchThermalQuadSa,t12YawThermalQuadSa,t21RollThermalQuadSa,t21PitchThermalQuadSa,t21YawThermalQuadSa,t23RollThermalQuadSa,t23PitchThermalQuadSa,t23YawThermalQuadSa,t32RollThermalQuadSa,t32PitchThermalQuadSa,t32YawThermalQuadSa,t34RollThermalQuadSa,t34PitchThermalQuadSa,t34YawThermalQuadSa,t43RollThermalQuadSa,t43PitchThermalQuadSa,t43YawThermalQuadSa,td20RollThermalQuadSa,td20PitchThermalQuadSa,td20YawThermalQuadSa,tk10RollThermalQuadSa,tk10PitchThermalQuadSa,tk10YawThermalQuadSa,
ct10RollThermalQuadSa,ct10PitchThermalQuadSa,ct10YawThermalQuadSa,ct12RollThermalQuadSa,ct12PitchThermalQuadSa,ct12YawThermalQuadSa,ct21RollThermalQuadSa,ct21PitchThermalQuadSa,ct21YawThermalQuadSa,ct23RollThermalQuadSa,ct23PitchThermalQuadSa,ct23YawThermalQuadSa,ct32RollThermalQuadSa,ct32PitchThermalQuadSa,ct32YawThermalQuadSa,ct34RollThermalQuadSa,ct34PitchThermalQuadSa,ct34YawThermalQuadSa,ct43RollThermalQuadSa,ct43PitchThermalQuadSa,ct43YawThermalQuadSa,ctd20RollThermalQuadSa,ctd20PitchThermalQuadSa,ctd20YawThermalQuadSa,
ctk10RollThermalQuadSa,ctk10PitchThermalQuadSa,ctk10YawThermalQuadSa,
pg01ZQuadSa,pg10ZQuadSa,pg12ZQuadSa,pg21ZQuadSa,pg23ZQuadSa,pg32ZQuadSa,pg34ZQuadSa,pg43ZQuadSa,
pgd02ZQuadSa,pgd20ZQuadSa,
pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,
d2DampQuadSa[f]
}

calculation for QuadSa pendulum

trfQuadSa[ll_,nn_,jj_,f_]:=trfAmpQuadSa[ll,nn,jj,
nItemQuadSa,f,
mass1QuadSa,iRoll1QuadSa,iPitch1QuadSa,iYaw1QuadSa,mass2QuadSa,iRoll2QuadSa,iPitch2QuadSa,iYaw2QuadSa,mass3QuadSa,iRoll3QuadSa,iPitch3QuadSa,iYaw3QuadSa,mass4QuadSa,iRoll4QuadSa,iPitch4QuadSa,iYaw4QuadSa,massd2QuadSa,iRolld2QuadSa,iPitchd2QuadSa,iYawd2QuadSa,
g10HQuadSa,g10VQuadSa,g12HQuadSa,g12VQuadSa,g21HQuadSa,g21VQuadSa,g23HQuadSa,g23VQuadSa,g32HQuadSa,g32VQuadSa,g34HQuadSa,g34VQuadSa,g43HQuadSa,g43VQuadSa,gd20HQuadSa,gd20VQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,
t10RollQuadSa,t10PitchQuadSa,t10YawQuadSa,t12RollQuadSa,t12PitchQuadSa,t12YawQuadSa,t21RollQuadSa,t21PitchQuadSa,t21YawQuadSa,t23RollQuadSa,t23PitchQuadSa,t23YawQuadSa,t32RollQuadSa,t32PitchQuadSa,t32YawQuadSa,t34RollQuadSa,t34PitchQuadSa,t34YawQuadSa,t43RollQuadSa,t43PitchQuadSa,t43YawQuadSa,td20RollQuadSa,td20PitchQuadSa,td20YawQuadSa,tk10RollQuadSa,tk10PitchQuadSa,tk10YawQuadSa,
ct10RollQuadSa,ct10PitchQuadSa,ct10YawQuadSa,ct12RollQuadSa,ct12PitchQuadSa,ct12YawQuadSa,ct21RollQuadSa,ct21PitchQuadSa,ct21YawQuadSa,ct23RollQuadSa,ct23PitchQuadSa,ct23YawQuadSa,ct32RollQuadSa,ct32PitchQuadSa,ct32YawQuadSa,ct34RollQuadSa,ct34PitchQuadSa,ct34YawQuadSa,ct43RollQuadSa,ct43PitchQuadSa,ct43YawQuadSa,ctd20RollQuadSa,ctd20PitchQuadSa,ctd20YawQuadSa,ctk10RollQuadSa,ctk10PitchQuadSa,ctk10YawQuadSa,
pg01ZQuadSa,pg10ZQuadSa,pg12ZQuadSa,pg21ZQuadSa,pg23ZQuadSa,pg32ZQuadSa,pg34ZQuadSa,pg43ZQuadSa,
pgd02ZQuadSa,pgd20ZQuadSa,
pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,

d2DampQuadSa[f]
]

noiseSeisQuadSa[nn_,jj_,f_]:=Part[coupleMatQuadSa,jj].seisQuadSa[vibAmpQuadSa,nn,jj,
nItemQuadSa,f,
mass1QuadSa,iRoll1QuadSa,iPitch1QuadSa,iYaw1QuadSa,mass2QuadSa,iRoll2QuadSa,iPitch2QuadSa,iYaw2QuadSa,mass3QuadSa,iRoll3QuadSa,iPitch3QuadSa,iYaw3QuadSa,mass4QuadSa,iRoll4QuadSa,iPitch4QuadSa,iYaw4QuadSa,massd2QuadSa,iRolld2QuadSa,iPitchd2QuadSa,iYawd2QuadSa,
g10HQuadSa,g10VQuadSa,g12HQuadSa,g12VQuadSa,g21HQuadSa,g21VQuadSa,g23HQuadSa,g23VQuadSa,g32HQuadSa,g32VQuadSa,g34HQuadSa,g34VQuadSa,g43HQuadSa,g43VQuadSa,gd20HQuadSa,gd20VQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,
t10RollQuadSa,t10PitchQuadSa,t10YawQuadSa,t12RollQuadSa,t12PitchQuadSa,t12YawQuadSa,t21RollQuadSa,t21PitchQuadSa,t21YawQuadSa,t23RollQuadSa,t23PitchQuadSa,t23YawQuadSa,t32RollQuadSa,t32PitchQuadSa,t32YawQuadSa,t34RollQuadSa,t34PitchQuadSa,t34YawQuadSa,t43RollQuadSa,t43PitchQuadSa,t43YawQuadSa,td20RollQuadSa,td20PitchQuadSa,td20YawQuadSa,tk10RollQuadSa,tk10PitchQuadSa,tk10YawQuadSa,
ct10RollQuadSa,ct10PitchQuadSa,ct10YawQuadSa,ct12RollQuadSa,ct12PitchQuadSa,ct12YawQuadSa,ct21RollQuadSa,ct21PitchQuadSa,ct21YawQuadSa,ct23RollQuadSa,ct23PitchQuadSa,ct23YawQuadSa,ct32RollQuadSa,ct32PitchQuadSa,ct32YawQuadSa,ct34RollQuadSa,ct34PitchQuadSa,ct34YawQuadSa,ct43RollQuadSa,ct43PitchQuadSa,ct43YawQuadSa,ctd20RollQuadSa,ctd20PitchQuadSa,ctd20YawQuadSa,ctk10RollQuadSa,ctk10PitchQuadSa,ctk10YawQuadSa,
pg01ZQuadSa,pg10ZQuadSa,pg12ZQuadSa,pg21ZQuadSa,pg23ZQuadSa,pg32ZQuadSa,pg34ZQuadSa,pg43ZQuadSa,
pgd02ZQuadSa,pgd20ZQuadSa,
pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,

d2DampQuadSa[f]
]

noiseSeisCryoQuadSa[nn_,jj_,f_] :=Part[coupleMatQuadSa,jj].seisCryoQuadSa[vibAmpQuadSa,nn,jj,
nItemQuadSa,f,
mass1QuadSa,iRoll1QuadSa,iPitch1QuadSa,iYaw1QuadSa,mass2QuadSa,iRoll2QuadSa,iPitch2QuadSa,iYaw2QuadSa,mass3QuadSa,iRoll3QuadSa,iPitch3QuadSa,iYaw3QuadSa,mass4QuadSa,iRoll4QuadSa,iPitch4QuadSa,iYaw4QuadSa,massd2QuadSa,iRolld2QuadSa,iPitchd2QuadSa,iYawd2QuadSa,
g10HQuadSa,g10VQuadSa,g12HQuadSa,g12VQuadSa,g21HQuadSa,g21VQuadSa,g23HQuadSa,g23VQuadSa,g32HQuadSa,g32VQuadSa,g34HQuadSa,g34VQuadSa,g43HQuadSa,g43VQuadSa,gd20HQuadSa,gd20VQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,
t10RollQuadSa,t10PitchQuadSa,t10YawQuadSa,t12RollQuadSa,t12PitchQuadSa,t12YawQuadSa,t21RollQuadSa,t21PitchQuadSa,t21YawQuadSa,t23RollQuadSa,t23PitchQuadSa,t23YawQuadSa,t32RollQuadSa,t32PitchQuadSa,t32YawQuadSa,t34RollQuadSa,t34PitchQuadSa,t34YawQuadSa,t43RollQuadSa,t43PitchQuadSa,t43YawQuadSa,td20RollQuadSa,td20PitchQuadSa,td20YawQuadSa,tk10RollQuadSa,tk10PitchQuadSa,tk10YawQuadSa,
ct10RollQuadSa,ct10PitchQuadSa,ct10YawQuadSa,ct12RollQuadSa,ct12PitchQuadSa,ct12YawQuadSa,ct21RollQuadSa,ct21PitchQuadSa,ct21YawQuadSa,ct23RollQuadSa,ct23PitchQuadSa,ct23YawQuadSa,ct32RollQuadSa,ct32PitchQuadSa,ct32YawQuadSa,ct34RollQuadSa,ct34PitchQuadSa,ct34YawQuadSa,ct43RollQuadSa,ct43PitchQuadSa,ct43YawQuadSa,ctd20RollQuadSa,ctd20PitchQuadSa,ctd20YawQuadSa,ctk10RollQuadSa,ctk10PitchQuadSa,ctk10YawQuadSa,
pg01ZQuadSa,pg10ZQuadSa,pg12ZQuadSa,pg21ZQuadSa,pg23ZQuadSa,pg32ZQuadSa,pg34ZQuadSa,pg43ZQuadSa,
pgd02ZQuadSa,pgd20ZQuadSa,
pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,

d2DampQuadSa[f]
]

dispTNoiseQuadSa[ll_,nn_,f_]:=tNoiseQuadSa[ll,nn,
f,
mass1QuadSa,iRoll1QuadSa,iPitch1QuadSa,iYaw1QuadSa,mass2QuadSa,iRoll2QuadSa,iPitch2QuadSa,iYaw2QuadSa,mass3QuadSa,iRoll3QuadSa,iPitch3QuadSa,iYaw3QuadSa,mass4QuadSa,iRoll4QuadSa,iPitch4QuadSa,iYaw4QuadSa,massd2QuadSa,iRolld2QuadSa,iPitchd2QuadSa,iYawd2QuadSa,
g10HThermalQuadSa,g10VThermalQuadSa,g12HThermalQuadSa,g12VThermalQuadSa,g21HThermalQuadSa,g21VThermalQuadSa,g23HThermalQuadSa,g23VThermalQuadSa,g32HThermalQuadSa,g32VThermalQuadSa,g34HThermalQuadSa,g34VThermalQuadSa,g43HThermalQuadSa,g43VThermalQuadSa,gd20HThermalQuadSa,gd20VThermalQuadSa,k10XThermalQuadSa,k10YThermalQuadSa,k10ZThermalQuadSa,
t10RollThermalQuadSa,t10PitchThermalQuadSa,t10YawThermalQuadSa,t12RollThermalQuadSa,t12PitchThermalQuadSa,t12YawThermalQuadSa,t21RollThermalQuadSa,t21PitchThermalQuadSa,t21YawThermalQuadSa,t23RollThermalQuadSa,t23PitchThermalQuadSa,t23YawThermalQuadSa,t32RollThermalQuadSa,t32PitchThermalQuadSa,t32YawThermalQuadSa,t34RollThermalQuadSa,t34PitchThermalQuadSa,t34YawThermalQuadSa,t43RollThermalQuadSa,t43PitchThermalQuadSa,t43YawThermalQuadSa,td20RollThermalQuadSa,td20PitchThermalQuadSa,td20YawThermalQuadSa,tk10RollThermalQuadSa,tk10PitchThermalQuadSa,tk10YawThermalQuadSa,
ct10RollThermalQuadSa,ct10PitchThermalQuadSa,ct10YawThermalQuadSa,ct12RollThermalQuadSa,ct12PitchThermalQuadSa,ct12YawThermalQuadSa,ct21RollThermalQuadSa,ct21PitchThermalQuadSa,ct21YawThermalQuadSa,ct23RollThermalQuadSa,ct23PitchThermalQuadSa,ct23YawThermalQuadSa,ct32RollThermalQuadSa,ct32PitchThermalQuadSa,ct32YawThermalQuadSa,ct34RollThermalQuadSa,ct34PitchThermalQuadSa,ct34YawThermalQuadSa,ct43RollThermalQuadSa,ct43PitchThermalQuadSa,ct43YawThermalQuadSa,ctd20RollThermalQuadSa,ctd20PitchThermalQuadSa,ctd20YawThermalQuadSa,
ctk10RollThermalQuadSa,ctk10PitchThermalQuadSa,ctk10YawThermalQuadSa,
pg01ZQuadSa,pg10ZQuadSa,pg12ZQuadSa,pg21ZQuadSa,pg23ZQuadSa,pg32ZQuadSa,pg34ZQuadSa,pg43ZQuadSa,
pgd02ZQuadSa,pgd20ZQuadSa,
pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,
d2DampQuadSa[f]
]

noiseTNoiseQuadSa[ll_,nn_,jj_,f_] := {1}.coupleMatQuadSa[[jj]]*trfQuadSa[ll,nn,jj,f]*dispTNoiseQuadSa[ll,nn,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)

seismic noise

noiseSeisSumQuadSa[f_] := Sqrt[Sum[Sum[noiseSeisQuadSa[nn,jj,f],{jj,1,6}]^2,{nn,1,6}]]

noiseSeisCryoSumQuadSa[f_] := Sqrt[Sum[Sum[noiseSeisCryoQuadSa[nn,jj,f],{jj,1,6}]^2,{nn,1,6}]]

noiseSeisCompQuadSa[jj_,f_] := Sqrt[Sum[noiseSeisQuadSa[nn,jj,f]^2,{nn,1,6}]]

noiseSeisSumQuadSa[17.63279198734363`]

noiseSeisCryoSumQuadSa[100]

suspension thermal noise (without violin mode)

noiseTNoiseSumQuadSa[f_] := Sqrt[Sum[Sum[Sum[noiseTNoiseQuadSa[ll,nn,jj,f],{jj,1,6}]^2,{ll,1,6}],{nn,1, nTotalQuadSa}]]

noiseTNoiseCompDouble[jj_,f_] := Sqrt[Sum[Sum[noiseTNoiseQuadSa[ll,nn,jj,f]^2,{ll,1,6}],{nn,1, nTotalQuadSa}]] (*sum up of noise in "jj" direction*)

noiseTNoiseSumQuadSa[100]

Q & resonant frequency

resQuadSa=f  /. NSolve[Det[matQuadSa[f,
mass1QuadSa,iRoll1QuadSa,iPitch1QuadSa,iYaw1QuadSa,mass2QuadSa,iRoll2QuadSa,iPitch2QuadSa,iYaw2QuadSa,mass3QuadSa,iRoll3QuadSa,iPitch3QuadSa,iYaw3QuadSa,mass4QuadSa,iRoll4QuadSa,iPitch4QuadSa,iYaw4QuadSa,massd2QuadSa,iRolld2QuadSa,iPitchd2QuadSa,iYawd2QuadSa,
g10HQuadSa,g10VQuadSa,g12HQuadSa,g12VQuadSa,g21HQuadSa,g21VQuadSa,g23HQuadSa,g23VQuadSa,g32HQuadSa,g32VQuadSa,g34HQuadSa,g34VQuadSa,g43HQuadSa,g43VQuadSa,gd20HQuadSa,gd20VQuadSa,kAXscQuadSa,kAYscQuadSa,kAZscQuadSa,
t10RollQuadSa,t10PitchQuadSa,t10YawQuadSa,t12RollQuadSa,t12PitchQuadSa,t12YawQuadSa,t21RollQuadSa,t21PitchQuadSa,t21YawQuadSa,t23RollQuadSa,t23PitchQuadSa,t23YawQuadSa,t32RollQuadSa,t32PitchQuadSa,t32YawQuadSa,t34RollQuadSa,t34PitchQuadSa,t34YawQuadSa,t43RollQuadSa,t43PitchQuadSa,t43YawQuadSa,td20RollQuadSa,td20PitchQuadSa,td20YawQuadSa,tk10RollQuadSa,tk10PitchQuadSa,tk10YawQuadSa,
ct10RollQuadSa,ct10PitchQuadSa,ct10YawQuadSa,ct12RollQuadSa,ct12PitchQuadSa,ct12YawQuadSa,ct21RollQuadSa,ct21PitchQuadSa,ct21YawQuadSa,ct23RollQuadSa,ct23PitchQuadSa,ct23YawQuadSa,ct32RollQuadSa,ct32PitchQuadSa,ct32YawQuadSa,ct34RollQuadSa,ct34PitchQuadSa,ct34YawQuadSa,ct43RollQuadSa,ct43PitchQuadSa,ct43YawQuadSa,ctd20RollQuadSa,ctd20PitchQuadSa,ctd20YawQuadSa,ctk10RollQuadSa,ctk10PitchQuadSa,ctk10YawQuadSa,
pg01ZQuadSa,pg10ZQuadSa,pg12ZQuadSa,pg21ZQuadSa,pg23ZQuadSa,pg32ZQuadSa,pg34ZQuadSa,pg43ZQuadSa,
pgd02ZQuadSa,pgd20ZQuadSa,
pk01XQuadSa,pk01YQuadSa,pk01ZQuadSa,pk10XQuadSa,pk10YQuadSa,pk10ZQuadSa,
d2DampQuadSa[f]]]==0,f];

Sort[resQuadSa/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

Plots

all components

plotSeis1QuadSa = LogLogPlot[{2*noiseSeisSumQuadSa[f],2*noiseSeisCryoSumQuadSa[f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis2QuadSa = LogLogPlot[{2*noiseSeisSumQuadSa[f],2*(f/3)^2*noiseSeisCryoSumQuadSa[f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis3QuadSa = LogLogPlot[{2*noiseSeisSumQuadSa[f],2*(f/3)^2*noiseSeisCryoSumQuadSa[f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeisQuadSa=Show[plotSeis1QuadSa,plotSeis2QuadSa,plotSeis3QuadSa,PlotRange -> All]

plotTN1QuadSa =LogLogPlot[2*noiseTNoiseSumQuadSa[f],{f,0.1,10},PlotStyle -> RGBColor[0,0,1]]

plotTN2QuadSa =LogLogPlot[2*noiseTNoiseSumQuadSa[f],{f,10,100},PlotStyle -> RGBColor[0,0,1]]

plotTN3QuadSa =LogLogPlot[2*noiseTNoiseSumQuadSa[f],{f,100,1000},PlotStyle -> RGBColor[0,0,1]]

plotTNQuadSa = Show[plotTN1QuadSa,plotTN2QuadSa,plotTN3QuadSa,PlotRange -> All]

plotShotQuadSa=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0.5,0]]

Show[plotSeisQuadSa,plotTNQuadSa,plotShotQuadSa,plotCLIOmodel]

Show[plotSeisQuadSa,plotTNQuadSa,plotCLIOmodel,plotCLIORoommodel,plotShotQuadSa,plotLISM030320]

Show[plotTN2QuadSa,plotTN3QuadSa,plotSeis2QuadSa,plotCLIOmodel,plotShotQuadSa,plotCLIOMTNRoom,PlotRange -> All ]

all components 2

plotSeis101QuadSa = LogLogPlot[2*noiseSeisSumQuadSa[f],{f,0.1,10},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis102QuadSa = LogLogPlot[2*noiseSeisSumQuadSa[f],{f,10,100},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis103QuadSa = LogLogPlot[2*noiseSeisSumQuadSa[f],{f,100,1000},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeisQuadSa2=Show[plotSeis101QuadSa,plotSeis102QuadSa,plotSeis103QuadSa,PlotRange -> All]

plotTN101QuadSa =LogLogPlot[2*noiseTNoiseSumQuadSa[f],{f,0.1,10},PlotStyle -> RGBColor[0.5,0,1]]

plotTN102QuadSa =LogLogPlot[2*noiseTNoiseSumQuadSa[f],{f,10,100},PlotStyle -> RGBColor[0.5,0,1]]

plotTN103QuadSa =LogLogPlot[2*noiseTNoiseSumQuadSa[f],{f,100,1000},PlotStyle -> RGBColor[0.5,0,1]]

plotTNQuadSa2 = Show[plotTN101QuadSa,plotTN102QuadSa,plotTN103QuadSa,PlotRange -> All]

plotShotQuadSa102=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0,0.5]]

Show[plotTN102QuadSa,plotTN2QuadSa,plotCLIO25model]

Show[plotTN102QuadSa,plotSeis102QuadSa,plotTN2QuadSa,plotSeis2QuadSa,plotCLIOmodel]

Show[plotSeis102QuadSa,plotSeis2QuadSa,plotCLIOmodel]

Show[plotTN102QuadSa,plotTN2QuadSa,plotCLIOmodel]

Show[plotSeisQuadSa2,plotTNQuadSa2,plotCLIOmodel,plotShotQuadSa102]

Show[plotSeisQuadSa2,plotTNQuadSa2,plotCLIOmodel,plotShotQuadSa102,plotLISM030320]

Show[plotSeisQuadSa,plotTNQuadSa,plotSeisQuadSa2,plotTNQuadSa2,plotShotQuadSa102,plotCLIOmodel]

Show[plotSeisQuadSa,plotSeisQuadSa2,plotShotQuadSa102,plotCLIOmodel]

Show[plotTNQuadSa,plotTNQuadSa2,plotShotQuadSa102,plotCLIOmodel]

Show[plotShotQuadSa,plotShotQuadSa102,plotCLIOmodel]

seismic noise - each component

plot1= LogLogPlot[{noiseSeisQuadSa[1,1,f],noiseSeisQuadSa[3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot2=LogLogPlot[{noiseSeisQuadSa[1,1,f],noiseSeisQuadSa[3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot3=LogLogPlot[{noiseSeisQuadSa[1,1,f],noiseSeisQuadSa[3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

Show[plotSeisQuadSa,plot1,plot2,plot3,PlotRange -> All]

thermal noise - each component

plot11= LogLogPlot[{noiseTNoiseQuadSa[1,4,1,f],noiseTNoiseQuadSa[5,4,1,f],noiseTNoiseQuadSa[6,4,1,f],noiseTNoiseQuadSa[3,4,3,f],noiseTNoiseQuadSa[4,4,3,f],noiseTNoiseQuadSa[5,4,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot12= LogLogPlot[{noiseTNoiseQuadSa[1,4,1,f],noiseTNoiseQuadSa[5,4,1,f],noiseTNoiseQuadSa[6,4,1,f],noiseTNoiseQuadSa[3,4,3,f],noiseTNoiseQuadSa[4,4,3,f],noiseTNoiseQuadSa[5,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot13= LogLogPlot[{noiseTNoiseQuadSa[1,4,1,f],noiseTNoiseQuadSa[5,4,1,f],noiseTNoiseQuadSa[6,4,1,f],noiseTNoiseQuadSa[3,4,3,f],noiseTNoiseQuadSa[4,4,3,f],noiseTNoiseQuadSa[5,4,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNQuadSa,plot11,plot12,plot13,plotCLIOmodel]

Show[plot12,plotTNQuadSa,plotCLIOmodel]

plot21= LogLogPlot[{noiseTNoiseQuadSa[1,3,1,f],noiseTNoiseQuadSa[5,3,1,f],noiseTNoiseQuadSa[6,3,1,f],noiseTNoiseQuadSa[3,3,3,f],noiseTNoiseQuadSa[4,3,3,f],noiseTNoiseQuadSa[5,3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot22= LogLogPlot[{noiseTNoiseQuadSa[1,3,1,f],noiseTNoiseQuadSa[5,3,1,f],noiseTNoiseQuadSa[6,3,1,f],noiseTNoiseQuadSa[3,3,3,f],noiseTNoiseQuadSa[4,3,3,f],noiseTNoiseQuadSa[5,3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot23= LogLogPlot[{noiseTNoiseQuadSa[1,3,1,f],noiseTNoiseQuadSa[5,3,1,f],noiseTNoiseQuadSa[6,3,1,f],noiseTNoiseQuadSa[3,3,3,f],noiseTNoiseQuadSa[4,3,3,f],noiseTNoiseQuadSa[5,3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNQuadSa,plot21,plot22,plot23,plotCLIOmodel]

Show[plot22,plotTNQuadSa,plotCLIOmodel]

Plot[{f,2 f,3 f,4 f,5 f,6 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot24= LogLogPlot[{noiseTNoiseQuadSa[3,3,3,f],noiseTNoiseQuadSa[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

plot25= LogLogPlot[{noiseTNoiseQuadSa[3,3,3,f],noiseTNoiseQuadSa[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

Show[plot24,plot24bc,plotCLIOmodel]

Show[plot25,plot24bc,plotCLIOmodel]

thermal noise - each direction

plot31= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot32= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot33= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

Show[plotTNQuadSa,plot31,plot32,plot33,plotCLIOmodel,PlotRange -> All]

plot34 =Show[plot32,plot33,PlotRange -> All]

Show[plot34,plotCLIOmodel,plotTN2QuadSa,plotTN3QuadSa]

Plot[{f,2 f,3 f,4 f,5 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

thermal noise - each dissipation g4

plot41= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.8]}]

plot42= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.8]}]

plot43= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.8]}]

Show[plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

Show[plotTNbcQuadSa,plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

thermal noise - each dissipation g3

plot51= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0.8]}]

plot52= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0.8]}]

plot53= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0.8]}]

plot54= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

Show[plotTNQuadSa,plot51,plot52,plot53,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plotTNQuadSa]

Show[plot54,plot52]

thermal noise - each dissipation magnet damping

plot61= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0]}]

plot62= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0]}]

plot63= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0]}]

Show[plotTNQuadSa,plot61,plot62,plot63,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plot62,plotTNQuadSa]

Quad pendulum simplified + heat link+heat link suspension 1(2004/01)

Parameters

intersting item

nItemQuadSb = 6 ;(*4:mirror*)

coupling & vibration amplification in cryostat

coupleZXQuadSb =5/100;(*coupling Z -> X*)
coupleYXQuadSb = 10/100;(*coupling Y -> X*)

offset of beam centering

offsetRollQuadSb = 0 mm;
offsetPitchQuadSb = 0.1 mm;
offsetYawQuadSb = 0.1 mm;

vibration amplification factor in cryostat

vibAmpQuadSb = 100;

dimensions of mass for quad pendulum

m1

m1DensQuadSb = alDens;
m1XQuadSb = 100mm;
m1YQuadSb = 100mm;
m1ZQuadSb = 70 mm;
mCube[m1DensQuadSb,m1XQuadSb,m1YQuadSb,m1ZQuadSb]

m2

m2DensQuadSb = alDens;
m2XQuadSb = 100mm;
m2YQuadSb = 100 mm;
m2ZQuadSb = 70 mm;
mCube[m2DensQuadSb,m2XQuadSb,m2YQuadSb,m2ZQuadSb]

m3

m3DensQuadSb = alDens;
m3XQuadSb = 100mm;
m3YQuadSb = 100 mm;
m3ZQuadSb = 70 mm;
mCube[m3DensQuadSb,m3XQuadSb,m3YQuadSb,m3ZQuadSb]

m4

m4DensQuadSb = saDens;
m4rQuadSb = rMass;
m4lQuadSb = lMass;

m2d

md2DensQuadSb = susDens;
md2XQuadSb = 120mm;
md2YQuadSb = 100 mm;
md2ZQuadSb = 50 mm;
md2dQuadSb = 5 mm;
mCage[md2DensQuadSb,md2XQuadSb,md2YQuadSb,md2ZQuadSb,md2dQuadSb]

m1k

mk1DensQuadSb = alDens;
mk1XQuadSb = 100mm;
mk1YQuadSb = 100 mm;
mk1ZQuadSb = 70 mm;
mCube[mk1DensQuadSb,mk1XQuadSb,mk1YQuadSb,mk1ZQuadSb]

spring for quad pendulum

g1

g1LengthQuadSb = 1 cm;
g1VFreqQuadSb = 4 Hz;

g2

g2LengthQuadSb = 25 cm;
g2VFreqQuadSb = 4 Hz;

g3

g3LengthQuadSb = 100 cm;
g3VFreqQuadSb = 4 Hz;

g4

g4LengthQuadSb = lSaPend ;

gd2

gd2LengthQuadSb = 25 cm;
gd2VFreqQuadSb = 4 Hz;

gk1

gk1LengthQuadSb = 100 cm;
gk1VFreqQuadSb = 4 Hz;

kA

kAUYoungQuadSb = alYoung;
kAUShearQuadSb = alShear;
kAURadQuadSb = Pi;
kAUDiaQuadSb = 0.2*10^(-3)m;
kAURadiusQuadSb = 7.5 cm;
kANumQuadSb = 1;

kB

kBUYoungQuadSb = alYoung;
kBUShearQuadSb = alShear;
kBURadQuadSb = Pi;
kBUDiaQuadSb = 0.2*10^(-3)m;
kBURadiusQuadSb = 15 cm;
kBNumQuadSb = 1;

heat check

kUslQuadSb := 1/(((lU[kAURadQuadSb,kAURadiusQuadSb])/(kANumQuadSb*aC[kAUDiaQuadSb])))

hAl2[tUMass,tISCryo,3000,kUslQuadSb](*heat transfered by heat link [W]*)

hAl2[tUMass,tISCryo,3000,kUslQuadSb]/heatSusMax(*show safety margin*)

position of wire clamp from COM (4 wires + symmetrical distribution) for quad pendulum

pg01XQuadSb = 20 mm;
pg01YQuadSb = 50 mm;
pg01ZQuadSb = 0 mm;
pg01dXQuadSb = 0.1 mm*10;
pg01dYQuadSb = 0.1 mm*10;
pg01dZQuadSb = 0.1 mm*10;

pg10XQuadSb = pg01XQuadSb;
pg10YQuadSb = pg01YQuadSb ;
pg10ZQuadSb = m1ZQuadSb/2;
pg10dXQuadSb = 0.1 mm*10;
pg10dYQuadSb = 0.1 mm*10 ;
pg10dZQuadSb = 0.1 mm*10;

pg12XQuadSb = 20 mm;
pg12YQuadSb = 50 mm;
pg12ZQuadSb = -m1ZQuadSb/2;
pg12dXQuadSb = 0.1 mm*10;
pg12dYQuadSb = 0.1 mm*10;
pg12dZQuadSb = 0.1 mm*10;

pg21XQuadSb = pg12XQuadSb;
pg21YQuadSb = pg12YQuadSb ;
pg21ZQuadSb = m2ZQuadSb/2;
pg21dXQuadSb = 0.1 mm*10;
pg21dYQuadSb = 0.1 mm*10 ;
pg21dZQuadSb = 0.1 mm*10;

pg23XQuadSb=10 mm;
pg23YQuadSb=50 mm;
pg23ZQuadSb=-m2ZQuadSb/2;
pg23dXQuadSb=0.1 mm*10;
pg23dYQuadSb=0.1 mm*10;
pg23dZQuadSb=0.1 mm*10;

pg32XQuadSb=pg23XQuadSb;
pg32YQuadSb=pg23YQuadSb;
pg32ZQuadSb=m3ZQuadSb/2;
pg32dXQuadSb=0.1 mm*10;
pg32dYQuadSb=0.1 mm*10;
pg32dZQuadSb=0.1 mm*10;

pg34XQuadSb=10 mm;
pg34YQuadSb=rMass/2-0 mm;
pg34ZQuadSb=-0 mm;
pg34dXQuadSb=0.1 mm*10;
pg34dYQuadSb=0.1 mm*10;
pg34dZQuadSb=0.1 mm*10;

pg43XQuadSb=pg34XQuadSb;
pg43YQuadSb=rMass/2;
pg43ZQuadSb= 0 mm;
pg43dXQuadSb=0.1 mm*10;
pg43dYQuadSb=0.1 mm*10;
pg43dZQuadSb= 0.1 mm*10;

pgd02XQuadSb = 180 mm/2;
pgd02YQuadSb = 130 mm/2 ;
pgd02ZQuadSb = -0 mm*1;
pgd02dXQuadSb = 0.1 mm*10;
pgd02dYQuadSb = 0.1 mm*10;
pgd02dZQuadSb = 0.1 mm*10;

pgd20XQuadSb = pgd02XQuadSb;
pgd20YQuadSb = pgd02YQuadSb ;
pgd20ZQuadSb = 0 mm*1;
pgd20dXQuadSb = 0.1 mm*10;
pgd20dYQuadSb = 0.1 mm*10;
pgd20dZQuadSb = 0.1 mm*10;

pgk01XQuadSb = 20 mm;
pgk01YQuadSb = 20 mm;
pgk01ZQuadSb = 0 mm;
pgk01dXQuadSb = 0.1 mm*10;
pgk01dYQuadSb = 0.1 mm*10;
pgk01dZQuadSb = 0.1 mm*10;

pgk10XQuadSb = pgk01XQuadSb;
pgk10YQuadSb = pgk01YQuadSb ;
pgk10ZQuadSb = mk1ZQuadSb/2;
pgk10dXQuadSb = 0.1 mm*10;
pgk10dYQuadSb = 0.1 mm*10 ;
pgk10dZQuadSb = 0.1 mm*10;

pk01XQuadSb =0 mm;
pk01YQuadSb = 0 mm /2;
pk01ZQuadSb = 0 mm;
pk01XQuadSb =  - m3XQuadSb/2;
pk01YQuadSb = 1 mm /2;
pk01ZQuadSb = 1 mm /2;

pk10XQuadSb =0 mm;
pk10YQuadSb = 0 mm /2;
pk10ZQuadSb = -mk1ZQuadSb/2;
pk10XQuadSb =  - m3XQuadSb/2;
pk10YQuadSb = 1 mm /2;
pk10ZQuadSb = 1 mm /2;

pk13XQuadSb =0 mm;
pk13YQuadSb = 0 mm /2;
pk13ZQuadSb = -mk1ZQuadSb/2;
pk13XQuadSb =  - m3XQuadSb/2;
pk13YQuadSb = 1 mm /2;
pk13ZQuadSb = 1 mm /2;

pk31XQuadSb =m3XQuadSb/2;
pk31YQuadSb = 0 mm /2;
pk31ZQuadSb = 0 mm;
pk31XQuadSb =  - m3XQuadSb/2;
pk31YQuadSb = 1 mm /2;
pk31ZQuadSb = 1 mm /2;

dissipation

qRoomHQuadSb = 10^6;
qCryoHQuadSb = 10^7;
qRoomVQuadSb = 10^4;
qCryoVQuadSb  =10^5;
qUAlQuadSb =  10^3;

qSaHQuadSb =  1/(3 10^(-7));
qSaVQuadSb =  10^6;

qg3VQuadSb = qCryoVQuadSb;

g3TempVQuadSb = m3TempQuadSb;(*縦防振の板ばねをcryoに入れるときはm3TempQuadSb,それ以外はm2TempQuadSb*)

in spring

g10HPhiQuadSb =  1/qRoomHQuadSb;
g10VPhiQuadSb =   1/qRoomVQuadSb;

g12HPhiQuadSb =   1/qRoomHQuadSb;
g12VPhiQuadSb =  1/qRoomVQuadSb;

g21HPhiQuadSb =  1/qRoomHQuadSb;
g21VPhiQuadSb =   1/qRoomVQuadSb;

g23HPhiQuadSb =   1/qCryoHQuadSb;
g23VPhiQuadSb =    1/qg3VQuadSb;

g32HPhiQuadSb =   1/qRoomHQuadSb;
g32VPhiQuadSb =    1/qg3VQuadSb;

g34HPhiQuadSb =  1/qSaHQuadSb;
g34VPhiQuadSb =  1/qSaVQuadSb;

g43HPhiQuadSb =  1/qSaHQuadSb;
g43VPhiQuadSb = 1/qSaVQuadSb;

gd20HPhiQuadSb =  1/qRoomHQuadSb;
gd20VPhiQuadSb =  1/qRoomVQuadSb;

gk10HPhiQuadSb =  1/qRoomHQuadSb;
gk10VPhiQuadSb =  1/qRoomVQuadSb;

kAPhiQuadSb =   1/qUAlQuadSb;
kBPhiQuadSb =   1/qUAlQuadSb;

magnet damping

d2DampFQuadSb = 5 Hz;
d2DampQQuadSb = 10*1;

kd1DampFQuadSb = 5 Hz;
kd1DampQQuadSb = 10*1;

temperature for triple pendulum

tISCryoQuadSb = 8 K;

m1TempQuadSb = 300 K;
m2TempQuadSb = 300 K;
m3TempQuadSb = 13 K;
m4TempQuadSb = 25 K;
md2TempQuadSb = 300 K;

mk1TempQuadSb = tISCryoQuadSb;

Preparation

coupling matrix

coupleMatQuadSb=(({{1}, {coupleYXQuadSb}, {coupleZXQuadSb}, {offsetRollQuadSb}, {offsetPitchQuadSb}, {offsetYawQuadSb}}));

mass & moment inertia for QuadSb pendulum

m1

mass1QuadSb = mCube[m1DensQuadSb, m1XQuadSb,m1YQuadSb, m1ZQuadSb]; 
iRoll1QuadSb = mIRollCube[m1DensQuadSb, m1XQuadSb,m1YQuadSb, m1ZQuadSb];
iPitch1QuadSb = mIPitchCube[m1DensQuadSb, m1XQuadSb,m1YQuadSb, m1ZQuadSb];
iYaw1QuadSb = mIYawCube[m1DensQuadSb, m1XQuadSb,m1YQuadSb, m1ZQuadSb];

m2

mass2QuadSb = mCube[m2DensQuadSb, m2XQuadSb,m2YQuadSb, m2ZQuadSb]; 
iRoll2QuadSb = mIRollCube[m2DensQuadSb, m2XQuadSb,m2YQuadSb, m2ZQuadSb];
iPitch2QuadSb = mIPitchCube[m2DensQuadSb, m2XQuadSb,m2YQuadSb, m2ZQuadSb];
iYaw2QuadSb = mIYawCube[m2DensQuadSb, m2XQuadSb,m2YQuadSb, m2ZQuadSb];

m3

mass3QuadSb = mCube[m3DensQuadSb, m3XQuadSb,m3YQuadSb, m3ZQuadSb]; 
iRoll3QuadSb = mIRollCube[m3DensQuadSb, m3XQuadSb,m3YQuadSb, m3ZQuadSb];
iPitch3QuadSb = mIPitchCube[m3DensQuadSb, m3XQuadSb,m3YQuadSb, m3ZQuadSb];
iYaw3QuadSb = mIYawCube[m3DensQuadSb, m3XQuadSb,m3YQuadSb, m3ZQuadSb];

m4

mass4QuadSb = mMass; (*see Parameters/Dimensions of final suspension/final mass*)
iRoll4QuadSb = mILCyl[m4DensQuadSb, m4rQuadSb,m4lQuadSb];
iPitch4QuadSb = mIRCyl[m4DensQuadSb, m4rQuadSb,m4lQuadSb];
iYaw4QuadSb = mIRCyl[m4DensQuadSb, m4rQuadSb,m4lQuadSb];

md2(cage)

massd2QuadSb = mCage[md2DensQuadSb, md2XQuadSb,md2YQuadSb, md2ZQuadSb,md2dQuadSb];
iRolld2QuadSb = mIRollCage[md2DensQuadSb, md2XQuadSb,md2YQuadSb, md2ZQuadSb,md2dQuadSb];
iPitchd2QuadSb = mIPitchCage[md2DensQuadSb, md2XQuadSb,md2YQuadSb, md2ZQuadSb,md2dQuadSb];
iYawd2QuadSb = mIYawCage[md2DensQuadSb, md2XQuadSb,md2YQuadSb, md2ZQuadSb,md2dQuadSb];

k1

massk1QuadSb = mCube[mk1DensQuadSb, mk1XQuadSb,mk1YQuadSb, mk1ZQuadSb]; 
iRollk1QuadSb = mIRollCube[mk1DensQuadSb, mk1XQuadSb,mk1YQuadSb, mk1ZQuadSb];
iPitchk1QuadSb = mIPitchCube[mk1DensQuadSb, mk1XQuadSb,mk1YQuadSb, mk1ZQuadSb];
iYawk1QuadSb = mIYawCube[mk1DensQuadSb, mk1XQuadSb,mk1YQuadSb, mk1ZQuadSb];

suspension wire for QuadSb pendulum

horizontal

g1HScQuadSb = scPend[mass1QuadSb+mass2QuadSb+mass3QuadSb+mass4QuadSb,g1LengthQuadSb];
g2HScQuadSb = scPend[mass2QuadSb+mass3QuadSb+mass4QuadSb,g2LengthQuadSb];
g3HScQuadSb = scPend[mass3QuadSb+mass4QuadSb,g3LengthQuadSb];
g4HScQuadSb = scPend[mass4QuadSb,g4LengthQuadSb];
gd2HScQuadSb = scPend[massd2QuadSb,gd2LengthQuadSb];
gk1HScQuadSb = scPend[massk1QuadSb,gk1LengthQuadSb];

vertical

g1VScQuadSb = scFreq[mass1QuadSb+mass2QuadSb+mass3QuadSb+mass4QuadSb,g1VFreqQuadSb];
g2VScQuadSb = scFreq[mass2QuadSb+mass3QuadSb+mass4QuadSb,g2VFreqQuadSb];
g3VScQuadSb = scFreq[mass3QuadSb+mass4QuadSb,g3VFreqQuadSb];
g4VScQuadSb = numSaPend*scVert[saYoung,diaSaPend,lSaPend];
gd2VScQuadSb = scFreq[massd2QuadSb,gd2VFreqQuadSb];
gk1VScQuadSb = scFreq[massk1QuadSb,gk1VFreqQuadSb];

g10

g10HQuadSb = g1HScQuadSb(1 +I g10HPhiQuadSb);
g10VQuadSb = g1VScQuadSb(1 +I g10VPhiQuadSb);

g10HThermalQuadSb = g1HScQuadSb(1 +tRoom I g10HPhiQuadSb);
g10VThermalQuadSb = g1VScQuadSb(1 +tRoom I g10VPhiQuadSb);

t10RollQuadSb = ctRoll[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,g1HScQuadSb,g10HPhiQuadSb,g1VScQuadSb,g10VPhiQuadSb];
t10PitchQuadSb = ctPitch[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,g1HScQuadSb,g10HPhiQuadSb,g1VScQuadSb,g10VPhiQuadSb];
t10YawQuadSb = ctYaw[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,g1HScQuadSb,g10HPhiQuadSb,g1VScQuadSb,g10VPhiQuadSb];

t10RollThermalQuadSb = ctRoll[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,g1HScQuadSb,tRoom g10HPhiQuadSb,g1VScQuadSb,tRoom g10VPhiQuadSb];
t10PitchThermalQuadSb = ctPitch[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,g1HScQuadSb,tRoom g10HPhiQuadSb,g1VScQuadSb,tRoom g10VPhiQuadSb];
t10YawThermalQuadSb = ctYaw[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,g1HScQuadSb,tRoom g10HPhiQuadSb,g1VScQuadSb,tRoom g10VPhiQuadSb];

ct10RollQuadSb = ctRoll[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg01XQuadSb,pg01YQuadSb,pg01ZQuadSb,g1HScQuadSb,g10HPhiQuadSb,g1VScQuadSb,g10VPhiQuadSb];
ct10PitchQuadSb = ctPitch[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg01XQuadSb,pg01YQuadSb,pg01ZQuadSb,g1HScQuadSb,g10HPhiQuadSb,g1VScQuadSb,g10VPhiQuadSb];
ct10YawQuadSb = ctYaw[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg01XQuadSb,pg01YQuadSb,pg01ZQuadSb,g1HScQuadSb,g10HPhiQuadSb,g1VScQuadSb,g10VPhiQuadSb];

ct10RollThermalQuadSb = ctRoll[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg01XQuadSb,pg01YQuadSb,pg01ZQuadSb,g1HScQuadSb,tRoom g10HPhiQuadSb,g1VScQuadSb,tRoom g10VPhiQuadSb];
ct10PitchThermalQuadSb = ctPitch[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg01XQuadSb,pg01YQuadSb,pg01ZQuadSb,g1HScQuadSb,tRoom g10HPhiQuadSb,g1VScQuadSb,tRoom g10VPhiQuadSb];
ct10YawThermalQuadSb = ctYaw[pg10XQuadSb,pg10YQuadSb,pg10ZQuadSb,pg01XQuadSb,pg01YQuadSb,pg01ZQuadSb,g1HScQuadSb,tRoom g10HPhiQuadSb,g1VScQuadSb,tRoom g10VPhiQuadSb];

g12

g12HQuadSb = g2HScQuadSb(1 +I g12HPhiQuadSb);
g12VQuadSb = g2VScQuadSb(1 +I g12VPhiQuadSb);

g12HThermalQuadSb = g2HScQuadSb(1 +m2TempQuadSb I g12HPhiQuadSb);
g12VThermalQuadSb = g2VScQuadSb(1 +m1TempQuadSb I g12VPhiQuadSb);

t12RollQuadSb = ctRoll[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,g12HPhiQuadSb,g2VScQuadSb,g12VPhiQuadSb];
t12PitchQuadSb = ctPitch[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,g12HPhiQuadSb,g2VScQuadSb,g12VPhiQuadSb];
t12YawQuadSb = ctYaw[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,g12HPhiQuadSb,g2VScQuadSb,g12VPhiQuadSb];

t12RollThermalQuadSb = ctRoll[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,m2TempQuadSb g12HPhiQuadSb,g2VScQuadSb,tRoom g12VPhiQuadSb];
t12PitchThermalQuadSb = ctPitch[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,m2TempQuadSb g12HPhiQuadSb,g2VScQuadSb,tRoom g12VPhiQuadSb];
t12YawThermalQuadSb = ctYaw[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,m2TempQuadSb g12HPhiQuadSb,g2VScQuadSb,tRoom g12VPhiQuadSb];

ct12RollQuadSb = ctRoll[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,g12HPhiQuadSb,g2VScQuadSb,g12VPhiQuadSb];
ct12PitchQuadSb = ctPitch[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,g12HPhiQuadSb,g2VScQuadSb,g12VPhiQuadSb];
ct12YawQuadSb = ctYaw[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,g12HPhiQuadSb,g2VScQuadSb,g12VPhiQuadSb];

ct12RollThermalQuadSb = ctRoll[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,m2TempQuadSb g12HPhiQuadSb,g2VScQuadSb,m1TempQuadSb g12VPhiQuadSb];
ct12PitchThermalQuadSb = ctPitch[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,m2TempQuadSb g12HPhiQuadSb,g2VScQuadSb,m1TempQuadSb g12VPhiQuadSb];
ct12YawThermalQuadSb = ctYaw[pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,m2TempQuadSb g12HPhiQuadSb,g2VScQuadSb,m1TempQuadSb g12VPhiQuadSb];

g21

g21HQuadSb = g2HScQuadSb(1 +I g21HPhiQuadSb);
g21VQuadSb = g2VScQuadSb(1 +I g21VPhiQuadSb);

g21HThermalQuadSb = g2HScQuadSb(1 +m1TempQuadSb I g21HPhiQuadSb);
g21VThermalQuadSb = g2VScQuadSb(1 +m1TempQuadSb I g21VPhiQuadSb);(*spring is attached to the mass1*)

t21RollQuadSb = ctRoll[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,g21HPhiQuadSb,g2VScQuadSb,g21VPhiQuadSb];
t21PitchQuadSb = ctPitch[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,g21HPhiQuadSb,g2VScQuadSb,g21VPhiQuadSb];
t21YawQuadSb = ctYaw[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,g21HPhiQuadSb,g2VScQuadSb,g21VPhiQuadSb];

t21RollThermalQuadSb = ctRoll[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,m1TempQuadSb g21HPhiQuadSb,g2VScQuadSb,m1TempQuadSb g21VPhiQuadSb];
t21PitchThermalQuadSb = ctPitch[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,m1TempQuadSb g21HPhiQuadSb,g2VScQuadSb,m1TempQuadSb g21VPhiQuadSb];
t21YawThermalQuadSb = ctYaw[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,g2HScQuadSb,m1TempQuadSb g21HPhiQuadSb,g2VScQuadSb,m1TempQuadSb g21VPhiQuadSb];

ct21RollQuadSb = ctRoll[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,g21HPhiQuadSb,g2VScQuadSb,g21VPhiQuadSb];
ct21PitchQuadSb = ctPitch[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,g21HPhiQuadSb,g2VScQuadSb,g21VPhiQuadSb];
ct21YawQuadSb = ctYaw[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,g21HPhiQuadSb,g2VScQuadSb,g21VPhiQuadSb];

ct21RollThermalQuadSb = ctRoll[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,m1TempQuadSb g21HPhiQuadSb,g2VScQuadSb,m1TempQuadSb g21VPhiQuadSb];
ct21PitchThermalQuadSb = ctPitch[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,m1TempQuadSb g21HPhiQuadSb,g2VScQuadSb,m1TempQuadSb g21VPhiQuadSb];
ct21YawThermalQuadSb = ctYaw[pg21XQuadSb,pg21YQuadSb,pg21ZQuadSb,pg12XQuadSb,pg12YQuadSb,pg12ZQuadSb,g2HScQuadSb,m1TempQuadSb g21HPhiQuadSb,g2VScQuadSb,m1TempQuadSb g21VPhiQuadSb];

g23

g23HQuadSb = g3HScQuadSb(1 +I g23HPhiQuadSb);
g23VQuadSb = g3VScQuadSb(1 +I g23VPhiQuadSb);

g23HThermalQuadSb = g3HScQuadSb(1 +m3TempQuadSb I g23HPhiQuadSb);
g23VThermalQuadSb = g3VScQuadSb(1 +g3TempVQuadSb I g23VPhiQuadSb);

t23RollQuadSb = ctRoll[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,g23HPhiQuadSb,g3VScQuadSb,g23VPhiQuadSb];
t23PitchQuadSb = ctPitch[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,g23HPhiQuadSb,g3VScQuadSb,g23VPhiQuadSb];
t23YawQuadSb = ctYaw[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,g23HPhiQuadSb,g3VScQuadSb,g23VPhiQuadSb];

t23RollThermalQuadSb = ctRoll[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,m3TempQuadSb g23HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g23VPhiQuadSb];
t23PitchThermalQuadSb = ctPitch[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,m3TempQuadSb g23HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g23VPhiQuadSb];
t23YawThermalQuadSb = ctYaw[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,m3TempQuadSb g23HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g23VPhiQuadSb];

ct23RollQuadSb = ctRoll[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,g23HPhiQuadSb,g3VScQuadSb,g23VPhiQuadSb];
ct23PitchQuadSb = ctPitch[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,g23HPhiQuadSb,g3VScQuadSb,g23VPhiQuadSb];
ct23YawQuadSb = ctYaw[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,g23HPhiQuadSb,g3VScQuadSb,g23VPhiQuadSb];

ct23RollThermalQuadSb = ctRoll[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,m3TempQuadSb g23HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g23VPhiQuadSb];
ct23PitchThermalQuadSb = ctPitch[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,m3TempQuadSb g23HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g23VPhiQuadSb];
ct23YawThermalQuadSb = ctYaw[pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,m3TempQuadSb g23HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g23VPhiQuadSb];

g32

g32HQuadSb = g3HScQuadSb(1 +I g32HPhiQuadSb);
g32VQuadSb = g3VScQuadSb(1 +I g32VPhiQuadSb);

g32HThermalQuadSb = g3HScQuadSb(1 +m2TempQuadSb I g32HPhiQuadSb);
g32VThermalQuadSb = g3VScQuadSb(1 +g3TempVQuadSb I g32VPhiQuadSb);

t32RollQuadSb = ctRoll[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,g32HPhiQuadSb,g3VScQuadSb,g32VPhiQuadSb];
t32PitchQuadSb = ctPitch[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,g32HPhiQuadSb,g3VScQuadSb,g32VPhiQuadSb];
t32YawQuadSb = ctYaw[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,g32HPhiQuadSb,g3VScQuadSb,g32VPhiQuadSb];

t32RollThermalQuadSb = ctRoll[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,m2TempQuadSb g32HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g32VPhiQuadSb];
t32PitchThermalQuadSb = ctPitch[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,m2TempQuadSb g32HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g32VPhiQuadSb];
t32YawThermalQuadSb = ctYaw[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,g3HScQuadSb,m2TempQuadSb g32HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g32VPhiQuadSb];

ct32RollQuadSb = ctRoll[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,g32HPhiQuadSb,g3VScQuadSb,g32VPhiQuadSb];
ct32PitchQuadSb = ctPitch[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,g32HPhiQuadSb,g3VScQuadSb,g32VPhiQuadSb];
ct32YawQuadSb = ctYaw[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,g32HPhiQuadSb,g3VScQuadSb,g32VPhiQuadSb];

ct32RollThermalQuadSb = ctRoll[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,m2TempQuadSb g32HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g32VPhiQuadSb];
ct32PitchThermalQuadSb = ctPitch[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,m2TempQuadSb g32HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g32VPhiQuadSb];
ct32YawThermalQuadSb = ctYaw[pg32XQuadSb,pg32YQuadSb,pg32ZQuadSb,pg23XQuadSb,pg23YQuadSb,pg23ZQuadSb,g3HScQuadSb,m2TempQuadSb g32HPhiQuadSb,g3VScQuadSb,g3TempVQuadSb g32VPhiQuadSb];

g34

g34HQuadSb = g4HScQuadSb(1 +I g34HPhiQuadSb);
g34VQuadSb = g4VScQuadSb(1 +I g34VPhiQuadSb);

g34HThermalQuadSb = g4HScQuadSb(1 +m4TempQuadSb I g34HPhiQuadSb);
g34VThermalQuadSb = g4VScQuadSb(1 +m4TempQuadSb I g34VPhiQuadSb);

t34RollQuadSb = ctRoll[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,g34HPhiQuadSb,g4VScQuadSb,g34VPhiQuadSb];
t34PitchQuadSb = ctPitch[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,g34HPhiQuadSb,g4VScQuadSb,g34VPhiQuadSb];
t34YawQuadSb = ctYaw[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,g34HPhiQuadSb,g4VScQuadSb,g34VPhiQuadSb];

t34RollThermalQuadSb = ctRoll[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,m4TempQuadSb g34HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g34VPhiQuadSb];
t34PitchThermalQuadSb = ctPitch[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,m4TempQuadSb g34HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g34VPhiQuadSb];
t34YawThermalQuadSb = ctYaw[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,m4TempQuadSb g34HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g34VPhiQuadSb];

ct34RollQuadSb = ctRoll[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,g34HPhiQuadSb,g4VScQuadSb,g34VPhiQuadSb];
ct34PitchQuadSb = ctPitch[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,g34HPhiQuadSb,g4VScQuadSb,g34VPhiQuadSb];
ct34YawQuadSb = ctYaw[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,g34HPhiQuadSb,g4VScQuadSb,g34VPhiQuadSb];

ct34RollThermalQuadSb = ctRoll[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,m4TempQuadSb g34HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g34VPhiQuadSb];
ct34PitchThermalQuadSb = ctPitch[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,m4TempQuadSb g34HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g34VPhiQuadSb];
ct34YawThermalQuadSb = ctYaw[pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,m4TempQuadSb g34HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g34VPhiQuadSb];

g43

g43HQuadSb = g4HScQuadSb(1 +I g43HPhiQuadSb);
g43VQuadSb = g4VScQuadSb(1 +I g43VPhiQuadSb);

g43HThermalQuadSb = g4HScQuadSb(1 +m3TempQuadSb I g43HPhiQuadSb);
g43VThermalQuadSb = g4VScQuadSb(1 +m4TempQuadSb I g43VPhiQuadSb);

t43RollQuadSb = ctRoll[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,g43HPhiQuadSb,g4VScQuadSb,g43VPhiQuadSb];
t43PitchQuadSb = ctPitch[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,g43HPhiQuadSb,g4VScQuadSb,g43VPhiQuadSb];
t43YawQuadSb = ctYaw[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,g43HPhiQuadSb,g4VScQuadSb,g43VPhiQuadSb];

t43RollThermalQuadSb = ctRoll[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,m3TempQuadSb g43HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g43VPhiQuadSb];
t43PitchThermalQuadSb = ctPitch[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,m3TempQuadSb g43HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g43VPhiQuadSb];
t43YawThermalQuadSb = ctYaw[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,g4HScQuadSb,m3TempQuadSb g43HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g43VPhiQuadSb];

ct43RollQuadSb = ctRoll[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,g43HPhiQuadSb,g4VScQuadSb,g43VPhiQuadSb];
ct43PitchQuadSb = ctPitch[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,g43HPhiQuadSb,g4VScQuadSb,g43VPhiQuadSb];
ct43YawQuadSb = ctYaw[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,g43HPhiQuadSb,g4VScQuadSb,g43VPhiQuadSb];

ct43RollThermalQuadSb = ctRoll[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,m3TempQuadSb g43HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g43VPhiQuadSb];
ct43PitchThermalQuadSb = ctPitch[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,m3TempQuadSb g43HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g43VPhiQuadSb];
ct43YawThermalQuadSb = ctYaw[pg43XQuadSb,pg43YQuadSb,pg43ZQuadSb,pg34XQuadSb,pg34YQuadSb,pg34ZQuadSb,g4HScQuadSb,m3TempQuadSb g43HPhiQuadSb,g4VScQuadSb,m4TempQuadSb g43VPhiQuadSb];

gd20

gd20HQuadSb = gd2HScQuadSb(1 +I gd20HPhiQuadSb);
gd20VQuadSb = gd2VScQuadSb(1 +I gd20VPhiQuadSb);

gd20HThermalQuadSb = gd2HScQuadSb(1 +tRoom I gd20HPhiQuadSb);
gd20VThermalQuadSb = gd2VScQuadSb(1 +tRoom I gd20VPhiQuadSb);

td20RollQuadSb = ctRoll[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,gd2HScQuadSb,gd20HPhiQuadSb,gd2VScQuadSb,gd20VPhiQuadSb];
td20PitchQuadSb = ctPitch[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,gd2HScQuadSb,gd20HPhiQuadSb,gd2VScQuadSb,gd20VPhiQuadSb];
td20YawQuadSb = ctYaw[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,gd2HScQuadSb,gd20HPhiQuadSb,gd2VScQuadSb,gd20VPhiQuadSb];

td20RollThermalQuadSb = ctRoll[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,gd2HScQuadSb,tRoom gd20HPhiQuadSb,gd2VScQuadSb,tRoom gd20VPhiQuadSb];
td20PitchThermalQuadSb = ctPitch[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,gd2HScQuadSb,tRoom gd20HPhiQuadSb,gd2VScQuadSb,tRoom gd20VPhiQuadSb];
td20YawThermalQuadSb = ctYaw[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,gd2HScQuadSb,tRoom gd20HPhiQuadSb,gd2VScQuadSb,tRoom gd20VPhiQuadSb];

ctd20RollQuadSb = ctRoll[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd02XQuadSb,pgd02YQuadSb,pgd02ZQuadSb,gd2HScQuadSb,gd20HPhiQuadSb,gd2VScQuadSb,gd20VPhiQuadSb];
ctd20PitchQuadSb = ctPitch[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd02XQuadSb,pgd02YQuadSb,pgd02ZQuadSb,gd2HScQuadSb,gd20HPhiQuadSb,gd2VScQuadSb,gd20VPhiQuadSb];
ctd20YawQuadSb = ctYaw[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd02XQuadSb,pgd02YQuadSb,pgd02ZQuadSb,gd2HScQuadSb,gd20HPhiQuadSb,gd2VScQuadSb,gd20VPhiQuadSb];

ctd20RollThermalQuadSb = ctRoll[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd02XQuadSb,pgd02YQuadSb,pgd02ZQuadSb,gd2HScQuadSb,tRoom gd20HPhiQuadSb,gd2VScQuadSb,tRoom gd20VPhiQuadSb];
ctd20PitchThermalQuadSb = ctPitch[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd02XQuadSb,pgd02YQuadSb,pgd02ZQuadSb,gd2HScQuadSb,tRoom gd20HPhiQuadSb,gd2VScQuadSb,tRoom gd20VPhiQuadSb];
ctd20YawThermalQuadSb = ctYaw[pgd20XQuadSb,pgd20YQuadSb,pgd20ZQuadSb,pgd02XQuadSb,pgd02YQuadSb,pgd02ZQuadSb,gd2HScQuadSb,tRoom gd20HPhiQuadSb,gd2VScQuadSb,tRoom gd20VPhiQuadSb];

gk10

gk10HQuadSb = gk1HScQuadSb(1 +I gk10HPhiQuadSb);
gk10VQuadSb = gk1VScQuadSb(1 +I gk10VPhiQuadSb);

gk10HThermalQuadSb = gk1HScQuadSb(1 +tRoom I gk10HPhiQuadSb);
gk10VThermalQuadSb = gk1VScQuadSb(1 +tRoom I gk10VPhiQuadSb);

tgk10RollQuadSb = ctRoll[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,gk1HScQuadSb,gk10HPhiQuadSb,gk1VScQuadSb,gk10VPhiQuadSb];
tgk10PitchQuadSb = ctPitch[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,gk1HScQuadSb,gk10HPhiQuadSb,gk1VScQuadSb,gk10VPhiQuadSb];
tgk10YawQuadSb = ctYaw[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,gk1HScQuadSb,gk10HPhiQuadSb,gk1VScQuadSb,gk10VPhiQuadSb];

tgk10RollThermalQuadSb = ctRoll[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,gk1HScQuadSb,tRoom gk10HPhiQuadSb,gk1VScQuadSb,tRoom gk10VPhiQuadSb];
tgk10PitchThermalQuadSb = ctPitch[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,gk1HScQuadSb,tRoom gk10HPhiQuadSb,gk1VScQuadSb,tRoom gk10VPhiQuadSb];
tgk10YawThermalQuadSb = ctYaw[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,gk1HScQuadSb,tRoom gk10HPhiQuadSb,gk1VScQuadSb,tRoom gk10VPhiQuadSb];

ctgk10RollQuadSb = ctRoll[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk01XQuadSb,pgk01YQuadSb,pgk01ZQuadSb,gk1HScQuadSb,gk10HPhiQuadSb,gk1VScQuadSb,gk10VPhiQuadSb];
ctgk10PitchQuadSb = ctPitch[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk01XQuadSb,pgk01YQuadSb,pgk01ZQuadSb,gk1HScQuadSb,gk10HPhiQuadSb,gk1VScQuadSb,gk10VPhiQuadSb];
ctgk10YawQuadSb = ctYaw[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk01XQuadSb,pgk01YQuadSb,pgk01ZQuadSb,gk1HScQuadSb,gk10HPhiQuadSb,gk1VScQuadSb,gk10VPhiQuadSb];

ctgk10RollThermalQuadSb = ctRoll[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk01XQuadSb,pgk01YQuadSb,pgk01ZQuadSb,gk1HScQuadSb,tRoom gk10HPhiQuadSb,gk1VScQuadSb,tRoom gk10VPhiQuadSb];
ctgk10PitchThermalQuadSb = ctPitch[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk01XQuadSb,pgk01YQuadSb,pgk01ZQuadSb,gk1HScQuadSb,tRoom gk10HPhiQuadSb,gk1VScQuadSb,tRoom gk10VPhiQuadSb];
ctgk10YawThermalQuadSb = ctYaw[pgk10XQuadSb,pgk10YQuadSb,pgk10ZQuadSb,pgk01XQuadSb,pgk01YQuadSb,pgk01ZQuadSb,gk1HScQuadSb,tRoom gk10HPhiQuadSb,gk1VScQuadSb,tRoom gk10VPhiQuadSb];

heat link

kA

kAXscQuadSb = kANumQuadSb*scUX[kAUYoungQuadSb,kAURadQuadSb,kAUDiaQuadSb,kAURadiusQuadSb];
kAYscQuadSb = kANumQuadSb*scUY[kAUShearQuadSb,kAUDiaQuadSb,kAURadiusQuadSb];
kAZscQuadSb = kANumQuadSb*scUZ[kAUYoungQuadSb,kAURadQuadSb,kAUDiaQuadSb,kAURadiusQuadSb];

kB

kBXscQuadSb = kBNumQuadSb*scUX[kBUYoungQuadSb,kBURadQuadSb,kBUDiaQuadSb,kBURadiusQuadSb];
kBYscQuadSb = kBNumQuadSb*scUY[kBUShearQuadSb,kBUDiaQuadSb,kBURadiusQuadSb];
kBZscQuadSb = kBNumQuadSb*scUZ[kBUYoungQuadSb,kBURadQuadSb,kBUDiaQuadSb,kBURadiusQuadSb];

k10

k10XQuadSb = kAXscQuadSb(1+ I kAPhiQuadSb);
k10YQuadSb = kAYscQuadSb(1+ I kAPhiQuadSb);
k10ZQuadSb = kAZscQuadSb(1+ I kAPhiQuadSb);

k10XThermalQuadSb = kAXscQuadSb(1+ tISCryoQuadSb I kAPhiQuadSb);
k10YThermalQuadSb = kAYscQuadSb(1+ tISCryoQuadSb I kAPhiQuadSb);
k10ZThermalQuadSb = kAZscQuadSb(1+ tISCryoQuadSb I kAPhiQuadSb);

tk10RollQuadSb = ctURoll[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb,kAPhiQuadSb];
tk10PitchQuadSb = ctUPitch[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb,kAPhiQuadSb];
tk10YawQuadSb = ctUYaw[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb,kAPhiQuadSb];

tk10RollThermalQuadSb = ctURoll[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb, tISCryoQuadSb kAPhiQuadSb];
tk10PitchThermalQuadSb = ctUPitch[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb, tISCryoQuadSb kAPhiQuadSb];
tk10YawThermalQuadSb = ctUYaw[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb, tISCryoQuadSb kAPhiQuadSb];

ctk10RollQuadSb = ctURoll[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb,kAPhiQuadSb];
ctk10PitchQuadSb = ctUPitch[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb,kAPhiQuadSb];
ctk10YawQuadSb = ctUYaw[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb,kAPhiQuadSb];

ctk10RollThermalQuadSb = ctURoll[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb, tISCryoQuadSb kAPhiQuadSb];
ctk10PitchThermalQuadSb = ctUPitch[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb, tISCryoQuadSb kAPhiQuadSb];
ctk10YawThermalQuadSb = ctUYaw[pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,kAXscQuadSb,kAYscQuadSb,kAZscQuadSb, tISCryoQuadSb kAPhiQuadSb];

k13

k13XQuadSb = kBXscQuadSb(1+ I kBPhiQuadSb);
k13YQuadSb = kBYscQuadSb(1+ I kBPhiQuadSb);
k13ZQuadSb = kBZscQuadSb(1+ I kBPhiQuadSb);

k13XThermalQuadSb = kBXscQuadSb(1+ mk1TempQuadSb I kBPhiQuadSb);
k13YThermalQuadSb = kBYscQuadSb(1+ mk1TempQuadSb I kBPhiQuadSb);
k13ZThermalQuadSb = kBZscQuadSb(1+ mk1TempQuadSb I kBPhiQuadSb);

tk13RollQuadSb = ctURoll[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];
tk13PitchQuadSb = ctUPitch[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];
tk13YawQuadSb = ctUYaw[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];

tk13RollThermalQuadSb = ctURoll[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, mk1TempQuadSb kBPhiQuadSb];
tk13PitchThermalQuadSb = ctUPitch[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, mk1TempQuadSb kBPhiQuadSb];
tk13YawThermalQuadSb = ctUYaw[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, mk1TempQuadSb kBPhiQuadSb];

ctk13RollQuadSb = ctURoll[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];
ctk13PitchQuadSb = ctUPitch[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];
ctk13YawQuadSb = ctUYaw[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];

ctk13RollThermalQuadSb = ctURoll[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, mk1TempQuadSb kBPhiQuadSb];
ctk13PitchThermalQuadSb = ctUPitch[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, mk1TempQuadSb kBPhiQuadSb];
ctk13YawThermalQuadSb = ctUYaw[pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, mk1TempQuadSb kBPhiQuadSb];

k31

k31XQuadSb = kBXscQuadSb(1+ I kBPhiQuadSb);
k31YQuadSb = kBYscQuadSb(1+ I kBPhiQuadSb);
k31ZQuadSb = kBZscQuadSb(1+ I kBPhiQuadSb);

k31XThermalQuadSb = kBXscQuadSb(1+ tISCryoQuadSb I kBPhiQuadSb);
k31YThermalQuadSb = kBYscQuadSb(1+ tISCryoQuadSb I kBPhiQuadSb);
k31ZThermalQuadSb = kBZscQuadSb(1+ tISCryoQuadSb I kBPhiQuadSb);

tk31RollQuadSb = ctURoll[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];
tk31PitchQuadSb = ctUPitch[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];
tk31YawQuadSb = ctUYaw[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];

tk31RollThermalQuadSb = ctURoll[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, m3TempQuadSb kBPhiQuadSb];
tk31PitchThermalQuadSb = ctUPitch[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, m3TempQuadSb kBPhiQuadSb];
tk31YawThermalQuadSb = ctUYaw[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, m3TempQuadSb kBPhiQuadSb];

ctk31RollQuadSb = ctURoll[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];
ctk31PitchQuadSb = ctUPitch[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];
ctk31YawQuadSb = ctUYaw[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb,kBPhiQuadSb];

ctk31RollThermalQuadSb = ctURoll[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, m3TempQuadSb kBPhiQuadSb];
ctk31PitchThermalQuadSb = ctUPitch[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, m3TempQuadSb kBPhiQuadSb];
ctk31YawThermalQuadSb = ctUYaw[pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,kBXscQuadSb,kBYscQuadSb,kBZscQuadSb, m3TempQuadSb kBPhiQuadSb];

damping

d2DampQuadSb[f_] := Damp[f,d2DampFQuadSb,d2DampQQuadSb];

k1DampQuadSb[f_] := Damp[f,kd1DampFQuadSb,kd1DampQQuadSb];

parameter set for QuadSb pendulum

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
mk1,ixk1,iyk1,izk1,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,
khd20,kvd20,
khk10,kvk10,
kxu10,kyu10,kzu10,kxu13,kyu13,kzu13,kxu31,kyu31,kzu31,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd20,tyd20,tzd20,txk10,tyk10,tzk10,
txu10,tyu10,tzu10,txu13,tyu13,tzu13,txu31,tyu31,tzu31,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd20,ctyd20,ctzd20,ctxk10,ctyk10,ctzk10,
ctxu10,ctyu10,ctzu10,ctxu13,ctyu13,ctzu13,ctxu31,ctyu31,ctzu31,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd02,zd20,zk01,zk10,
xu01,yu01,zu01,xu10,yu10,zu10,xu13,yu13,zu13,xu31,yu31,zu31,
d2,dk1};

{nItemQuadSb,f,
mass1QuadSb,iRoll1QuadSb,iPitch1QuadSb,iYaw1QuadSb,mass2QuadSb,iRoll2QuadSb,iPitch2QuadSb,iYaw2QuadSb,mass3QuadSb,iRoll3QuadSb,iPitch3QuadSb,iYaw3QuadSb,mass4QuadSb,iRoll4QuadSb,iPitch4QuadSb,iYaw4QuadSb,massd2QuadSb,iRolld2QuadSb,iPitchd2QuadSb,iYawd2QuadSb,
massk1QuadSb,iRollk1QuadSb,iPitchk1QuadSb,iYawk1QuadSb,

g10HQuadSb,g10VQuadSb,g12HQuadSb,g12VQuadSb,g21HQuadSb,g21VQuadSb,g23HQuadSb,g23VQuadSb,g32HQuadSb,g32VQuadSb,g34HQuadSb,g34VQuadSb,g43HQuadSb,g43VQuadSb,
gd20HQuadSb,gd20VQuadSb,
gk10HQuadSb,gk10VQuadSb,
k10XQuadSb,k10YQuadSb,k10ZQuadSb,k13XQuadSb,k13YQuadSb,k13ZQuadSb,k31XQuadSb,k31YQuadSb,k31ZQuadSb,

t10RollQuadSb,t10PitchQuadSb,t10YawQuadSb,t12RollQuadSb,t12PitchQuadSb,t12YawQuadSb,t21RollQuadSb,t21PitchQuadSb,t21YawQuadSb,t23RollQuadSb,t23PitchQuadSb,t23YawQuadSb,t32RollQuadSb,t32PitchQuadSb,t32YawQuadSb,t34RollQuadSb,t34PitchQuadSb,t34YawQuadSb,t43RollQuadSb,t43PitchQuadSb,t43YawQuadSb,td20RollQuadSb,td20PitchQuadSb,td20YawQuadSb,tgk10RollQuadSb,tgk10PitchQuadSb,tgk10YawQuadSb,
tk10RollQuadSb,tk10PitchQuadSb,tk10YawQuadSb,tk13RollQuadSb,tk13PitchQuadSb,tk13YawQuadSb,tk31RollQuadSb,tk31PitchQuadSb,tk31YawQuadSb,

ct10RollQuadSb,ct10PitchQuadSb,ct10YawQuadSb,ct12RollQuadSb,ct12PitchQuadSb,ct12YawQuadSb,ct21RollQuadSb,ct21PitchQuadSb,ct21YawQuadSb,ct23RollQuadSb,ct23PitchQuadSb,ct23YawQuadSb,ct32RollQuadSb,ct32PitchQuadSb,ct32YawQuadSb,ct34RollQuadSb,ct34PitchQuadSb,ct34YawQuadSb,ct43RollQuadSb,ct43PitchQuadSb,ct43YawQuadSb,ctd20RollQuadSb,ctd20PitchQuadSb,ctd20YawQuadSb,ctgk10RollQuadSb,ctgk10PitchQuadSb,ctgk10YawQuadSb,
ctk10RollQuadSb,ctk10PitchQuadSb,ctk10YawQuadSb,ctk13RollQuadSb,ctk13PitchQuadSb,ctk13YawQuadSb,ctk31RollQuadSb,ctk31PitchQuadSb,ctk31YawQuadSb,

pg01ZQuadSb,pg10ZQuadSb,pg12ZQuadSb,pg21ZQuadSb,pg23ZQuadSb,pg32ZQuadSb,pg34ZQuadSb,pg43ZQuadSb,
pgd02ZQuadSb,pgd20ZQuadSb,pgk01ZQuadSb,pgk10ZQuadSb,
pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,
pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,

d2DampQuadSb[f],k1DampQuadSb[f]
}

{f,
mass1QuadSb,iRoll1QuadSb,iPitch1QuadSb,iYaw1QuadSb,mass2QuadSb,iRoll2QuadSb,iPitch2QuadSb,iYaw2QuadSb,mass3QuadSb,iRoll3QuadSb,iPitch3QuadSb,iYaw3QuadSb,mass4QuadSb,iRoll4QuadSb,iPitch4QuadSb,iYaw4QuadSb,massd2QuadSb,iRolld2QuadSb,iPitchd2QuadSb,iYawd2QuadSb,
massk1QuadSb,iRollk1QuadSb,iPitchk1QuadSb,iYawk1QuadSb,

g10HThermalQuadSb,g10VThermalQuadSb,g12HThermalQuadSb,g12VThermalQuadSb,g21HThermalQuadSb,g21VThermalQuadSb,g23HThermalQuadSb,g23VThermalQuadSb,g32HThermalQuadSb,g32VThermalQuadSb,g34HThermalQuadSb,g34VThermalQuadSb,g43HThermalQuadSb,g43VThermalQuadSb,gd20HThermalQuadSb,gd20VThermalQuadSb,gk10HThermalQuadSb,gk10VThermalQuadSb,
k10XThermalQuadSb,k10YThermalQuadSb,k10ZThermalQuadSb,k13XThermalQuadSb,k13YThermalQuadSb,k13ZThermalQuadSb,k31XThermalQuadSb,k31YThermalQuadSb,k31ZThermalQuadSb,

t10RollThermalQuadSb,t10PitchThermalQuadSb,t10YawThermalQuadSb,t12RollThermalQuadSb,t12PitchThermalQuadSb,t12YawThermalQuadSb,t21RollThermalQuadSb,t21PitchThermalQuadSb,t21YawThermalQuadSb,t23RollThermalQuadSb,t23PitchThermalQuadSb,t23YawThermalQuadSb,t32RollThermalQuadSb,t32PitchThermalQuadSb,t32YawThermalQuadSb,t34RollThermalQuadSb,t34PitchThermalQuadSb,t34YawThermalQuadSb,t43RollThermalQuadSb,t43PitchThermalQuadSb,t43YawThermalQuadSb,td20RollThermalQuadSb,td20PitchThermalQuadSb,td20YawThermalQuadSb,tgk10RollThermalQuadSb,tgk10PitchThermalQuadSb,tgk10YawThermalQuadSb,
tk10RollThermalQuadSb,tk10PitchThermalQuadSb,tk10YawThermalQuadSb,tk13RollThermalQuadSb,tk13PitchThermalQuadSb,tk13YawThermalQuadSb,tk31RollThermalQuadSb,tk31PitchThermalQuadSb,tk31YawThermalQuadSb,

ct10RollThermalQuadSb,ct10PitchThermalQuadSb,ct10YawThermalQuadSb,ct12RollThermalQuadSb,ct12PitchThermalQuadSb,ct12YawThermalQuadSb,ct21RollThermalQuadSb,ct21PitchThermalQuadSb,ct21YawThermalQuadSb,ct23RollThermalQuadSb,ct23PitchThermalQuadSb,ct23YawThermalQuadSb,ct32RollThermalQuadSb,ct32PitchThermalQuadSb,ct32YawThermalQuadSb,ct34RollThermalQuadSb,ct34PitchThermalQuadSb,ct34YawThermalQuadSb,ct43RollThermalQuadSb,ct43PitchThermalQuadSb,ct43YawThermalQuadSb,ctd20RollThermalQuadSb,ctd20PitchThermalQuadSb,ctd20YawThermalQuadSb,
ctgk10RollThermalQuadSb,ctgk10PitchThermalQuadSb,ctgk10YawThermalQuadSb,
ctk10RollThermalQuadSb,ctk10PitchThermalQuadSb,ctk10YawThermalQuadSb,ctk13RollThermalQuadSb,ctk13PitchThermalQuadSb,ctk13YawThermalQuadSb,ctk31RollThermalQuadSb,ctk31PitchThermalQuadSb,ctk31YawThermalQuadSb,

pg01ZQuadSb,pg10ZQuadSb,pg12ZQuadSb,pg21ZQuadSb,pg23ZQuadSb,pg32ZQuadSb,pg34ZQuadSb,pg43ZQuadSb,
pgd02ZQuadSb,pgd20ZQuadSb,pgk01ZQuadSb,pgk10ZQuadSb,
pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,
pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,

d2DampQuadSb[f],k1DampQuadSb[f]
}

calculation for QuadSb pendulum

trfQuadSb[ll_,nn_,jj_,f_]:=trfAmpQuadSb[ll,nn,jj,
nItemQuadSb,f,
mass1QuadSb,iRoll1QuadSb,iPitch1QuadSb,iYaw1QuadSb,mass2QuadSb,iRoll2QuadSb,iPitch2QuadSb,iYaw2QuadSb,mass3QuadSb,iRoll3QuadSb,iPitch3QuadSb,iYaw3QuadSb,mass4QuadSb,iRoll4QuadSb,iPitch4QuadSb,iYaw4QuadSb,massd2QuadSb,iRolld2QuadSb,iPitchd2QuadSb,iYawd2QuadSb,
massk1QuadSb,iRollk1QuadSb,iPitchk1QuadSb,iYawk1QuadSb,

g10HQuadSb,g10VQuadSb,g12HQuadSb,g12VQuadSb,g21HQuadSb,g21VQuadSb,g23HQuadSb,g23VQuadSb,g32HQuadSb,g32VQuadSb,g34HQuadSb,g34VQuadSb,g43HQuadSb,g43VQuadSb,
gd20HQuadSb,gd20VQuadSb,
gk10HQuadSb,gk10VQuadSb,
k10XQuadSb,k10YQuadSb,k10ZQuadSb,k13XQuadSb,k13YQuadSb,k13ZQuadSb,k31XQuadSb,k31YQuadSb,k31ZQuadSb,

t10RollQuadSb,t10PitchQuadSb,t10YawQuadSb,t12RollQuadSb,t12PitchQuadSb,t12YawQuadSb,t21RollQuadSb,t21PitchQuadSb,t21YawQuadSb,t23RollQuadSb,t23PitchQuadSb,t23YawQuadSb,t32RollQuadSb,t32PitchQuadSb,t32YawQuadSb,t34RollQuadSb,t34PitchQuadSb,t34YawQuadSb,t43RollQuadSb,t43PitchQuadSb,t43YawQuadSb,td20RollQuadSb,td20PitchQuadSb,td20YawQuadSb,tgk10RollQuadSb,tgk10PitchQuadSb,tgk10YawQuadSb,
tk10RollQuadSb,tk10PitchQuadSb,tk10YawQuadSb,tk13RollQuadSb,tk13PitchQuadSb,tk13YawQuadSb,tk31RollQuadSb,tk31PitchQuadSb,tk31YawQuadSb,

ct10RollQuadSb,ct10PitchQuadSb,ct10YawQuadSb,ct12RollQuadSb,ct12PitchQuadSb,ct12YawQuadSb,ct21RollQuadSb,ct21PitchQuadSb,ct21YawQuadSb,ct23RollQuadSb,ct23PitchQuadSb,ct23YawQuadSb,ct32RollQuadSb,ct32PitchQuadSb,ct32YawQuadSb,ct34RollQuadSb,ct34PitchQuadSb,ct34YawQuadSb,ct43RollQuadSb,ct43PitchQuadSb,ct43YawQuadSb,ctd20RollQuadSb,ctd20PitchQuadSb,ctd20YawQuadSb,ctgk10RollQuadSb,ctgk10PitchQuadSb,ctgk10YawQuadSb,
ctk10RollQuadSb,ctk10PitchQuadSb,ctk10YawQuadSb,ctk13RollQuadSb,ctk13PitchQuadSb,ctk13YawQuadSb,ctk31RollQuadSb,ctk31PitchQuadSb,ctk31YawQuadSb,

pg01ZQuadSb,pg10ZQuadSb,pg12ZQuadSb,pg21ZQuadSb,pg23ZQuadSb,pg32ZQuadSb,pg34ZQuadSb,pg43ZQuadSb,
pgd02ZQuadSb,pgd20ZQuadSb,pgk01ZQuadSb,pgk10ZQuadSb,
pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,
pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,

d2DampQuadSb[f],k1DampQuadSb[f]
]

noiseSeisQuadSb[nn_,jj_,f_]:=Part[coupleMatQuadSb,jj].seisQuadSb[vibAmpQuadSb,nn,jj,
nItemQuadSb,f,
mass1QuadSb,iRoll1QuadSb,iPitch1QuadSb,iYaw1QuadSb,mass2QuadSb,iRoll2QuadSb,iPitch2QuadSb,iYaw2QuadSb,mass3QuadSb,iRoll3QuadSb,iPitch3QuadSb,iYaw3QuadSb,mass4QuadSb,iRoll4QuadSb,iPitch4QuadSb,iYaw4QuadSb,massd2QuadSb,iRolld2QuadSb,iPitchd2QuadSb,iYawd2QuadSb,
massk1QuadSb,iRollk1QuadSb,iPitchk1QuadSb,iYawk1QuadSb,

g10HQuadSb,g10VQuadSb,g12HQuadSb,g12VQuadSb,g21HQuadSb,g21VQuadSb,g23HQuadSb,g23VQuadSb,g32HQuadSb,g32VQuadSb,g34HQuadSb,g34VQuadSb,g43HQuadSb,g43VQuadSb,
gd20HQuadSb,gd20VQuadSb,
gk10HQuadSb,gk10VQuadSb,
k10XQuadSb,k10YQuadSb,k10ZQuadSb,k13XQuadSb,k13YQuadSb,k13ZQuadSb,k31XQuadSb,k31YQuadSb,k31ZQuadSb,

t10RollQuadSb,t10PitchQuadSb,t10YawQuadSb,t12RollQuadSb,t12PitchQuadSb,t12YawQuadSb,t21RollQuadSb,t21PitchQuadSb,t21YawQuadSb,t23RollQuadSb,t23PitchQuadSb,t23YawQuadSb,t32RollQuadSb,t32PitchQuadSb,t32YawQuadSb,t34RollQuadSb,t34PitchQuadSb,t34YawQuadSb,t43RollQuadSb,t43PitchQuadSb,t43YawQuadSb,td20RollQuadSb,td20PitchQuadSb,td20YawQuadSb,tgk10RollQuadSb,tgk10PitchQuadSb,tgk10YawQuadSb,
tk10RollQuadSb,tk10PitchQuadSb,tk10YawQuadSb,tk13RollQuadSb,tk13PitchQuadSb,tk13YawQuadSb,tk31RollQuadSb,tk31PitchQuadSb,tk31YawQuadSb,

ct10RollQuadSb,ct10PitchQuadSb,ct10YawQuadSb,ct12RollQuadSb,ct12PitchQuadSb,ct12YawQuadSb,ct21RollQuadSb,ct21PitchQuadSb,ct21YawQuadSb,ct23RollQuadSb,ct23PitchQuadSb,ct23YawQuadSb,ct32RollQuadSb,ct32PitchQuadSb,ct32YawQuadSb,ct34RollQuadSb,ct34PitchQuadSb,ct34YawQuadSb,ct43RollQuadSb,ct43PitchQuadSb,ct43YawQuadSb,ctd20RollQuadSb,ctd20PitchQuadSb,ctd20YawQuadSb,ctgk10RollQuadSb,ctgk10PitchQuadSb,ctgk10YawQuadSb,
ctk10RollQuadSb,ctk10PitchQuadSb,ctk10YawQuadSb,ctk13RollQuadSb,ctk13PitchQuadSb,ctk13YawQuadSb,ctk31RollQuadSb,ctk31PitchQuadSb,ctk31YawQuadSb,

pg01ZQuadSb,pg10ZQuadSb,pg12ZQuadSb,pg21ZQuadSb,pg23ZQuadSb,pg32ZQuadSb,pg34ZQuadSb,pg43ZQuadSb,
pgd02ZQuadSb,pgd20ZQuadSb,pgk01ZQuadSb,pgk10ZQuadSb,
pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,
pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,

d2DampQuadSb[f],k1DampQuadSb[f]
]

noiseSeisCryoQuadSb[nn_,jj_,f_] :=Part[coupleMatQuadSb,jj].seisCryoQuadSb[vibAmpQuadSb,nn,jj,
nItemQuadSb,f,
mass1QuadSb,iRoll1QuadSb,iPitch1QuadSb,iYaw1QuadSb,mass2QuadSb,iRoll2QuadSb,iPitch2QuadSb,iYaw2QuadSb,mass3QuadSb,iRoll3QuadSb,iPitch3QuadSb,iYaw3QuadSb,mass4QuadSb,iRoll4QuadSb,iPitch4QuadSb,iYaw4QuadSb,massd2QuadSb,iRolld2QuadSb,iPitchd2QuadSb,iYawd2QuadSb,
massk1QuadSb,iRollk1QuadSb,iPitchk1QuadSb,iYawk1QuadSb,

g10HQuadSb,g10VQuadSb,g12HQuadSb,g12VQuadSb,g21HQuadSb,g21VQuadSb,g23HQuadSb,g23VQuadSb,g32HQuadSb,g32VQuadSb,g34HQuadSb,g34VQuadSb,g43HQuadSb,g43VQuadSb,
gd20HQuadSb,gd20VQuadSb,
gk10HQuadSb,gk10VQuadSb,
k10XQuadSb,k10YQuadSb,k10ZQuadSb,k13XQuadSb,k13YQuadSb,k13ZQuadSb,k31XQuadSb,k31YQuadSb,k31ZQuadSb,

t10RollQuadSb,t10PitchQuadSb,t10YawQuadSb,t12RollQuadSb,t12PitchQuadSb,t12YawQuadSb,t21RollQuadSb,t21PitchQuadSb,t21YawQuadSb,t23RollQuadSb,t23PitchQuadSb,t23YawQuadSb,t32RollQuadSb,t32PitchQuadSb,t32YawQuadSb,t34RollQuadSb,t34PitchQuadSb,t34YawQuadSb,t43RollQuadSb,t43PitchQuadSb,t43YawQuadSb,td20RollQuadSb,td20PitchQuadSb,td20YawQuadSb,tgk10RollQuadSb,tgk10PitchQuadSb,tgk10YawQuadSb,
tk10RollQuadSb,tk10PitchQuadSb,tk10YawQuadSb,tk13RollQuadSb,tk13PitchQuadSb,tk13YawQuadSb,tk31RollQuadSb,tk31PitchQuadSb,tk31YawQuadSb,

ct10RollQuadSb,ct10PitchQuadSb,ct10YawQuadSb,ct12RollQuadSb,ct12PitchQuadSb,ct12YawQuadSb,ct21RollQuadSb,ct21PitchQuadSb,ct21YawQuadSb,ct23RollQuadSb,ct23PitchQuadSb,ct23YawQuadSb,ct32RollQuadSb,ct32PitchQuadSb,ct32YawQuadSb,ct34RollQuadSb,ct34PitchQuadSb,ct34YawQuadSb,ct43RollQuadSb,ct43PitchQuadSb,ct43YawQuadSb,ctd20RollQuadSb,ctd20PitchQuadSb,ctd20YawQuadSb,ctgk10RollQuadSb,ctgk10PitchQuadSb,ctgk10YawQuadSb,
ctk10RollQuadSb,ctk10PitchQuadSb,ctk10YawQuadSb,ctk13RollQuadSb,ctk13PitchQuadSb,ctk13YawQuadSb,ctk31RollQuadSb,ctk31PitchQuadSb,ctk31YawQuadSb,

pg01ZQuadSb,pg10ZQuadSb,pg12ZQuadSb,pg21ZQuadSb,pg23ZQuadSb,pg32ZQuadSb,pg34ZQuadSb,pg43ZQuadSb,
pgd02ZQuadSb,pgd20ZQuadSb,pgk01ZQuadSb,pgk10ZQuadSb,
pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,
pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,

d2DampQuadSb[f],k1DampQuadSb[f]
]

dispTNoiseQuadSb[ll_,nn_,f_]:=tNoiseQuadSb[ll,nn,
f,
mass1QuadSb,iRoll1QuadSb,iPitch1QuadSb,iYaw1QuadSb,mass2QuadSb,iRoll2QuadSb,iPitch2QuadSb,iYaw2QuadSb,mass3QuadSb,iRoll3QuadSb,iPitch3QuadSb,iYaw3QuadSb,mass4QuadSb,iRoll4QuadSb,iPitch4QuadSb,iYaw4QuadSb,massd2QuadSb,iRolld2QuadSb,iPitchd2QuadSb,iYawd2QuadSb,
massk1QuadSb,iRollk1QuadSb,iPitchk1QuadSb,iYawk1QuadSb,

g10HThermalQuadSb,g10VThermalQuadSb,g12HThermalQuadSb,g12VThermalQuadSb,g21HThermalQuadSb,g21VThermalQuadSb,g23HThermalQuadSb,g23VThermalQuadSb,g32HThermalQuadSb,g32VThermalQuadSb,g34HThermalQuadSb,g34VThermalQuadSb,g43HThermalQuadSb,g43VThermalQuadSb,gd20HThermalQuadSb,gd20VThermalQuadSb,gk10HThermalQuadSb,gk10VThermalQuadSb,
k10XThermalQuadSb,k10YThermalQuadSb,k10ZThermalQuadSb,k13XThermalQuadSb,k13YThermalQuadSb,k13ZThermalQuadSb,k31XThermalQuadSb,k31YThermalQuadSb,k31ZThermalQuadSb,

t10RollThermalQuadSb,t10PitchThermalQuadSb,t10YawThermalQuadSb,t12RollThermalQuadSb,t12PitchThermalQuadSb,t12YawThermalQuadSb,t21RollThermalQuadSb,t21PitchThermalQuadSb,t21YawThermalQuadSb,t23RollThermalQuadSb,t23PitchThermalQuadSb,t23YawThermalQuadSb,t32RollThermalQuadSb,t32PitchThermalQuadSb,t32YawThermalQuadSb,t34RollThermalQuadSb,t34PitchThermalQuadSb,t34YawThermalQuadSb,t43RollThermalQuadSb,t43PitchThermalQuadSb,t43YawThermalQuadSb,td20RollThermalQuadSb,td20PitchThermalQuadSb,td20YawThermalQuadSb,tgk10RollThermalQuadSb,tgk10PitchThermalQuadSb,tgk10YawThermalQuadSb,
tk10RollThermalQuadSb,tk10PitchThermalQuadSb,tk10YawThermalQuadSb,tk13RollThermalQuadSb,tk13PitchThermalQuadSb,tk13YawThermalQuadSb,tk31RollThermalQuadSb,tk31PitchThermalQuadSb,tk31YawThermalQuadSb,

ct10RollThermalQuadSb,ct10PitchThermalQuadSb,ct10YawThermalQuadSb,ct12RollThermalQuadSb,ct12PitchThermalQuadSb,ct12YawThermalQuadSb,ct21RollThermalQuadSb,ct21PitchThermalQuadSb,ct21YawThermalQuadSb,ct23RollThermalQuadSb,ct23PitchThermalQuadSb,ct23YawThermalQuadSb,ct32RollThermalQuadSb,ct32PitchThermalQuadSb,ct32YawThermalQuadSb,ct34RollThermalQuadSb,ct34PitchThermalQuadSb,ct34YawThermalQuadSb,ct43RollThermalQuadSb,ct43PitchThermalQuadSb,ct43YawThermalQuadSb,ctd20RollThermalQuadSb,ctd20PitchThermalQuadSb,ctd20YawThermalQuadSb,
ctgk10RollThermalQuadSb,ctgk10PitchThermalQuadSb,ctgk10YawThermalQuadSb,
ctk10RollThermalQuadSb,ctk10PitchThermalQuadSb,ctk10YawThermalQuadSb,ctk13RollThermalQuadSb,ctk13PitchThermalQuadSb,ctk13YawThermalQuadSb,ctk31RollThermalQuadSb,ctk31PitchThermalQuadSb,ctk31YawThermalQuadSb,

pg01ZQuadSb,pg10ZQuadSb,pg12ZQuadSb,pg21ZQuadSb,pg23ZQuadSb,pg32ZQuadSb,pg34ZQuadSb,pg43ZQuadSb,
pgd02ZQuadSb,pgd20ZQuadSb,pgk01ZQuadSb,pgk10ZQuadSb,
pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,
pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,

d2DampQuadSb[f],k1DampQuadSb[f]
]

noiseTNoiseQuadSb[ll_,nn_,jj_,f_] := {1}.coupleMatQuadSb[[jj]]*trfQuadSb[ll,nn,jj,f]*dispTNoiseQuadSb[ll,nn,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)

seismic noise

noiseSeisSumQuadSb[f_] := Sqrt[Sum[Sum[noiseSeisQuadSb[nn,jj,f],{jj,1,6}]^2,{nn,1,6}]]

noiseSeisCryoSumQuadSb[f_] := Sqrt[Sum[Sum[noiseSeisCryoQuadSb[nn,jj,f],{jj,1,6}]^2,{nn,1,6}]]

noiseSeisCompQuadSb[jj_,f_] := Sqrt[Sum[noiseSeisQuadSb[nn,jj,f]^2,{nn,1,6}]]

noiseSeisSumQuadSb[100]

noiseSeisCryoSumQuadSb[100]

suspension thermal noise (without violin mode)

noiseTNoiseSumQuadSb[f_] := Sqrt[Sum[Sum[Sum[noiseTNoiseQuadSb[ll,nn,jj,f],{jj,1,6}]^2,{ll,1,6}],{nn,1, nTotalQuadSb}]]

noiseTNoiseCompDouble[jj_,f_] := Sqrt[Sum[Sum[noiseTNoiseQuadSb[ll,nn,jj,f]^2,{ll,1,6}],{nn,1, nTotalQuadSb}]] (*sum up of noise in "jj" direction*)

noiseTNoiseSumQuadSb[100]

Q & resonant frequency

resQuadSb=f  /. NSolve[Det[matQuadSb[f,
mass1QuadSb,iRoll1QuadSb,iPitch1QuadSb,iYaw1QuadSb,mass2QuadSb,iRoll2QuadSb,iPitch2QuadSb,iYaw2QuadSb,mass3QuadSb,iRoll3QuadSb,iPitch3QuadSb,iYaw3QuadSb,mass4QuadSb,iRoll4QuadSb,iPitch4QuadSb,iYaw4QuadSb,massd2QuadSb,iRolld2QuadSb,iPitchd2QuadSb,iYawd2QuadSb,
massk1QuadSb,iRollk1QuadSb,iPitchk1QuadSb,iYawk1QuadSb,

g10HQuadSb,g10VQuadSb,g12HQuadSb,g12VQuadSb,g21HQuadSb,g21VQuadSb,g23HQuadSb,g23VQuadSb,g32HQuadSb,g32VQuadSb,g34HQuadSb,g34VQuadSb,g43HQuadSb,g43VQuadSb,
gd20HQuadSb,gd20VQuadSb,
gk10HQuadSb,gk10VQuadSb,
k10XQuadSb,k10YQuadSb,k10ZQuadSb,k13XQuadSb,k13YQuadSb,k13ZQuadSb,k31XQuadSb,k31YQuadSb,k31ZQuadSb,

t10RollQuadSb,t10PitchQuadSb,t10YawQuadSb,t12RollQuadSb,t12PitchQuadSb,t12YawQuadSb,t21RollQuadSb,t21PitchQuadSb,t21YawQuadSb,t23RollQuadSb,t23PitchQuadSb,t23YawQuadSb,t32RollQuadSb,t32PitchQuadSb,t32YawQuadSb,t34RollQuadSb,t34PitchQuadSb,t34YawQuadSb,t43RollQuadSb,t43PitchQuadSb,t43YawQuadSb,td20RollQuadSb,td20PitchQuadSb,td20YawQuadSb,tgk10RollQuadSb,tgk10PitchQuadSb,tgk10YawQuadSb,
tk10RollQuadSb,tk10PitchQuadSb,tk10YawQuadSb,tk13RollQuadSb,tk13PitchQuadSb,tk13YawQuadSb,tk31RollQuadSb,tk31PitchQuadSb,tk31YawQuadSb,

ct10RollQuadSb,ct10PitchQuadSb,ct10YawQuadSb,ct12RollQuadSb,ct12PitchQuadSb,ct12YawQuadSb,ct21RollQuadSb,ct21PitchQuadSb,ct21YawQuadSb,ct23RollQuadSb,ct23PitchQuadSb,ct23YawQuadSb,ct32RollQuadSb,ct32PitchQuadSb,ct32YawQuadSb,ct34RollQuadSb,ct34PitchQuadSb,ct34YawQuadSb,ct43RollQuadSb,ct43PitchQuadSb,ct43YawQuadSb,ctd20RollQuadSb,ctd20PitchQuadSb,ctd20YawQuadSb,ctgk10RollQuadSb,ctgk10PitchQuadSb,ctgk10YawQuadSb,
ctk10RollQuadSb,ctk10PitchQuadSb,ctk10YawQuadSb,ctk13RollQuadSb,ctk13PitchQuadSb,ctk13YawQuadSb,ctk31RollQuadSb,ctk31PitchQuadSb,ctk31YawQuadSb,

pg01ZQuadSb,pg10ZQuadSb,pg12ZQuadSb,pg21ZQuadSb,pg23ZQuadSb,pg32ZQuadSb,pg34ZQuadSb,pg43ZQuadSb,
pgd02ZQuadSb,pgd20ZQuadSb,pgk01ZQuadSb,pgk10ZQuadSb,
pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,
pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,

d2DampQuadSb[f],k1DampQuadSb[f]]]==0,f];

Sort[resQuadSb/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

Plots

LogLogPlot[Abs[Part[Inverse[matQuadSb[
f,
mass1QuadSb,iRoll1QuadSb,iPitch1QuadSb,iYaw1QuadSb,mass2QuadSb,iRoll2QuadSb,iPitch2QuadSb,iYaw2QuadSb,mass3QuadSb,iRoll3QuadSb,iPitch3QuadSb,iYaw3QuadSb,mass4QuadSb,iRoll4QuadSb,iPitch4QuadSb,iYaw4QuadSb,massd2QuadSb,iRolld2QuadSb,iPitchd2QuadSb,iYawd2QuadSb,
massk1QuadSb,iRollk1QuadSb,iPitchk1QuadSb,iYawk1QuadSb,

g10HQuadSb,g10VQuadSb,g12HQuadSb,g12VQuadSb,g21HQuadSb,g21VQuadSb,g23HQuadSb,g23VQuadSb,g32HQuadSb,g32VQuadSb,g34HQuadSb,g34VQuadSb,g43HQuadSb,g43VQuadSb,
gd20HQuadSb,gd20VQuadSb,
gk10HQuadSb,gk10VQuadSb,
k10XQuadSb,k10YQuadSb,k10ZQuadSb,k13XQuadSb,k13YQuadSb,k13ZQuadSb,k31XQuadSb,k31YQuadSb,k31ZQuadSb,

t10RollQuadSb,t10PitchQuadSb,t10YawQuadSb,t12RollQuadSb,t12PitchQuadSb,t12YawQuadSb,t21RollQuadSb,t21PitchQuadSb,t21YawQuadSb,t23RollQuadSb,t23PitchQuadSb,t23YawQuadSb,t32RollQuadSb,t32PitchQuadSb,t32YawQuadSb,t34RollQuadSb,t34PitchQuadSb,t34YawQuadSb,t43RollQuadSb,t43PitchQuadSb,t43YawQuadSb,td20RollQuadSb,td20PitchQuadSb,td20YawQuadSb,tgk10RollQuadSb,tgk10PitchQuadSb,tgk10YawQuadSb,
tk10RollQuadSb,tk10PitchQuadSb,tk10YawQuadSb,tk13RollQuadSb,tk13PitchQuadSb,tk13YawQuadSb,tk31RollQuadSb,tk31PitchQuadSb,tk31YawQuadSb,

ct10RollQuadSb,ct10PitchQuadSb,ct10YawQuadSb,ct12RollQuadSb,ct12PitchQuadSb,ct12YawQuadSb,ct21RollQuadSb,ct21PitchQuadSb,ct21YawQuadSb,ct23RollQuadSb,ct23PitchQuadSb,ct23YawQuadSb,ct32RollQuadSb,ct32PitchQuadSb,ct32YawQuadSb,ct34RollQuadSb,ct34PitchQuadSb,ct34YawQuadSb,ct43RollQuadSb,ct43PitchQuadSb,ct43YawQuadSb,ctd20RollQuadSb,ctd20PitchQuadSb,ctd20YawQuadSb,ctgk10RollQuadSb,ctgk10PitchQuadSb,ctgk10YawQuadSb,
ctk10RollQuadSb,ctk10PitchQuadSb,ctk10YawQuadSb,ctk13RollQuadSb,ctk13PitchQuadSb,ctk13YawQuadSb,ctk31RollQuadSb,ctk31PitchQuadSb,ctk31YawQuadSb,

pg01ZQuadSb,pg10ZQuadSb,pg12ZQuadSb,pg21ZQuadSb,pg23ZQuadSb,pg32ZQuadSb,pg34ZQuadSb,pg43ZQuadSb,
pgd02ZQuadSb,pgd20ZQuadSb,pgk01ZQuadSb,pgk10ZQuadSb,
pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,
pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,

d2DampQuadSb[f],k1DampQuadSb[f]

]],(6(6-1)+1),(6(6-1)+1)]],{f,0.1,100}]

LogLogPlot[trfAmpQuadSb[1,6,1,4,
f,
mass1QuadSb,iRoll1QuadSb,iPitch1QuadSb,iYaw1QuadSb,mass2QuadSb,iRoll2QuadSb,iPitch2QuadSb,iYaw2QuadSb,mass3QuadSb,iRoll3QuadSb,iPitch3QuadSb,iYaw3QuadSb,mass4QuadSb,iRoll4QuadSb,iPitch4QuadSb,iYaw4QuadSb,massd2QuadSb,iRolld2QuadSb,iPitchd2QuadSb,iYawd2QuadSb,
massk1QuadSb,iRollk1QuadSb,iPitchk1QuadSb,iYawk1QuadSb,

g10HQuadSb,g10VQuadSb,g12HQuadSb,g12VQuadSb,g21HQuadSb,g21VQuadSb,g23HQuadSb,g23VQuadSb,g32HQuadSb,g32VQuadSb,g34HQuadSb,g34VQuadSb,g43HQuadSb,g43VQuadSb,
gd20HQuadSb,gd20VQuadSb,
gk10HQuadSb,gk10VQuadSb,
k10XQuadSb,k10YQuadSb,k10ZQuadSb,k13XQuadSb,k13YQuadSb,k13ZQuadSb,k31XQuadSb,k31YQuadSb,k31ZQuadSb,

t10RollQuadSb,t10PitchQuadSb,t10YawQuadSb,t12RollQuadSb,t12PitchQuadSb,t12YawQuadSb,t21RollQuadSb,t21PitchQuadSb,t21YawQuadSb,t23RollQuadSb,t23PitchQuadSb,t23YawQuadSb,t32RollQuadSb,t32PitchQuadSb,t32YawQuadSb,t34RollQuadSb,t34PitchQuadSb,t34YawQuadSb,t43RollQuadSb,t43PitchQuadSb,t43YawQuadSb,td20RollQuadSb,td20PitchQuadSb,td20YawQuadSb,tgk10RollQuadSb,tgk10PitchQuadSb,tgk10YawQuadSb,
tk10RollQuadSb,tk10PitchQuadSb,tk10YawQuadSb,tk13RollQuadSb,tk13PitchQuadSb,tk13YawQuadSb,tk31RollQuadSb,tk31PitchQuadSb,tk31YawQuadSb,

ct10RollQuadSb,ct10PitchQuadSb,ct10YawQuadSb,ct12RollQuadSb,ct12PitchQuadSb,ct12YawQuadSb,ct21RollQuadSb,ct21PitchQuadSb,ct21YawQuadSb,ct23RollQuadSb,ct23PitchQuadSb,ct23YawQuadSb,ct32RollQuadSb,ct32PitchQuadSb,ct32YawQuadSb,ct34RollQuadSb,ct34PitchQuadSb,ct34YawQuadSb,ct43RollQuadSb,ct43PitchQuadSb,ct43YawQuadSb,ctd20RollQuadSb,ctd20PitchQuadSb,ctd20YawQuadSb,ctgk10RollQuadSb,ctgk10PitchQuadSb,ctgk10YawQuadSb,
ctk10RollQuadSb,ctk10PitchQuadSb,ctk10YawQuadSb,ctk13RollQuadSb,ctk13PitchQuadSb,ctk13YawQuadSb,ctk31RollQuadSb,ctk31PitchQuadSb,ctk31YawQuadSb,

pg01ZQuadSb,pg10ZQuadSb,pg12ZQuadSb,pg21ZQuadSb,pg23ZQuadSb,pg32ZQuadSb,pg34ZQuadSb,pg43ZQuadSb,
pgd02ZQuadSb,pgd20ZQuadSb,pgk01ZQuadSb,pgk10ZQuadSb,
pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,
pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,

d2DampQuadSb[f],k1DampQuadSb[f]
],{f,0.1,100}]

LogLogPlot[trfSeisCryoQuadSb[1,1,nItemQuadSb,f,
mass1QuadSb,iRoll1QuadSb,iPitch1QuadSb,iYaw1QuadSb,mass2QuadSb,iRoll2QuadSb,iPitch2QuadSb,iYaw2QuadSb,mass3QuadSb,iRoll3QuadSb,iPitch3QuadSb,iYaw3QuadSb,mass4QuadSb,iRoll4QuadSb,iPitch4QuadSb,iYaw4QuadSb,massd2QuadSb,iRolld2QuadSb,iPitchd2QuadSb,iYawd2QuadSb,
massk1QuadSb,iRollk1QuadSb,iPitchk1QuadSb,iYawk1QuadSb,

g10HQuadSb,g10VQuadSb,g12HQuadSb,g12VQuadSb,g21HQuadSb,g21VQuadSb,g23HQuadSb,g23VQuadSb,g32HQuadSb,g32VQuadSb,g34HQuadSb,g34VQuadSb,g43HQuadSb,g43VQuadSb,
gd20HQuadSb,gd20VQuadSb,
gk10HQuadSb,gk10VQuadSb,
k10XQuadSb,k10YQuadSb,k10ZQuadSb,k13XQuadSb,k13YQuadSb,k13ZQuadSb,k31XQuadSb,k31YQuadSb,k31ZQuadSb,

t10RollQuadSb,t10PitchQuadSb,t10YawQuadSb,t12RollQuadSb,t12PitchQuadSb,t12YawQuadSb,t21RollQuadSb,t21PitchQuadSb,t21YawQuadSb,t23RollQuadSb,t23PitchQuadSb,t23YawQuadSb,t32RollQuadSb,t32PitchQuadSb,t32YawQuadSb,t34RollQuadSb,t34PitchQuadSb,t34YawQuadSb,t43RollQuadSb,t43PitchQuadSb,t43YawQuadSb,td20RollQuadSb,td20PitchQuadSb,td20YawQuadSb,tgk10RollQuadSb,tgk10PitchQuadSb,tgk10YawQuadSb,
tk10RollQuadSb,tk10PitchQuadSb,tk10YawQuadSb,tk13RollQuadSb,tk13PitchQuadSb,tk13YawQuadSb,tk31RollQuadSb,tk31PitchQuadSb,tk31YawQuadSb,

ct10RollQuadSb,ct10PitchQuadSb,ct10YawQuadSb,ct12RollQuadSb,ct12PitchQuadSb,ct12YawQuadSb,ct21RollQuadSb,ct21PitchQuadSb,ct21YawQuadSb,ct23RollQuadSb,ct23PitchQuadSb,ct23YawQuadSb,ct32RollQuadSb,ct32PitchQuadSb,ct32YawQuadSb,ct34RollQuadSb,ct34PitchQuadSb,ct34YawQuadSb,ct43RollQuadSb,ct43PitchQuadSb,ct43YawQuadSb,ctd20RollQuadSb,ctd20PitchQuadSb,ctd20YawQuadSb,ctgk10RollQuadSb,ctgk10PitchQuadSb,ctgk10YawQuadSb,
ctk10RollQuadSb,ctk10PitchQuadSb,ctk10YawQuadSb,ctk13RollQuadSb,ctk13PitchQuadSb,ctk13YawQuadSb,ctk31RollQuadSb,ctk31PitchQuadSb,ctk31YawQuadSb,

pg01ZQuadSb,pg10ZQuadSb,pg12ZQuadSb,pg21ZQuadSb,pg23ZQuadSb,pg32ZQuadSb,pg34ZQuadSb,pg43ZQuadSb,
pgd02ZQuadSb,pgd20ZQuadSb,pgk01ZQuadSb,pgk10ZQuadSb,
pk01XQuadSb,pk01YQuadSb,pk01ZQuadSb,
pk10XQuadSb,pk10YQuadSb,pk10ZQuadSb,pk13XQuadSb,pk13YQuadSb,pk13ZQuadSb,pk31XQuadSb,pk31YQuadSb,pk31ZQuadSb,

d2DampQuadSb[f],k1DampQuadSb[f]],{f,0.1,100}]

all components

plotSeis1QuadSb = LogLogPlot[{2*noiseSeisSumQuadSb[f],2*noiseSeisCryoSumQuadSb[f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis2QuadSb = LogLogPlot[{2*noiseSeisSumQuadSb[f],2*noiseSeisCryoSumQuadSb[f]*(f/1)^2},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis3QuadSb = LogLogPlot[{2*noiseSeisSumQuadSb[f],2*noiseSeisCryoSumQuadSb[f]*(f/1)^2},{f,100,1000},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeisQuadSb=Show[plotSeis1QuadSb,plotSeis2QuadSb,plotSeis3QuadSb,PlotRange -> All]

plotTN1QuadSb =LogLogPlot[2*noiseTNoiseSumQuadSb[f],{f,0.1,10},PlotStyle -> RGBColor[0,0,1]]

plotTN2QuadSb =LogLogPlot[2*noiseTNoiseSumQuadSb[f],{f,10,100},PlotStyle -> RGBColor[0,0,1]]

plotTN3QuadSb =LogLogPlot[2*noiseTNoiseSumQuadSb[f],{f,100,1000},PlotStyle -> RGBColor[0,0,1]]

plotTNQuadSb = Show[plotTN1QuadSb,plotTN2QuadSb,plotTN3QuadSb,PlotRange -> All]

plotShotQuadSb=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0.5,0]]

Show[plotSeisQuadSb,plotTNQuadSb,plotShotQuadSb,plotCLIOmodel]

Show[plotSeisQuadSb,plotTNQuadSb,plotCLIOmodel,plotCLIORoommodel,plotShotQuadSb,plotLISM030320]

Show[plotTN2QuadSb,plotTN3QuadSb,plotSeis2QuadSb,plotCLIOmodel,plotShotQuadSb,plotCLIOMTNRoom,PlotRange -> All ]

all components 2

plotSeis101QuadSb = LogLogPlot[2*noiseSeisSumQuadSb[f],{f,0.1,10},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis102QuadSb = LogLogPlot[2*noiseSeisSumQuadSb[f],{f,10,100},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis103QuadSb = LogLogPlot[2*noiseSeisSumQuadSb[f],{f,100,1000},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeisQuadSb2=Show[plotSeis101QuadSb,plotSeis102QuadSb,plotSeis103QuadSb,PlotRange -> All]

plotTN101QuadSb =LogLogPlot[2*noiseTNoiseSumQuadSb[f],{f,0.1,10},PlotStyle -> RGBColor[0.5,0,1]]

plotTN102QuadSb =LogLogPlot[2*noiseTNoiseSumQuadSb[f],{f,10,100},PlotStyle -> RGBColor[0.5,0,1]]

plotTN103QuadSb =LogLogPlot[2*noiseTNoiseSumQuadSb[f],{f,100,1000},PlotStyle -> RGBColor[0.5,0,1]]

plotTNQuadSb2 = Show[plotTN101QuadSb,plotTN102QuadSb,plotTN103QuadSb,PlotRange -> All]

plotShotQuadSb102=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0,0.5]]

Show[plotTN102QuadSb,plotTN2QuadSb,plotCLIO25model]

Show[plotTN102QuadSb,plotSeis102QuadSb,plotTN2QuadSb,plotSeis2QuadSb,plotCLIOmodel]

Show[plotSeis102QuadSb,plotSeis2QuadSb,plotCLIOmodel]

Show[plotTN102QuadSb,plotTN2QuadSb,plotCLIOmodel]

Show[plotSeisQuadSb2,plotTNQuadSb2,plotCLIOmodel,plotShotQuadSb102]

Show[plotSeisQuadSb2,plotTNQuadSb2,plotCLIOmodel,plotShotQuadSb102,plotLISM030320]

Show[plotSeisQuadSb,plotTNQuadSb,plotSeisQuadSb2,plotTNQuadSb2,plotShotQuadSb102,plotCLIOmodel]

Show[plotSeisQuadSb,plotSeisQuadSb2,plotShotQuadSb102,plotCLIOmodel]

Show[plotTNQuadSb,plotTNQuadSb2,plotShotQuadSb102,plotCLIOmodel]

Show[plotShotQuadSb,plotShotQuadSb102,plotCLIOmodel]

seismic noise - each component

plot1= LogLogPlot[{noiseSeisQuadSb[1,1,f],noiseSeisQuadSb[3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot2=LogLogPlot[{noiseSeisQuadSb[1,1,f],noiseSeisQuadSb[3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot3=LogLogPlot[{noiseSeisQuadSb[1,1,f],noiseSeisQuadSb[3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

Show[plotSeisQuadSb,plot1,plot2,plot3,PlotRange -> All]

thermal noise - each component

plot11= LogLogPlot[{noiseTNoiseQuadSb[1,4,1,f],noiseTNoiseQuadSb[5,4,1,f],noiseTNoiseQuadSb[6,4,1,f],noiseTNoiseQuadSb[3,4,3,f],noiseTNoiseQuadSb[4,4,3,f],noiseTNoiseQuadSb[5,4,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot12= LogLogPlot[{noiseTNoiseQuadSb[1,4,1,f],noiseTNoiseQuadSb[5,4,1,f],noiseTNoiseQuadSb[6,4,1,f],noiseTNoiseQuadSb[3,4,3,f],noiseTNoiseQuadSb[4,4,3,f],noiseTNoiseQuadSb[5,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot13= LogLogPlot[{noiseTNoiseQuadSb[1,4,1,f],noiseTNoiseQuadSb[5,4,1,f],noiseTNoiseQuadSb[6,4,1,f],noiseTNoiseQuadSb[3,4,3,f],noiseTNoiseQuadSb[4,4,3,f],noiseTNoiseQuadSb[5,4,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNQuadSb,plot11,plot12,plot13,plotCLIOmodel]

Show[plot12,plotTNQuadSb,plotCLIOmodel]

plot21= LogLogPlot[{noiseTNoiseQuadSb[1,3,1,f],noiseTNoiseQuadSb[5,3,1,f],noiseTNoiseQuadSb[6,3,1,f],noiseTNoiseQuadSb[3,3,3,f],noiseTNoiseQuadSb[4,3,3,f],noiseTNoiseQuadSb[5,3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot22= LogLogPlot[{noiseTNoiseQuadSb[1,3,1,f],noiseTNoiseQuadSb[5,3,1,f],noiseTNoiseQuadSb[6,3,1,f],noiseTNoiseQuadSb[3,3,3,f],noiseTNoiseQuadSb[4,3,3,f],noiseTNoiseQuadSb[5,3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot23= LogLogPlot[{noiseTNoiseQuadSb[1,3,1,f],noiseTNoiseQuadSb[5,3,1,f],noiseTNoiseQuadSb[6,3,1,f],noiseTNoiseQuadSb[3,3,3,f],noiseTNoiseQuadSb[4,3,3,f],noiseTNoiseQuadSb[5,3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNQuadSb,plot21,plot22,plot23,plotCLIOmodel]

Show[plot22,plotTNQuadSb,plotCLIOmodel]

Plot[{f,2 f,3 f,4 f,5 f,6 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot24= LogLogPlot[{noiseTNoiseQuadSb[3,3,3,f],noiseTNoiseQuadSb[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

plot25= LogLogPlot[{noiseTNoiseQuadSb[3,3,3,f],noiseTNoiseQuadSb[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

Show[plot24,plot24bc,plotCLIOmodel]

Show[plot25,plot24bc,plotCLIOmodel]

thermal noise - each direction

plot31= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot32= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot33= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

Show[plotTNQuadSb,plot31,plot32,plot33,plotCLIOmodel,PlotRange -> All]

plot34 =Show[plot32,plot33,PlotRange -> All]

Show[plot34,plotCLIOmodel,plotTN2QuadSb,plotTN3QuadSb]

Plot[{f,2 f,3 f,4 f,5 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

thermal noise - each dissipation g4

plot41= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.8]}]

plot42= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.8]}]

plot43= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.8]}]

Show[plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

Show[plotTNbcQuadSb,plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

thermal noise - each dissipation g3

plot51= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0.8]}]

plot52= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0.8]}]

plot53= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0.8]}]

plot54= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

Show[plotTNQuadSb,plot51,plot52,plot53,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plotTNQuadSb]

Show[plot54,plot52]

thermal noise - each dissipation magnet damping

plot61= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0]}]

plot62= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0]}]

plot63= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0]}]

Show[plotTNQuadSb,plot61,plot62,plot63,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plot62,plotTNQuadSb]

New Quad pendulum simplified (2004/02)

Parameters

intersting item

nItemQuadN = 4 ;

coupling & vibration amplification in cryostat

coupleZXQuadN =5/100;(*coupling Z -> X*)
coupleYXQuadN = 10/100;(*coupling Y -> X*)

offset of beam centering

offsetRollQuadN = 0 mm;
offsetPitchQuadN = 0.1 mm;
offsetYawQuadN = 0.1 mm;

dimensions of mass for quad pendulum

m1

m1DensQuadN = alDens;
m1XQuadN = 100mm;
m1YQuadN = 100mm;
m1ZQuadN = 70 mm;
mCube[m1DensQuadN,m1XQuadN,m1YQuadN,m1ZQuadN]

m2

m2DensQuadN = alDens;
m2XQuadN = 100mm;
m2YQuadN = 100 mm;
m2ZQuadN = 70 mm;
mCube[m2DensQuadN,m2XQuadN,m2YQuadN,m2ZQuadN]

m3

m3DensQuadN =susDens;
m3XQuadN = 70mm;
m3YQuadN = 70 mm;
m3ZQuadN = 50 mm;
mCube[m3DensQuadN,m3XQuadN,m3YQuadN,m3ZQuadN]

m4

m4DensQuadN = saDens;
m4rQuadN = rMass;
m4lQuadN = lMass;

m2d

md2DensQuadN = susDens;
md2XQuadN = 120mm;
md2YQuadN = 100 mm;
md2ZQuadN = 50 mm;
md2dQuadN = 5 mm;
mCage[md2DensQuadN,md2XQuadN,md2YQuadN,md2ZQuadN,md2dQuadN]

spring for quad pendulum

g1

g1LengthQuadN = 1 cm;
g1VFreqQuadN = 4 Hz;

g2

g2LengthQuadN = 25 cm;
g2VFreqQuadN = 4 Hz;

g3

g3LengthQuadN = 100 cm;
g3VFreqQuadN = 4 Hz;

g4

g4LengthQuadN = lSaPend ;

gd2

gd2LengthQuadN = 100 cm;
gd2VFreqQuadN = 5 Hz;

position of wire clamp from COM (4 wires + symmetrical distribution) for quad pendulum

pg01XQuadN = 20 mm;
pg01YQuadN = 50 mm;
pg01ZQuadN = 0 mm;
pg01dXQuadN = 0.1 mm*10;
pg01dYQuadN = 0.1 mm*10;
pg01dZQuadN = 0.1 mm*10;

pg10XQuadN = pg01XQuadN;
pg10YQuadN = pg01YQuadN ;
pg10ZQuadN = m1ZQuadN/2;
pg10dXQuadN = 0.1 mm*10;
pg10dYQuadN = 0.1 mm*10 ;
pg10dZQuadN = 0.1 mm*10;

pg12XQuadN = 20 mm;
pg12YQuadN = 50 mm;
pg12ZQuadN = -m1ZQuadN/2;
pg12dXQuadN = 0.1 mm*10;
pg12dYQuadN = 0.1 mm*10;
pg12dZQuadN = 0.1 mm*10;

pg21XQuadN = pg12XQuadN;
pg21YQuadN = pg12YQuadN ;
pg21ZQuadN = m2ZQuadN/2;
pg21dXQuadN = 0.1 mm*10;
pg21dYQuadN = 0.1 mm*10 ;
pg21dZQuadN = 0.1 mm*10;

pg23XQuadN=50 mm;
pg23YQuadN=50 mm;
pg23ZQuadN=-m2ZQuadN/2;
pg23dXQuadN=0.1 mm*10;
pg23dYQuadN=0.1 mm*10;
pg23dZQuadN=0.1 mm*10;

pg32XQuadN=-pg23XQuadN;
pg32YQuadN=pg23YQuadN;
pg32ZQuadN=m3ZQuadN/2;
pg32dXQuadN=0.1 mm*10;
pg32dYQuadN=0.1 mm*10;
pg32dZQuadN=0.1 mm*10;

pg34XQuadN=10 mm;
pg34YQuadN=rMass/2-0 mm;
pg34ZQuadN=-0 mm;
pg34dXQuadN=0.1 mm*10;
pg34dYQuadN=0.1 mm*10;
pg34dZQuadN=0.1 mm*10;

pg43XQuadN=pg34XQuadN;
pg43YQuadN=rMass/2;
pg43ZQuadN= 0 mm;
pg43dXQuadN=0.1 mm*10;
pg43dYQuadN=0.1 mm*10;
pg43dZQuadN= 0.1 mm*10;

pgd12XQuadN = 100 mm/2;
pgd12YQuadN = 100 mm/2 ;
pgd12ZQuadN = -0 mm*1;
pgd12dXQuadN = 0.1 mm*10;
pgd12dYQuadN = 0.1 mm*10;
pgd12dZQuadN = 0.1 mm*10;

pgd21XQuadN = pgd12XQuadN;
pgd21YQuadN = pgd12YQuadN ;
pgd21ZQuadN = 0 mm*1;
pgd21dXQuadN = 0.1 mm*10;
pgd21dYQuadN = 0.1 mm*10;
pgd21dZQuadN = 0.1 mm*10;

dissipation

qRoomHQuadN = 10^6;
qCryoHQuadN = 10^7;
qRoomVQuadN = 10^4;
qCryoVQuadN  =10^5;

qSaHQuadN =  1/(3 10^(-7));
qSaVQuadN =  10^6;

qg2VQuadN = qRoomVQuadN;
qg3VQuadN = qCryoVQuadN;

g2TempVQuadN = m1TempQuadN;(*縦防振の板ばねをcryoに入れるときはm2TempQuadN,それ以外はm1TempQuadN*)
g3TempVQuadN = m3TempQuadN;(*縦防振の板ばねをcryoに入れるときはm3TempQuadN,それ以外はm2TempQuadN*)

in spring

g10HPhiQuadN = 0 1/qRoomHQuadN;
g10VPhiQuadN = 0 1/qRoomVQuadN;

g12HPhiQuadN = 0 1/qRoomHQuadN;
g12VPhiQuadN = 0 1/qg2VQuadN;

g21HPhiQuadN =  0 1/qRoomHQuadN;
g21VPhiQuadN =  0 1/qg2VQuadN;

g23HPhiQuadN = 0  1/qCryoHQuadN;
g23VPhiQuadN =  0 1/qg3VQuadN;

g32HPhiQuadN =   0 1/qRoomHQuadN;
g32VPhiQuadN =    0 1/qg3VQuadN;

g34HPhiQuadN =   1/qSaHQuadN;
g34VPhiQuadN =   1/qSaVQuadN;

g43HPhiQuadN =   1/qSaHQuadN;
g43VPhiQuadN =   1/qSaVQuadN;

gd12HPhiQuadN =0 1/qRoomHQuadN;
gd12VPhiQuadN =0 1/qRoomVQuadN;

gd21HPhiQuadN =0 1/qRoomHQuadN;
gd21VPhiQuadN =0 1/qRoomVQuadN;

magnet damping

d2DampFQuadN = 0 5 Hz;
d2DampQQuadN = 10*1;

temperature for triple pendulum

m1TempQuadN = 300 K;
m2TempQuadN = 20 K;
m3TempQuadN = 13 K;
m4TempQuadN = 25 K;
md2TempQuadN = 20 K;

Preparation

coupling matrix

coupleMatQuadN=(({{1}, {coupleYXQuadN}, {coupleZXQuadN}, {offsetRollQuadN}, {offsetPitchQuadN}, {offsetYawQuadN}}));

mass & moment inertia for QuadN pendulum

m1

mass1QuadN = mCube[m1DensQuadN, m1XQuadN,m1YQuadN, m1ZQuadN]; 
iRoll1QuadN = mIRollCube[m1DensQuadN, m1XQuadN,m1YQuadN, m1ZQuadN];
iPitch1QuadN = mIPitchCube[m1DensQuadN, m1XQuadN,m1YQuadN, m1ZQuadN];
iYaw1QuadN = mIYawCube[m1DensQuadN, m1XQuadN,m1YQuadN, m1ZQuadN];

m2

mass2QuadN = mCube[m2DensQuadN, m2XQuadN,m2YQuadN, m2ZQuadN]; 
iRoll2QuadN = mIRollCube[m2DensQuadN, m2XQuadN,m2YQuadN, m2ZQuadN];
iPitch2QuadN = mIPitchCube[m2DensQuadN, m2XQuadN,m2YQuadN, m2ZQuadN];
iYaw2QuadN = mIYawCube[m2DensQuadN, m2XQuadN,m2YQuadN, m2ZQuadN];

m3

mass3QuadN = mCube[m3DensQuadN, m3XQuadN,m3YQuadN, m3ZQuadN]; 
iRoll3QuadN = mIRollCube[m3DensQuadN, m3XQuadN,m3YQuadN, m3ZQuadN];
iPitch3QuadN = mIPitchCube[m3DensQuadN, m3XQuadN,m3YQuadN, m3ZQuadN];
iYaw3QuadN = mIYawCube[m3DensQuadN, m3XQuadN,m3YQuadN, m3ZQuadN];

m4

mass4QuadN = mMass; (*see Parameters/Dimensions of final suspension/final mass*)
iRoll4QuadN = mILCyl[m4DensQuadN, m4rQuadN,m4lQuadN];
iPitch4QuadN = mIRCyl[m4DensQuadN, m4rQuadN,m4lQuadN];
iYaw4QuadN = mIRCyl[m4DensQuadN, m4rQuadN,m4lQuadN];

md2(cage)

massd2QuadN = mCage[md2DensQuadN, md2XQuadN,md2YQuadN, md2ZQuadN,md2dQuadN];
iRolld2QuadN = mIRollCage[md2DensQuadN, md2XQuadN,md2YQuadN, md2ZQuadN,md2dQuadN];
iPitchd2QuadN = mIPitchCage[md2DensQuadN, md2XQuadN,md2YQuadN, md2ZQuadN,md2dQuadN];
iYawd2QuadN = mIYawCage[md2DensQuadN, md2XQuadN,md2YQuadN, md2ZQuadN,md2dQuadN];

suspension wire for QuadN pendulum

horizontal

g1HScQuadN = scPend[mass1QuadN+mass2QuadN+mass3QuadN+mass4QuadN,g1LengthQuadN];
g2HScQuadN = scPend[mass2QuadN+mass3QuadN+mass4QuadN,g2LengthQuadN];
g3HScQuadN = scPend[mass3QuadN+mass4QuadN,g3LengthQuadN];
g4HScQuadN = scPend[mass4QuadN,g4LengthQuadN];
gd2HScQuadN = scPend[massd2QuadN,gd2LengthQuadN];

vertical

g1VScQuadN = scFreq[mass1QuadN+mass2QuadN+mass3QuadN+mass4QuadN,g1VFreqQuadN];
g2VScQuadN = scFreq[mass2QuadN+mass3QuadN+mass4QuadN,g2VFreqQuadN];
g3VScQuadN = scFreq[mass3QuadN+mass4QuadN,g3VFreqQuadN];
g4VScQuadN = numSaPend*scVert[saYoung,diaSaPend,lSaPend];
gd2VScQuadN = scFreq[massd2QuadN,gd2VFreqQuadN];

g10

g10HQuadN = g1HScQuadN(1 +I g10HPhiQuadN);
g10VQuadN = g1VScQuadN(1 +I g10VPhiQuadN);

g10HThermalQuadN = g1HScQuadN(1 +tRoom I g10HPhiQuadN);
g10VThermalQuadN = g1VScQuadN(1 +tRoom I g10VPhiQuadN);

t10RollQuadN = ctRoll[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg10XQuadN,pg10YQuadN,pg10ZQuadN,g1HScQuadN,g10HPhiQuadN,g1VScQuadN,g10VPhiQuadN];
t10PitchQuadN = ctPitch[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg10XQuadN,pg10YQuadN,pg10ZQuadN,g1HScQuadN,g10HPhiQuadN,g1VScQuadN,g10VPhiQuadN];
t10YawQuadN = ctYaw[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg10XQuadN,pg10YQuadN,pg10ZQuadN,g1HScQuadN,g10HPhiQuadN,g1VScQuadN,g10VPhiQuadN];

t10RollThermalQuadN = ctRoll[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg10XQuadN,pg10YQuadN,pg10ZQuadN,g1HScQuadN,tRoom g10HPhiQuadN,g1VScQuadN,tRoom g10VPhiQuadN];
t10PitchThermalQuadN = ctPitch[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg10XQuadN,pg10YQuadN,pg10ZQuadN,g1HScQuadN,tRoom g10HPhiQuadN,g1VScQuadN,tRoom g10VPhiQuadN];
t10YawThermalQuadN = ctYaw[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg10XQuadN,pg10YQuadN,pg10ZQuadN,g1HScQuadN,tRoom g10HPhiQuadN,g1VScQuadN,tRoom g10VPhiQuadN];

ct10RollQuadN = ctRoll[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg01XQuadN,pg01YQuadN,pg01ZQuadN,g1HScQuadN,g10HPhiQuadN,g1VScQuadN,g10VPhiQuadN];
ct10PitchQuadN = ctPitch[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg01XQuadN,pg01YQuadN,pg01ZQuadN,g1HScQuadN,g10HPhiQuadN,g1VScQuadN,g10VPhiQuadN];
ct10YawQuadN = ctYaw[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg01XQuadN,pg01YQuadN,pg01ZQuadN,g1HScQuadN,g10HPhiQuadN,g1VScQuadN,g10VPhiQuadN];

ct10RollThermalQuadN = ctRoll[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg01XQuadN,pg01YQuadN,pg01ZQuadN,g1HScQuadN,tRoom g10HPhiQuadN,g1VScQuadN,tRoom g10VPhiQuadN];
ct10PitchThermalQuadN = ctPitch[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg01XQuadN,pg01YQuadN,pg01ZQuadN,g1HScQuadN,tRoom g10HPhiQuadN,g1VScQuadN,tRoom g10VPhiQuadN];
ct10YawThermalQuadN = ctYaw[pg10XQuadN,pg10YQuadN,pg10ZQuadN,pg01XQuadN,pg01YQuadN,pg01ZQuadN,g1HScQuadN,tRoom g10HPhiQuadN,g1VScQuadN,tRoom g10VPhiQuadN];

g12

g12HQuadN = g2HScQuadN(1 +I g12HPhiQuadN);
g12VQuadN = g2VScQuadN(1 +I g12VPhiQuadN);

g12HThermalQuadN = g2HScQuadN(1 +m2TempQuadN I g12HPhiQuadN);
g12VThermalQuadN = g2VScQuadN(1 +g2TempVQuadN I g12VPhiQuadN);

t12RollQuadN = ctRoll[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,g12HPhiQuadN,g2VScQuadN,g12VPhiQuadN];
t12PitchQuadN = ctPitch[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,g12HPhiQuadN,g2VScQuadN,g12VPhiQuadN];
t12YawQuadN = ctYaw[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,g12HPhiQuadN,g2VScQuadN,g12VPhiQuadN];

t12RollThermalQuadN = ctRoll[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,m2TempQuadN g12HPhiQuadN,g2VScQuadN,g2TempVQuadN g12VPhiQuadN];
t12PitchThermalQuadN = ctPitch[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,m2TempQuadN g12HPhiQuadN,g2VScQuadN,g2TempVQuadN g12VPhiQuadN];
t12YawThermalQuadN = ctYaw[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,m2TempQuadN g12HPhiQuadN,g2VScQuadN,g2TempVQuadN g12VPhiQuadN];

ct12RollQuadN = ctRoll[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,g12HPhiQuadN,g2VScQuadN,g12VPhiQuadN];
ct12PitchQuadN = ctPitch[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,g12HPhiQuadN,g2VScQuadN,g12VPhiQuadN];
ct12YawQuadN = ctYaw[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,g12HPhiQuadN,g2VScQuadN,g12VPhiQuadN];

ct12RollThermalQuadN = ctRoll[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,m2TempQuadN g12HPhiQuadN,g2VScQuadN,g2TempVQuadN g12VPhiQuadN];
ct12PitchThermalQuadN = ctPitch[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,m2TempQuadN g12HPhiQuadN,g2VScQuadN,g2TempVQuadN g12VPhiQuadN];
ct12YawThermalQuadN = ctYaw[pg12XQuadN,pg12YQuadN,pg12ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,m2TempQuadN g12HPhiQuadN,g2VScQuadN,g2TempVQuadN g12VPhiQuadN];

g21

g21HQuadN = g2HScQuadN(1 +I g21HPhiQuadN);
g21VQuadN = g2VScQuadN(1 +I g21VPhiQuadN);

g21HThermalQuadN = g2HScQuadN(1 +m1TempQuadN I g21HPhiQuadN);
g21VThermalQuadN = g2VScQuadN(1 +g2TempVQuadN I g21VPhiQuadN);

t21RollQuadN = ctRoll[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,g21HPhiQuadN,g2VScQuadN,g21VPhiQuadN];
t21PitchQuadN = ctPitch[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,g21HPhiQuadN,g2VScQuadN,g21VPhiQuadN];
t21YawQuadN = ctYaw[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,g21HPhiQuadN,g2VScQuadN,g21VPhiQuadN];

t21RollThermalQuadN = ctRoll[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,m1TempQuadN g21HPhiQuadN,g2VScQuadN,g2TempVQuadN g21VPhiQuadN];
t21PitchThermalQuadN = ctPitch[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,m1TempQuadN g21HPhiQuadN,g2VScQuadN,g2TempVQuadN g21VPhiQuadN];
t21YawThermalQuadN = ctYaw[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg21XQuadN,pg21YQuadN,pg21ZQuadN,g2HScQuadN,m1TempQuadN g21HPhiQuadN,g2VScQuadN,g2TempVQuadN g21VPhiQuadN];

ct21RollQuadN = ctRoll[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,g21HPhiQuadN,g2VScQuadN,g21VPhiQuadN];
ct21PitchQuadN = ctPitch[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,g21HPhiQuadN,g2VScQuadN,g21VPhiQuadN];
ct21YawQuadN = ctYaw[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,g21HPhiQuadN,g2VScQuadN,g21VPhiQuadN];

ct21RollThermalQuadN = ctRoll[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,m1TempQuadN g21HPhiQuadN,g2VScQuadN,g2TempVQuadN g21VPhiQuadN];
ct21PitchThermalQuadN = ctPitch[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,m1TempQuadN g21HPhiQuadN,g2VScQuadN,g2TempVQuadN g21VPhiQuadN];
ct21YawThermalQuadN = ctYaw[pg21XQuadN,pg21YQuadN,pg21ZQuadN,pg12XQuadN,pg12YQuadN,pg12ZQuadN,g2HScQuadN,m1TempQuadN g21HPhiQuadN,g2VScQuadN,g2TempVQuadN g21VPhiQuadN];

g23

g23HQuadN = g3HScQuadN(1 +I g23HPhiQuadN);
g23VQuadN = g3VScQuadN(1 +I g23VPhiQuadN);

g23HThermalQuadN = g3HScQuadN(1 +m3TempQuadN I g23HPhiQuadN);
g23VThermalQuadN = g3VScQuadN(1 +g3TempVQuadN I g23VPhiQuadN);

t23RollQuadN = ctRoll[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,g23HPhiQuadN,g3VScQuadN,g23VPhiQuadN];
t23PitchQuadN = ctPitch[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,g23HPhiQuadN,g3VScQuadN,g23VPhiQuadN];
t23YawQuadN = ctYaw[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,g23HPhiQuadN,g3VScQuadN,g23VPhiQuadN];

t23RollThermalQuadN = ctRoll[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,m3TempQuadN g23HPhiQuadN,g3VScQuadN,g3TempVQuadN g23VPhiQuadN];
t23PitchThermalQuadN = ctPitch[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,m3TempQuadN g23HPhiQuadN,g3VScQuadN,g3TempVQuadN g23VPhiQuadN];
t23YawThermalQuadN = ctYaw[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,m3TempQuadN g23HPhiQuadN,g3VScQuadN,g3TempVQuadN g23VPhiQuadN];

ct23RollQuadN = ctRoll[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,g23HPhiQuadN,g3VScQuadN,g23VPhiQuadN];
ct23PitchQuadN = ctPitch[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,g23HPhiQuadN,g3VScQuadN,g23VPhiQuadN];
ct23YawQuadN = ctYaw[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,g23HPhiQuadN,g3VScQuadN,g23VPhiQuadN];

ct23RollThermalQuadN = ctRoll[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,m3TempQuadN g23HPhiQuadN,g3VScQuadN,g3TempVQuadN g23VPhiQuadN];
ct23PitchThermalQuadN = ctPitch[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,m3TempQuadN g23HPhiQuadN,g3VScQuadN,g3TempVQuadN g23VPhiQuadN];
ct23YawThermalQuadN = ctYaw[pg23XQuadN,pg23YQuadN,pg23ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,m3TempQuadN g23HPhiQuadN,g3VScQuadN,g3TempVQuadN g23VPhiQuadN];

g32

g32HQuadN = g3HScQuadN(1 +I g32HPhiQuadN);
g32VQuadN = g3VScQuadN(1 +I g32VPhiQuadN);

g32HThermalQuadN = g3HScQuadN(1 +m2TempQuadN I g32HPhiQuadN);
g32VThermalQuadN = g3VScQuadN(1 +g3TempVQuadN I g32VPhiQuadN);

t32RollQuadN = ctRoll[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,g32HPhiQuadN,g3VScQuadN,g32VPhiQuadN];
t32PitchQuadN = ctPitch[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,g32HPhiQuadN,g3VScQuadN,g32VPhiQuadN];
t32YawQuadN = ctYaw[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,g32HPhiQuadN,g3VScQuadN,g32VPhiQuadN];

t32RollThermalQuadN = ctRoll[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,m2TempQuadN g32HPhiQuadN,g3VScQuadN,g3TempVQuadN g32VPhiQuadN];
t32PitchThermalQuadN = ctPitch[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,m2TempQuadN g32HPhiQuadN,g3VScQuadN,g3TempVQuadN g32VPhiQuadN];
t32YawThermalQuadN = ctYaw[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg32XQuadN,pg32YQuadN,pg32ZQuadN,g3HScQuadN,m2TempQuadN g32HPhiQuadN,g3VScQuadN,g3TempVQuadN g32VPhiQuadN];

ct32RollQuadN = ctRoll[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,g32HPhiQuadN,g3VScQuadN,g32VPhiQuadN];
ct32PitchQuadN = ctPitch[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,g32HPhiQuadN,g3VScQuadN,g32VPhiQuadN];
ct32YawQuadN = ctYaw[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,g32HPhiQuadN,g3VScQuadN,g32VPhiQuadN];

ct32RollThermalQuadN = ctRoll[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,m2TempQuadN g32HPhiQuadN,g3VScQuadN,g3TempVQuadN g32VPhiQuadN];
ct32PitchThermalQuadN = ctPitch[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,m2TempQuadN g32HPhiQuadN,g3VScQuadN,g3TempVQuadN g32VPhiQuadN];
ct32YawThermalQuadN = ctYaw[pg32XQuadN,pg32YQuadN,pg32ZQuadN,pg23XQuadN,pg23YQuadN,pg23ZQuadN,g3HScQuadN,m2TempQuadN g32HPhiQuadN,g3VScQuadN,g3TempVQuadN g32VPhiQuadN];

g34

g34HQuadN = g4HScQuadN(1 +I g34HPhiQuadN);
g34VQuadN = g4VScQuadN(1 +I g34VPhiQuadN);

g34HThermalQuadN = g4HScQuadN(1 +m4TempQuadN I g34HPhiQuadN);
g34VThermalQuadN = g4VScQuadN(1 +m4TempQuadN I g34VPhiQuadN);

t34RollQuadN = ctRoll[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,g34HPhiQuadN,g4VScQuadN,g34VPhiQuadN];
t34PitchQuadN = ctPitch[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,g34HPhiQuadN,g4VScQuadN,g34VPhiQuadN];
t34YawQuadN = ctYaw[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,g34HPhiQuadN,g4VScQuadN,g34VPhiQuadN];

t34RollThermalQuadN = ctRoll[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,m4TempQuadN g34HPhiQuadN,g4VScQuadN,m4TempQuadN g34VPhiQuadN];
t34PitchThermalQuadN = ctPitch[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,m4TempQuadN g34HPhiQuadN,g4VScQuadN,m4TempQuadN g34VPhiQuadN];
t34YawThermalQuadN = ctYaw[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,m4TempQuadN g34HPhiQuadN,g4VScQuadN,m4TempQuadN g34VPhiQuadN];

ct34RollQuadN = ctRoll[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,g34HPhiQuadN,g4VScQuadN,g34VPhiQuadN];
ct34PitchQuadN = ctPitch[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,g34HPhiQuadN,g4VScQuadN,g34VPhiQuadN];
ct34YawQuadN = ctYaw[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,g34HPhiQuadN,g4VScQuadN,g34VPhiQuadN];

ct34RollThermalQuadN = ctRoll[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,m4TempQuadN g34HPhiQuadN,g4VScQuadN,m4TempQuadN g34VPhiQuadN];
ct34PitchThermalQuadN = ctPitch[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,m4TempQuadN g34HPhiQuadN,g4VScQuadN,m4TempQuadN g34VPhiQuadN];
ct34YawThermalQuadN = ctYaw[pg34XQuadN,pg34YQuadN,pg34ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,m4TempQuadN g34HPhiQuadN,g4VScQuadN,m4TempQuadN g34VPhiQuadN];

g43

g43HQuadN = g4HScQuadN(1 +I g43HPhiQuadN);
g43VQuadN = g4VScQuadN(1 +I g43VPhiQuadN);

g43HThermalQuadN = g4HScQuadN(1 +m3TempQuadN I g43HPhiQuadN);
g43VThermalQuadN = g4VScQuadN(1 +m4TempQuadN I g43VPhiQuadN);

t43RollQuadN = ctRoll[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,g43HPhiQuadN,g4VScQuadN,g43VPhiQuadN];
t43PitchQuadN = ctPitch[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,g43HPhiQuadN,g4VScQuadN,g43VPhiQuadN];
t43YawQuadN = ctYaw[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,g43HPhiQuadN,g4VScQuadN,g43VPhiQuadN];

t43RollThermalQuadN = ctRoll[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,m3TempQuadN g43HPhiQuadN,g4VScQuadN,m4TempQuadN g43VPhiQuadN];
t43PitchThermalQuadN = ctPitch[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,m3TempQuadN g43HPhiQuadN,g4VScQuadN,m4TempQuadN g43VPhiQuadN];
t43YawThermalQuadN = ctYaw[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg43XQuadN,pg43YQuadN,pg43ZQuadN,g4HScQuadN,m3TempQuadN g43HPhiQuadN,g4VScQuadN,m4TempQuadN g43VPhiQuadN];

ct43RollQuadN = ctRoll[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,g43HPhiQuadN,g4VScQuadN,g43VPhiQuadN];
ct43PitchQuadN = ctPitch[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,g43HPhiQuadN,g4VScQuadN,g43VPhiQuadN];
ct43YawQuadN = ctYaw[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,g43HPhiQuadN,g4VScQuadN,g43VPhiQuadN];

ct43RollThermalQuadN = ctRoll[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,m3TempQuadN g43HPhiQuadN,g4VScQuadN,m4TempQuadN g43VPhiQuadN];
ct43PitchThermalQuadN = ctPitch[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,m3TempQuadN g43HPhiQuadN,g4VScQuadN,m4TempQuadN g43VPhiQuadN];
ct43YawThermalQuadN = ctYaw[pg43XQuadN,pg43YQuadN,pg43ZQuadN,pg34XQuadN,pg34YQuadN,pg34ZQuadN,g4HScQuadN,m3TempQuadN g43HPhiQuadN,g4VScQuadN,m4TempQuadN g43VPhiQuadN];

gd12

gd12HQuadN = gd2HScQuadN(1 +I gd12HPhiQuadN);
gd12VQuadN = gd2VScQuadN(1 +I gd12VPhiQuadN);

gd12HThermalQuadN = gd2HScQuadN(1 +m2TempQuadN I gd12HPhiQuadN);
gd12VThermalQuadN = gd2VScQuadN(1 +g2TempVQuadN I gd12VPhiQuadN);

td12RollQuadN = ctRoll[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,gd12HPhiQuadN,gd2VScQuadN,gd12VPhiQuadN];
td12PitchQuadN = ctPitch[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,gd12HPhiQuadN,gd2VScQuadN,gd12VPhiQuadN];
td12YawQuadN = ctYaw[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,gd12HPhiQuadN,gd2VScQuadN,gd12VPhiQuadN];

td12RollThermalQuadN = ctRoll[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,m2TempQuadN gd12HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd12VPhiQuadN];
td12PitchThermalQuadN = ctPitch[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,m2TempQuadN gd12HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd12VPhiQuadN];
td12YawThermalQuadN = ctYaw[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,m2TempQuadN gd12HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd12VPhiQuadN];

ctd12RollQuadN = ctRoll[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,gd12HPhiQuadN,gd2VScQuadN,gd12VPhiQuadN];
ctd12PitchQuadN = ctPitch[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,gd12HPhiQuadN,gd2VScQuadN,gd12VPhiQuadN];
ctd12YawQuadN = ctYaw[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,gd12HPhiQuadN,gd2VScQuadN,gd12VPhiQuadN];

ctd12RollThermalQuadN = ctRoll[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,m2TempQuadN gd12HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd12VPhiQuadN];
ctd12PitchThermalQuadN = ctPitch[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,m2TempQuadN gd12HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd12VPhiQuadN];
ctd12YawThermalQuadN = ctYaw[pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,m2TempQuadN gd12HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd12VPhiQuadN];

gd21

gd21HQuadN = gd2HScQuadN(1 +I gd21HPhiQuadN);
gd21VQuadN = gd2VScQuadN(1 +I gd21VPhiQuadN);

gd21HThermalQuadN = gd2HScQuadN(1 +m1TempQuadN I gd21HPhiQuadN);
gd21VThermalQuadN = gd2VScQuadN(1 +g2TempVQuadN I gd21VPhiQuadN);

td21RollQuadN = ctRoll[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,gd21HPhiQuadN,gd2VScQuadN,gd21VPhiQuadN];
td21PitchQuadN = ctPitch[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,gd21HPhiQuadN,gd2VScQuadN,gd21VPhiQuadN];
td21YawQuadN = ctYaw[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,gd21HPhiQuadN,gd2VScQuadN,gd21VPhiQuadN];

td21RollThermalQuadN = ctRoll[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,m1TempQuadN gd21HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd21VPhiQuadN];
td21PitchThermalQuadN = ctPitch[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,m1TempQuadN gd21HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd21VPhiQuadN];
td21YawThermalQuadN = ctYaw[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,gd2HScQuadN,m1TempQuadN gd21HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd21VPhiQuadN];

ctd21RollQuadN = ctRoll[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,gd21HPhiQuadN,gd2VScQuadN,gd21VPhiQuadN];
ctd21PitchQuadN = ctPitch[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,gd21HPhiQuadN,gd2VScQuadN,gd21VPhiQuadN];
ctd21YawQuadN = ctYaw[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,gd21HPhiQuadN,gd2VScQuadN,gd21VPhiQuadN];

ctd21RollThermalQuadN = ctRoll[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,m1TempQuadN gd21HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd21VPhiQuadN];
ctd21PitchThermalQuadN = ctPitch[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,m1TempQuadN gd21HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd21VPhiQuadN];
ctd21YawThermalQuadN = ctYaw[pgd21XQuadN,pgd21YQuadN,pgd21ZQuadN,pgd12XQuadN,pgd12YQuadN,pgd12ZQuadN,gd2HScQuadN,m1TempQuadN gd21HPhiQuadN,gd2VScQuadN,g2TempVQuadN gd21VPhiQuadN];

damping

d2DampQuadN[f_] := Damp[f,d2DampFQuadN,d2DampQQuadN];

parameter set for QuadN pendulum

{f,
m1,ix1,iy1,iz1,
m2,ix2,iy2,iz2,
m3,ix3,iy3,iz3,
m4,ix4,iy4,iz4,
md2,ixd2,iyd2,izd2,
kh10,kv10,kh12,kv12,kh21,kv21,kh23,kv23,kh32,kv32,kh34,kv34,kh43,kv43,khd12,kvd12,khd21,kvd21,
tx10,ty10,tz10,tx12,ty12,tz12,tx21,ty21,tz21,tx23,ty23,tz23,tx32,ty32,tz32,tx34,ty34,tz34,tx43,ty43,tz43,txd12,tyd12,tzd12,txd21,tyd21,tzd21,
ctx10,cty10,ctz10,ctx12,cty12,ctz12,ctx21,cty21,ctz21,ctx23,cty23,ctz23,ctx32,cty32,ctz32,ctx34,cty34,ctz34,ctx43,cty43,ctz43,ctxd12,ctyd12,ctzd12,ctxd21,ctyd21,ctzd21,
z01,
z10,z12,z21,z23,z32,z34,z43,
zd12,zd21,
d2};

{nItemQuadN,f,
mass1QuadN,iRoll1QuadN,iPitch1QuadN,iYaw1QuadN,mass2QuadN,iRoll2QuadN,iPitch2QuadN,iYaw2QuadN,mass3QuadN,iRoll3QuadN,iPitch3QuadN,iYaw3QuadN,mass4QuadN,iRoll4QuadN,iPitch4QuadN,iYaw4QuadN,massd2QuadN,iRolld2QuadN,iPitchd2QuadN,iYawd2QuadN,
g10HQuadN,g10VQuadN,g12HQuadN,g12VQuadN,g21HQuadN,g21VQuadN,g23HQuadN,g23VQuadN,g32HQuadN,g32VQuadN,g34HQuadN,g34VQuadN,g43HQuadN,g43VQuadN,gd12HQuadN,gd12VQuadN,gd21HQuadN,gd21VQuadN,
t10RollQuadN,t10PitchQuadN,t10YawQuadN,t12RollQuadN,t12PitchQuadN,t12YawQuadN,t21RollQuadN,t21PitchQuadN,t21YawQuadN,t23RollQuadN,t23PitchQuadN,t23YawQuadN,t32RollQuadN,t32PitchQuadN,t32YawQuadN,t34RollQuadN,t34PitchQuadN,t34YawQuadN,t43RollQuadN,t43PitchQuadN,t43YawQuadN,td12RollQuadN,td12PitchQuadN,td12YawQuadN,td21RollQuadN,td21PitchQuadN,td21YawQuadN,
ct10RollQuadN,ct10PitchQuadN,ct10YawQuadN,ct12RollQuadN,ct12PitchQuadN,ct12YawQuadN,ct21RollQuadN,ct21PitchQuadN,ct21YawQuadN,ct23RollQuadN,ct23PitchQuadN,ct23YawQuadN,ct32RollQuadN,ct32PitchQuadN,ct32YawQuadN,ct34RollQuadN,ct34PitchQuadN,ct34YawQuadN,ct43RollQuadN,ct43PitchQuadN,ct43YawQuadN,ctd12RollQuadN,ctd12PitchQuadN,ctd12YawQuadN,ctd21RollQuadN,ctd21PitchQuadN,ctd21YawQuadN,
pg01ZQuadN,pg10ZQuadN,pg12ZQuadN,pg21ZQuadN,pg23ZQuadN,pg32ZQuadN,pg34ZQuadN,pg43ZQuadN,
pgd12ZQuadN,pgd21ZQuadN,
d2DampQuadN[f]
}

{f,
mass1QuadN,iRoll1QuadN,iPitch1QuadN,iYaw1QuadN,mass2QuadN,iRoll2QuadN,iPitch2QuadN,iYaw2QuadN,mass3QuadN,iRoll3QuadN,iPitch3QuadN,iYaw3QuadN,mass4QuadN,iRoll4QuadN,iPitch4QuadN,iYaw4QuadN,massd2QuadN,iRolld2QuadN,iPitchd2QuadN,iYawd2QuadN,
g10HThermalQuadN,g10VThermalQuadN,g12HThermalQuadN,g12VThermalQuadN,g21HThermalQuadN,g21VThermalQuadN,g23HThermalQuadN,g23VThermalQuadN,g32HThermalQuadN,g32VThermalQuadN,g34HThermalQuadN,g34VThermalQuadN,g43HThermalQuadN,g43VThermalQuadN,gd12HThermalQuadN,gd12VThermalQuadN,gd21HThermalQuadN,gd21VThermalQuadN,
t10RollThermalQuadN,t10PitchThermalQuadN,t10YawThermalQuadN,t12RollThermalQuadN,t12PitchThermalQuadN,t12YawThermalQuadN,t21RollThermalQuadN,t21PitchThermalQuadN,t21YawThermalQuadN,t23RollThermalQuadN,t23PitchThermalQuadN,t23YawThermalQuadN,t32RollThermalQuadN,t32PitchThermalQuadN,t32YawThermalQuadN,t34RollThermalQuadN,t34PitchThermalQuadN,t34YawThermalQuadN,t43RollThermalQuadN,t43PitchThermalQuadN,t43YawThermalQuadN,td12RollThermalQuadN,td12PitchThermalQuadN,td12YawThermalQuadN,td21RollThermalQuadN,td21PitchThermalQuadN,td21YawThermalQuadN,
ct10RollThermalQuadN,ct10PitchThermalQuadN,ct10YawThermalQuadN,ct12RollThermalQuadN,ct12PitchThermalQuadN,ct12YawThermalQuadN,ct21RollThermalQuadN,ct21PitchThermalQuadN,ct21YawThermalQuadN,ct23RollThermalQuadN,ct23PitchThermalQuadN,ct23YawThermalQuadN,ct32RollThermalQuadN,ct32PitchThermalQuadN,ct32YawThermalQuadN,ct34RollThermalQuadN,ct34PitchThermalQuadN,ct34YawThermalQuadN,ct43RollThermalQuadN,ct43PitchThermalQuadN,ct43YawThermalQuadN,ctd12RollThermalQuadN,ctd12PitchThermalQuadN,ctd12YawThermalQuadN,ctd21RollThermalQuadN,ctd21PitchThermalQuadN,ctd21YawThermalQuadN,
pg01ZQuadN,pg10ZQuadN,pg12ZQuadN,pg21ZQuadN,pg23ZQuadN,pg32ZQuadN,pg34ZQuadN,pg43ZQuadN,
pgd12ZQuadN,pgd21ZQuadN,
d2DampQuadN[f]
}

calculation for QuadN pendulum

trfQuadN[ll_,nn_,jj_,f_]:=trfAmpQuadN[ll,nn,jj,
nItemQuadN,f,
mass1QuadN,iRoll1QuadN,iPitch1QuadN,iYaw1QuadN,mass2QuadN,iRoll2QuadN,iPitch2QuadN,iYaw2QuadN,mass3QuadN,iRoll3QuadN,iPitch3QuadN,iYaw3QuadN,mass4QuadN,iRoll4QuadN,iPitch4QuadN,iYaw4QuadN,massd2QuadN,iRolld2QuadN,iPitchd2QuadN,iYawd2QuadN,
g10HQuadN,g10VQuadN,g12HQuadN,g12VQuadN,g21HQuadN,g21VQuadN,g23HQuadN,g23VQuadN,g32HQuadN,g32VQuadN,g34HQuadN,g34VQuadN,g43HQuadN,g43VQuadN,gd12HQuadN,gd12VQuadN,gd21HQuadN,gd21VQuadN,
t10RollQuadN,t10PitchQuadN,t10YawQuadN,t12RollQuadN,t12PitchQuadN,t12YawQuadN,t21RollQuadN,t21PitchQuadN,t21YawQuadN,t23RollQuadN,t23PitchQuadN,t23YawQuadN,t32RollQuadN,t32PitchQuadN,t32YawQuadN,t34RollQuadN,t34PitchQuadN,t34YawQuadN,t43RollQuadN,t43PitchQuadN,t43YawQuadN,td12RollQuadN,td12PitchQuadN,td12YawQuadN,td21RollQuadN,td21PitchQuadN,td21YawQuadN,
ct10RollQuadN,ct10PitchQuadN,ct10YawQuadN,ct12RollQuadN,ct12PitchQuadN,ct12YawQuadN,ct21RollQuadN,ct21PitchQuadN,ct21YawQuadN,ct23RollQuadN,ct23PitchQuadN,ct23YawQuadN,ct32RollQuadN,ct32PitchQuadN,ct32YawQuadN,ct34RollQuadN,ct34PitchQuadN,ct34YawQuadN,ct43RollQuadN,ct43PitchQuadN,ct43YawQuadN,ctd12RollQuadN,ctd12PitchQuadN,ctd12YawQuadN,ctd21RollQuadN,ctd21PitchQuadN,ctd21YawQuadN,
pg01ZQuadN,pg10ZQuadN,pg12ZQuadN,pg21ZQuadN,pg23ZQuadN,pg32ZQuadN,pg34ZQuadN,pg43ZQuadN,
pgd12ZQuadN,pgd21ZQuadN,
d2DampQuadN[f]
]

noiseSeisQuadN[nn_,jj_,f_]:=Part[coupleMatQuadN,jj].seisQuadN[nn,jj,
nItemQuadN,f,
mass1QuadN,iRoll1QuadN,iPitch1QuadN,iYaw1QuadN,mass2QuadN,iRoll2QuadN,iPitch2QuadN,iYaw2QuadN,mass3QuadN,iRoll3QuadN,iPitch3QuadN,iYaw3QuadN,mass4QuadN,iRoll4QuadN,iPitch4QuadN,iYaw4QuadN,massd2QuadN,iRolld2QuadN,iPitchd2QuadN,iYawd2QuadN,
g10HQuadN,g10VQuadN,g12HQuadN,g12VQuadN,g21HQuadN,g21VQuadN,g23HQuadN,g23VQuadN,g32HQuadN,g32VQuadN,g34HQuadN,g34VQuadN,g43HQuadN,g43VQuadN,gd12HQuadN,gd12VQuadN,gd21HQuadN,gd21VQuadN,
t10RollQuadN,t10PitchQuadN,t10YawQuadN,t12RollQuadN,t12PitchQuadN,t12YawQuadN,t21RollQuadN,t21PitchQuadN,t21YawQuadN,t23RollQuadN,t23PitchQuadN,t23YawQuadN,t32RollQuadN,t32PitchQuadN,t32YawQuadN,t34RollQuadN,t34PitchQuadN,t34YawQuadN,t43RollQuadN,t43PitchQuadN,t43YawQuadN,td12RollQuadN,td12PitchQuadN,td12YawQuadN,td21RollQuadN,td21PitchQuadN,td21YawQuadN,
ct10RollQuadN,ct10PitchQuadN,ct10YawQuadN,ct12RollQuadN,ct12PitchQuadN,ct12YawQuadN,ct21RollQuadN,ct21PitchQuadN,ct21YawQuadN,ct23RollQuadN,ct23PitchQuadN,ct23YawQuadN,ct32RollQuadN,ct32PitchQuadN,ct32YawQuadN,ct34RollQuadN,ct34PitchQuadN,ct34YawQuadN,ct43RollQuadN,ct43PitchQuadN,ct43YawQuadN,ctd12RollQuadN,ctd12PitchQuadN,ctd12YawQuadN,ctd21RollQuadN,ctd21PitchQuadN,ctd21YawQuadN,
pg01ZQuadN,pg10ZQuadN,pg12ZQuadN,pg21ZQuadN,pg23ZQuadN,pg32ZQuadN,pg34ZQuadN,pg43ZQuadN,
pgd12ZQuadN,pgd21ZQuadN,
d2DampQuadN[f]
]

dispTNoiseQuadN[ll_,nn_,f_]:=tNoiseQuadN[ll,nn,
f,
mass1QuadN,iRoll1QuadN,iPitch1QuadN,iYaw1QuadN,mass2QuadN,iRoll2QuadN,iPitch2QuadN,iYaw2QuadN,mass3QuadN,iRoll3QuadN,iPitch3QuadN,iYaw3QuadN,mass4QuadN,iRoll4QuadN,iPitch4QuadN,iYaw4QuadN,massd2QuadN,iRolld2QuadN,iPitchd2QuadN,iYawd2QuadN,
g10HThermalQuadN,g10VThermalQuadN,g12HThermalQuadN,g12VThermalQuadN,g21HThermalQuadN,g21VThermalQuadN,g23HThermalQuadN,g23VThermalQuadN,g32HThermalQuadN,g32VThermalQuadN,g34HThermalQuadN,g34VThermalQuadN,g43HThermalQuadN,g43VThermalQuadN,gd12HThermalQuadN,gd12VThermalQuadN,gd21HThermalQuadN,gd21VThermalQuadN,
t10RollThermalQuadN,t10PitchThermalQuadN,t10YawThermalQuadN,t12RollThermalQuadN,t12PitchThermalQuadN,t12YawThermalQuadN,t21RollThermalQuadN,t21PitchThermalQuadN,t21YawThermalQuadN,t23RollThermalQuadN,t23PitchThermalQuadN,t23YawThermalQuadN,t32RollThermalQuadN,t32PitchThermalQuadN,t32YawThermalQuadN,t34RollThermalQuadN,t34PitchThermalQuadN,t34YawThermalQuadN,t43RollThermalQuadN,t43PitchThermalQuadN,t43YawThermalQuadN,td12RollThermalQuadN,td12PitchThermalQuadN,td12YawThermalQuadN,td21RollThermalQuadN,td21PitchThermalQuadN,td21YawThermalQuadN,
ct10RollThermalQuadN,ct10PitchThermalQuadN,ct10YawThermalQuadN,ct12RollThermalQuadN,ct12PitchThermalQuadN,ct12YawThermalQuadN,ct21RollThermalQuadN,ct21PitchThermalQuadN,ct21YawThermalQuadN,ct23RollThermalQuadN,ct23PitchThermalQuadN,ct23YawThermalQuadN,ct32RollThermalQuadN,ct32PitchThermalQuadN,ct32YawThermalQuadN,ct34RollThermalQuadN,ct34PitchThermalQuadN,ct34YawThermalQuadN,ct43RollThermalQuadN,ct43PitchThermalQuadN,ct43YawThermalQuadN,ctd12RollThermalQuadN,ctd12PitchThermalQuadN,ctd12YawThermalQuadN,ctd21RollThermalQuadN,ctd21PitchThermalQuadN,ctd21YawThermalQuadN,
pg01ZQuadN,pg10ZQuadN,pg12ZQuadN,pg21ZQuadN,pg23ZQuadN,pg32ZQuadN,pg34ZQuadN,pg43ZQuadN,
pgd12ZQuadN,pgd21ZQuadN,
d2DampQuadN[f]
]

noiseTNoiseQuadN[ll_,nn_,jj_,f_] := {1}.coupleMatQuadN[[jj]]*trfQuadN[ll,nn,jj,f]*dispTNoiseQuadN[ll,nn,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)

seismic noise

noiseSeisSumQuadN[f_] := Sqrt[Sum[Sum[noiseSeisQuadN[nn,jj,f],{jj,1,6}]^2,{nn,1,6}]]

noiseSeisCompQuadN[jj_,f_] := Sqrt[Sum[noiseSeisQuadN[nn,jj,f]^2,{nn,1,6}]]

suspension thermal noise (without violin mode)

noiseTNoiseSumQuadN[f_] := Sqrt[Sum[Sum[Sum[noiseTNoiseQuadN[ll,nn,jj,f],{jj,1,6}]^2,{ll,1,6}],{nn,1, nTotalQuadN}]]

noiseTNoiseCompDouble[jj_,f_] := Sqrt[Sum[Sum[noiseTNoiseQuadN[ll,nn,jj,f]^2,{ll,1,6}],{nn,1, nTotalQuadN}]] (*sum up of noise in "jj" direction*)

Q & resonant frequency

resQuadN=f  /. NSolve[Det[matQuadN[f,
mass1QuadN,iRoll1QuadN,iPitch1QuadN,iYaw1QuadN,mass2QuadN,iRoll2QuadN,iPitch2QuadN,iYaw2QuadN,mass3QuadN,iRoll3QuadN,iPitch3QuadN,iYaw3QuadN,mass4QuadN,iRoll4QuadN,iPitch4QuadN,iYaw4QuadN,massd2QuadN,iRolld2QuadN,iPitchd2QuadN,iYawd2QuadN,
g10HQuadN,g10VQuadN,g12HQuadN,g12VQuadN,g21HQuadN,g21VQuadN,g23HQuadN,g23VQuadN,g32HQuadN,g32VQuadN,g34HQuadN,g34VQuadN,g43HQuadN,g43VQuadN,gd12HQuadN,gd12VQuadN,gd21HQuadN,gd21VQuadN,
t10RollQuadN,t10PitchQuadN,t10YawQuadN,t12RollQuadN,t12PitchQuadN,t12YawQuadN,t21RollQuadN,t21PitchQuadN,t21YawQuadN,t23RollQuadN,t23PitchQuadN,t23YawQuadN,t32RollQuadN,t32PitchQuadN,t32YawQuadN,t34RollQuadN,t34PitchQuadN,t34YawQuadN,t43RollQuadN,t43PitchQuadN,t43YawQuadN,td12RollQuadN,td12PitchQuadN,td12YawQuadN,td21RollQuadN,td21PitchQuadN,td21YawQuadN,
ct10RollQuadN,ct10PitchQuadN,ct10YawQuadN,ct12RollQuadN,ct12PitchQuadN,ct12YawQuadN,ct21RollQuadN,ct21PitchQuadN,ct21YawQuadN,ct23RollQuadN,ct23PitchQuadN,ct23YawQuadN,ct32RollQuadN,ct32PitchQuadN,ct32YawQuadN,ct34RollQuadN,ct34PitchQuadN,ct34YawQuadN,ct43RollQuadN,ct43PitchQuadN,ct43YawQuadN,ctd12RollQuadN,ctd12PitchQuadN,ctd12YawQuadN,ctd21RollQuadN,ctd21PitchQuadN,ctd21YawQuadN,
pg01ZQuadN,pg10ZQuadN,pg12ZQuadN,pg21ZQuadN,pg23ZQuadN,pg32ZQuadN,pg34ZQuadN,pg43ZQuadN,
pgd12ZQuadN,pgd21ZQuadN,
d2DampQuadN[f]]]==0,f];

Sort[resQuadN/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

Plots

all components

plotSeis1QuadN = LogLogPlot[2*noiseSeisSumQuadN[f],{f,0.1,10},PlotStyle -> RGBColor[0,1,0]]

plotSeis2QuadN = LogLogPlot[2*noiseSeisSumQuadN[f],{f,10,100},PlotStyle -> RGBColor[0,1,0]]

plotSeis3QuadN = LogLogPlot[2*noiseSeisSumQuadN[f],{f,100,1000},PlotStyle -> RGBColor[0,1,0]]

plotSeisQuadN=Show[plotSeis1QuadN,plotSeis2QuadN,plotSeis3QuadN,PlotRange -> All]

plotTN1QuadN =LogLogPlot[2*noiseTNoiseSumQuadN[f],{f,0.1,10},PlotStyle -> RGBColor[0,0,1]]

plotTN2QuadN =LogLogPlot[2*noiseTNoiseSumQuadN[f],{f,10,100},PlotStyle -> RGBColor[0,0,1]]

plotTN3QuadN =LogLogPlot[2*noiseTNoiseSumQuadN[f],{f,100,1000},PlotStyle -> RGBColor[0,0,1]]

plotTNQuadN = Show[plotTN1QuadN,plotTN2QuadN,plotTN3QuadN,PlotRange -> All]

plotShotQuadN=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0.5,0]]

Show[plotSeisQuadN,plotTNQuadN,plotShotQuadN,plotCLIOmodel]

Show[plotSeisQuadN,plotTNQuadN,plotCLIOmodel,plotCLIORoommodel,plotShotQuadN,plotLISM030320]

2 noiseTNoiseSumQuadN[100]

Show[plotTN2QuadN,plotTN3QuadN,plotSeis2QuadN,plotCLIOmodel,plotShotQuadN,plotCLIOMTNRoom,PlotRange -> All ]

all components 2

plotSeis101QuadN = LogLogPlot[2*noiseSeisSumQuadN[f],{f,0.1,10},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis102QuadN = LogLogPlot[2*noiseSeisSumQuadN[f],{f,10,100},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis103QuadN = LogLogPlot[2*noiseSeisSumQuadN[f],{f,100,1000},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeisQuadN2=Show[plotSeis101QuadN,plotSeis102QuadN,plotSeis103QuadN,PlotRange -> All]

plotTN101QuadN =LogLogPlot[2*noiseTNoiseSumQuadN[f],{f,0.1,10},PlotStyle -> RGBColor[0.5,0,1]]

plotTN102QuadN =LogLogPlot[2*noiseTNoiseSumQuadN[f],{f,10,100},PlotStyle -> RGBColor[0.5,0,1]]

plotTN103QuadN =LogLogPlot[2*noiseTNoiseSumQuadN[f],{f,100,1000},PlotStyle -> RGBColor[0.5,0,1]]

plotTNQuadN2 = Show[plotTN101QuadN,plotTN102QuadN,plotTN103QuadN,PlotRange -> All]

plotShotQuadN102=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0,0.5]]

Show[plotTN102QuadN,plotTN2QuadN,plotCLIO25model]

Show[plotTN102QuadN,plotSeis102QuadN,plotTN2QuadN,plotSeis2QuadN,plotCLIOmodel]

Show[plotSeis102QuadN,plotSeis2QuadN,plotCLIOmodel]

Show[plotTN102QuadN,plotTN2QuadN,plotCLIOmodel]

Show[plotSeisQuadN2,plotTNQuadN2,plotCLIOmodel,plotShotQuadN102]

Show[plotSeisQuadN2,plotTNQuadN2,plotCLIOmodel,plotShotQuadN102,plotLISM030320]

Show[plotSeisQuadN,plotTNQuadN,plotSeisQuadN2,plotTNQuadN2,plotShotQuadN102,plotCLIOmodel]

Show[plotSeisQuadN,plotSeisQuadN2,plotShotQuadN102,plotCLIOmodel]

Show[plotTNQuadN,plotTNQuadN2,plotShotQuadN102,plotCLIOmodel]

Show[plotShotQuadN,plotShotQuadN102,plotCLIOmodel]

seismic noise - each component

plot1= LogLogPlot[{noiseSeisQuadN[1,1,f],noiseSeisQuadN[3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot2=LogLogPlot[{noiseSeisQuadN[1,1,f],noiseSeisQuadN[3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

plot3=LogLogPlot[{noiseSeisQuadN[1,1,f],noiseSeisQuadN[3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1]}]

Show[plotSeisQuadN,plot1,plot2,plot3,PlotRange -> All]

thermal noise - each component

plot11= LogLogPlot[{noiseTNoiseQuadN[1,4,1,f],noiseTNoiseQuadN[5,4,1,f],noiseTNoiseQuadN[6,4,1,f],noiseTNoiseQuadN[3,4,3,f],noiseTNoiseQuadN[4,4,3,f],noiseTNoiseQuadN[5,4,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot12= LogLogPlot[{noiseTNoiseQuadN[1,4,1,f],noiseTNoiseQuadN[5,4,1,f],noiseTNoiseQuadN[6,4,1,f],noiseTNoiseQuadN[3,4,3,f],noiseTNoiseQuadN[4,4,3,f],noiseTNoiseQuadN[5,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot13= LogLogPlot[{noiseTNoiseQuadN[1,4,1,f],noiseTNoiseQuadN[5,4,1,f],noiseTNoiseQuadN[6,4,1,f],noiseTNoiseQuadN[3,4,3,f],noiseTNoiseQuadN[4,4,3,f],noiseTNoiseQuadN[5,4,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNQuadN,plot11,plot12,plot13,plotCLIOmodel]

Show[plot12,plotTNQuadN,plotCLIOmodel]

plot21= LogLogPlot[{noiseTNoiseQuadN[1,3,1,f],noiseTNoiseQuadN[5,3,1,f],noiseTNoiseQuadN[6,3,1,f],noiseTNoiseQuadN[3,3,3,f],noiseTNoiseQuadN[4,3,3,f],noiseTNoiseQuadN[5,3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot22= LogLogPlot[{noiseTNoiseQuadN[1,3,1,f],noiseTNoiseQuadN[5,3,1,f],noiseTNoiseQuadN[6,3,1,f],noiseTNoiseQuadN[3,3,3,f],noiseTNoiseQuadN[4,3,3,f],noiseTNoiseQuadN[5,3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot23= LogLogPlot[{noiseTNoiseQuadN[1,3,1,f],noiseTNoiseQuadN[5,3,1,f],noiseTNoiseQuadN[6,3,1,f],noiseTNoiseQuadN[3,3,3,f],noiseTNoiseQuadN[4,3,3,f],noiseTNoiseQuadN[5,3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNQuadN,plot21,plot22,plot23,plotCLIOmodel]

Show[plot22,plotTNQuadN,plotCLIOmodel]

Plot[{f,2 f,3 f,4 f,5 f,6 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot24= LogLogPlot[{noiseTNoiseQuadN[3,3,3,f],noiseTNoiseQuadN[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

plot25= LogLogPlot[{noiseTNoiseQuadN[3,3,3,f],noiseTNoiseQuadN[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

Show[plot24,plot24bc,plotCLIOmodel]

Show[plot25,plot24bc,plotCLIOmodel]

thermal noise - each direction

plot31= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot32= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

plot33= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f],noiseTNoiseCompDouble[5,f],noiseTNoiseCompDouble[6,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

Show[plotTNQuadN,plot31,plot32,plot33,plotCLIOmodel,PlotRange -> All]

plot34 =Show[plot32,plot33,PlotRange -> All]

Show[plot34,plotCLIOmodel,plotTN2QuadN,plotTN3QuadN]

Plot[{f,2 f,3 f,4 f,5 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

thermal noise - each dissipation g4

plot41= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.8]}]

plot42= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.8]}]

plot43= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.8]}]

Show[plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

thermal noise - each dissipation g3

plot51= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0.8]}]

plot52= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0.8]}]

plot53= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0.8]}]

plot54= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

Show[plotTNQuadN,plot51,plot52,plot53,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plotTNQuadN]

Show[plot54,plot52]

thermal noise - each dissipation g2

plot51= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0.8]}]

plot52= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0.8]}]

plot53= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0.8]}]

plot54= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

Show[plotTNQuadN,plot51,plot52,plot53,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plotTNQuadN]

Show[plot54,plot52]

thermal noise - each dissipation magnet damping

plot61= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0]}]

plot62= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0]}]

plot63= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0]}]

Show[plotTNQuadN,plot61,plot62,plot63,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plot62,plotTNQuadN]

LCGT cryogenic suspension (2004/04)

Parameters

intersting item

nItemLCGT = 3;(*3:mirror*)

coupling & vibration amplification in cryostat

coupleZXLCGT =1/100;(*coupling Z -> X*)
coupleYXLCGT = 1/100;(*coupling Y -> X*)

SPIMatLCGT = (({{1/100}, {1}, {1/100}}));

offset of beam centering

offsetRollLCGT = 0 mm;
offsetPitchLCGT = 0.1 mm;
offsetYawLCGT = 0.1 mm;

vibration amplification factor in cryostat

vibAmpLCGT = 10/10;

dimensions of mass for quad pendulum

m1

m1DensLCGT = SpMassDens;
m1XLCGT = SpMassX;
m1YLCGT = SpMassY;
m1ZLCGT = SpMassZ;
mCube[SpMassDens,SpMassX,SpMassY,SpMassZ]

m2

m2DensLCGT = UMassDens;
m2rLCGT = rUMass;
m2lLCGT = lUMass;

m3

m3DensLCGT = MassDens;
m3rLCGT = rMass;
m3lLCGT = lMass;

m4

m4DensLCGT = RUMassDens;
m4rLCGT = rRUMass;
m4lLCGT = lRUMass;

m5

m5DensLCGT = RMassDens;
m5rLCGT = rRMass;
m5lLCGT = lRMass;

spring for quad pendulum

g1

g1LengthLCGT = lSpMassPend;
g1VFreqLCGT = 0.3 Hz;

g2

g2LengthLCGT = lUMassPend;
g2VFreqLCGT = 0.7 Hz;

g3

g3LengthLCGT = lSaPend;

g4

g4LengthLCGT = lUMassPend;
g4VFreqLCGT =0.7 Hz;

g5

g5LengthLCGT = lSaPend;

kA

kAUYoungLCGT = alYoung;
kAUShearLCGT = alShear;
kAURadLCGT = Pi;
kAURadMinLCGT = 1.4 mm;
kAURadiusLCGT = 25 cm;
kANumLCGT = Ceiling[kAURadMinLCGT^2 /(kAUDiaLCGT/2)^2];
kAUDiaLCGT = 1 mm;
2*Sqrt[kAURadMinLCGT^2/kANumLCGT] 1000
Ceiling[kAURadMinLCGT^2 /(kAUDiaLCGT/2)^2]

kB

kBUYoungLCGT = alYoung;
kBUShearLCGT = alShear;
kBURadLCGT = Pi;
kBURadMinLCGT = 5 mm;
kBURadiusLCGT = 25 cm;
kBNumLCGT = Ceiling[kBURadMinLCGT^2 /(kBUDiaLCGT/2)^2];
kBUDiaLCGT =3 mm;
2*Sqrt[kBURadMinLCGT^2/kBNumLCGT] 1000
Ceiling[kBURadMinLCGT^2 /(kBUDiaLCGT/2)^2]

kC

kCUYoungLCGT = alYoung;
kCUShearLCGT = alShear;
kCURadLCGT = Pi;
kCUDiaLCGT = kBUDiaLCGT;
kCURadiusLCGT = 25 cm;
kCNumLCGT =  kBNumLCGT;

dissipation

qRoomHLCGT = 10^6;
qCryoHLCGT = 10^7;
qRoomVLCGT = 10^3;
qCryoVLCGT  =10^5;
qUAlLCGT =  10^3;

qSaHLCGT =  10^8;
qSaVLCGT =  10^6;

qg3VLCGT = qCryoVLCGT;

g3TempVLCGT = m3TempLCGT;(*縦防振の板ばねをcryoに入れるときはm3TempLCGT,それ以外はm2TempLCGT*)

in spring

g10HPhiLCGT =  1/qRoomHLCGT;
g10VPhiLCGT =   1/qRoomVLCGT;

g12HPhiLCGT =   1/qCryoHLCGT;
g12VPhiLCGT =  1/qUAlLCGT;

g21HPhiLCGT =  1/qCryoHLCGT;
g21VPhiLCGT =   1/qUAlLCGT;

g23HPhiLCGT =   1/qSaHLCGT;
g23VPhiLCGT =    1/qSaVLCGT;

g32HPhiLCGT =   1/qSaHLCGT;
g32VPhiLCGT =    1/qSaVLCGT;

g14HPhiLCGT =  1/qCryoHLCGT;
g14VPhiLCGT =  1/qUAlLCGT;

g41HPhiLCGT =  1/qCryoHLCGT;
g41VPhiLCGT = 1/qUAlLCGT;

g45HPhiLCGT =  1/qCryoHLCGT;
g45VPhiLCGT =  1/qCryoVLCGT;

g54HPhiLCGT =  1/qCryoHLCGT;
g54VPhiLCGT =  1/qCryoVLCGT;

kAPhiLCGT =   1/qUAlLCGT;
kBPhiLCGT =   1/qUAlLCGT;
kCPhiLCGT =   1/qUAlLCGT;

temperature for triple pendulum

tISCryoLCGT = 8 K;

m1TempLCGT = 13.1 K;
m2TempLCGT = 13.6 K;
m3TempLCGT = 20 K;
m4TempLCGT = 13.1 K;
m5TempLCGT = 13.1 K;

mk1TempLCGT = tISCryoLCGT;

Preparation

coupling matrix

coupleMatLCGT=SPIMatLCGT (({{1}, {coupleYXLCGT}, {coupleZXLCGT}}));

mass & moment inertia for LCGT pendulum

m1

mass1LCGT = mSpMass;

m2

mass2LCGT = mUMass;

m3

mass3LCGT = mMass;

m4

mass4LCGT = mRUMass; (*see Parameters/Dimensions of final suspension/final mass*)

m5

mass5LCGT =mRMass;

suspension wire for LCGT pendulum

horizontal

g1HScLCGT = scPend[mass1LCGT+mass2LCGT+mass3LCGT+mass4LCGT+mass5LCGT,g1LengthLCGT];
g2HScLCGT = scPend[mass2LCGT+mass3LCGT,g2LengthLCGT];
g3HScLCGT = scPend[mass3LCGT,g3LengthLCGT];
g4HScLCGT = scPend[mass4LCGT+mass5LCGT,g4LengthLCGT];
g5HScLCGT = scPend[mass5LCGT,g5LengthLCGT];

vertical

g1VScLCGT = scFreq[mass1LCGT+mass2LCGT+mass3LCGT+mass4LCGT+mass5LCGT,g1VFreqLCGT];
g2VScLCGT = scFreq[mass2LCGT+mass3LCGT,g2VFreqLCGT];
g3VScLCGT = numSaPend*scVert[saYoung,diaSaPend,lSaPend];
g4VScLCGT = scFreq[mass4LCGT+mass5LCGT,g2VFreqLCGT];
g5VScLCGT = numSaPend*scVert[saYoung,diaSaPend,lSaPend];

g10

g10HLCGT = g1HScLCGT(1 +I g10HPhiLCGT);
g10VLCGT = g1VScLCGT(1 +I g10VPhiLCGT);

g10HThermalLCGT = g1HScLCGT(1 +tRoom I g10HPhiLCGT);
g10VThermalLCGT = g1VScLCGT(1 +tRoom I g10VPhiLCGT);

g12

g12HLCGT = g2HScLCGT(1 +I g12HPhiLCGT);
g12VLCGT = g2VScLCGT(1 +I g12VPhiLCGT);

g12HThermalLCGT = g2HScLCGT(1 +m2TempLCGT I g12HPhiLCGT);
g12VThermalLCGT = g2VScLCGT(1 +m1TempLCGT I g12VPhiLCGT);

g21

g21HLCGT = g2HScLCGT(1 +I g21HPhiLCGT);
g21VLCGT = g2VScLCGT(1 +I g21VPhiLCGT);

g21HThermalLCGT = g2HScLCGT(1 +m1TempLCGT I g21HPhiLCGT);
g21VThermalLCGT = g2VScLCGT(1 +m1TempLCGT I g21VPhiLCGT);

g23

g23HLCGT = g3HScLCGT(1 +I g23HPhiLCGT);
g23VLCGT = g3VScLCGT(1 +I g23VPhiLCGT);

g23HThermalLCGT = g3HScLCGT(1 +m3TempLCGT I g23HPhiLCGT);
g23VThermalLCGT = g3VScLCGT(1 +m3TempLCGT I g23VPhiLCGT);

g32

g32HLCGT = g3HScLCGT(1 +I g32HPhiLCGT);
g32VLCGT = g3VScLCGT(1 +I g32VPhiLCGT);

g32HThermalLCGT = g3HScLCGT(1 +m2TempLCGT I g32HPhiLCGT);
g32VThermalLCGT = g3VScLCGT(1 +m3TempLCGT I g32VPhiLCGT);

g14

g14HLCGT = g4HScLCGT(1 +I g14HPhiLCGT);
g14VLCGT = g4VScLCGT(1 +I g14VPhiLCGT);

g14HThermalLCGT = g4HScLCGT(1 +m4TempLCGT I g14HPhiLCGT);
g14VThermalLCGT = g4VScLCGT(1 +m1TempLCGT I g14VPhiLCGT);

g41

g41HLCGT = g4HScLCGT(1 +I g41HPhiLCGT);
g41VLCGT = g4VScLCGT(1 +I g41VPhiLCGT);

g41HThermalLCGT = g4HScLCGT(1 +m1TempLCGT I g41HPhiLCGT);
g41VThermalLCGT = g4VScLCGT(1 +m1TempLCGT I g41VPhiLCGT);

g45

g45HLCGT = g4HScLCGT(1 +I g45HPhiLCGT);
g45VLCGT = g4VScLCGT(1 +I g45VPhiLCGT);

g45HThermalLCGT = g5HScLCGT(1 +m5TempLCGT I g45HPhiLCGT);
g45VThermalLCGT = g5VScLCGT(1 +m5TempLCGT I g45VPhiLCGT);

g54

g54HLCGT = g5HScLCGT(1 +I g54HPhiLCGT);
g54VLCGT = g5VScLCGT(1 +I g54VPhiLCGT);

g54HThermalLCGT = g5HScLCGT(1 +m4TempLCGT I g54HPhiLCGT);
g54VThermalLCGT = g5VScLCGT(1 +m5TempLCGT I g54VPhiLCGT);

heat link

kA

kAXscLCGT = kANumLCGT*scUX[kAUYoungLCGT,kAURadLCGT,kAUDiaLCGT,kAURadiusLCGT];
kAYscLCGT = kANumLCGT*scUY[kAUShearLCGT,kAUDiaLCGT,kAURadiusLCGT];
kAZscLCGT = kANumLCGT*scUZ[kAUYoungLCGT,kAURadLCGT,kAUDiaLCGT,kAURadiusLCGT];

kB

kBXscLCGT = kBNumLCGT*scUZ[kBUYoungLCGT,kBURadLCGT,kBUDiaLCGT,kBURadiusLCGT];
kBYscLCGT = kBNumLCGT*scUY[kBUShearLCGT,kBUDiaLCGT,kBURadiusLCGT];
kBZscLCGT = kBNumLCGT*scUX[kBUYoungLCGT,kBURadLCGT,kBUDiaLCGT,kBURadiusLCGT];

kC

kCXscLCGT = kCNumLCGT*scUZ[kCUYoungLCGT,kCURadLCGT,kCUDiaLCGT,kCURadiusLCGT];
kCYscLCGT = kCNumLCGT*scUY[kCUShearLCGT,kCUDiaLCGT,kCURadiusLCGT];
kCZscLCGT = kCNumLCGT*scUX[kCUYoungLCGT,kCURadLCGT,kCUDiaLCGT,kCURadiusLCGT];

k10

k10XLCGT = kAXscLCGT(1+ I kAPhiLCGT);
k10YLCGT = kAYscLCGT(1+ I kAPhiLCGT);
k10ZLCGT = kAZscLCGT(1+ I kAPhiLCGT);

k10XThermalLCGT = kAXscLCGT(1+ tISCryoLCGT I kAPhiLCGT);
k10YThermalLCGT = kAYscLCGT(1+ tISCryoLCGT I kAPhiLCGT);
k10ZThermalLCGT = kAZscLCGT(1+ tISCryoLCGT I kAPhiLCGT);

k12

k12XLCGT = kBXscLCGT(1+ I kBPhiLCGT);
k12YLCGT = kBYscLCGT(1+ I kBPhiLCGT);
k12ZLCGT = kBZscLCGT(1+ I kBPhiLCGT);

k12XThermalLCGT = kBXscLCGT(1+ m2TempLCGT I kBPhiLCGT);
k12YThermalLCGT = kBYscLCGT(1+ m2TempLCGT I kBPhiLCGT);
k12ZThermalLCGT = kBZscLCGT(1+ m2TempLCGT I kBPhiLCGT);

k21

k21XLCGT = kBXscLCGT(1+ I kBPhiLCGT);
k21YLCGT = kBYscLCGT(1+ I kBPhiLCGT);
k21ZLCGT = kBZscLCGT(1+ I kBPhiLCGT);

k21XThermalLCGT = kBXscLCGT(1+ m2TempLCGT I kBPhiLCGT);
k21YThermalLCGT = kBYscLCGT(1+ m2TempLCGT I kBPhiLCGT);
k21ZThermalLCGT = kBZscLCGT(1+ m2TempLCGT I kBPhiLCGT);

k14

k14XLCGT = kCXscLCGT(1+ I kCPhiLCGT);
k14YLCGT = kCYscLCGT(1+ I kCPhiLCGT);
k14ZLCGT = kCZscLCGT(1+ I kCPhiLCGT);

k14XThermalLCGT = kCXscLCGT(1+ m4TempLCGT I kCPhiLCGT);
k14YThermalLCGT = kCYscLCGT(1+ m4TempLCGT I kCPhiLCGT);
k14ZThermalLCGT = kCZscLCGT(1+ m4TempLCGT I kCPhiLCGT);

k14

k41XLCGT = kCXscLCGT(1+ I kCPhiLCGT);
k41YLCGT = kCYscLCGT(1+ I kCPhiLCGT);
k41ZLCGT = kCZscLCGT(1+ I kCPhiLCGT);

k41XThermalLCGT = kCXscLCGT(1+ m4TempLCGT I kCPhiLCGT);
k41YThermalLCGT = kCYscLCGT(1+ m4TempLCGT I kCPhiLCGT);
k41ZThermalLCGT = kCZscLCGT(1+ m4TempLCGT I kCPhiLCGT);

parameter set for LCGT pendulum

{f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_}

{nItemLCGT,f,
mass1LCGT,mass2LCGT,mass3LCGT,mass4LCGT,mass5LCGT,
g10HLCGT,g10VLCGT,g12HLCGT,g12VLCGT,g21HLCGT,g21VLCGT,g23HLCGT,g23VLCGT,g32HLCGT,g32VLCGT,g14HLCGT,g14VLCGT,g41HLCGT,g41VLCGT,g45HLCGT,g45VLCGT,g54HLCGT,g54VLCGT,
k10XLCGT,k10YLCGT,k10ZLCGT,k12XLCGT,k12YLCGT,k12ZLCGT,k21XLCGT,k21YLCGT,k21ZLCGT,k14XLCGT,k14YLCGT,k14ZLCGT,k41XLCGT,k41YLCGT,k41ZLCGT
}

{g12HLCGT,g12VLCGT,g23HLCGT,g23VLCGT,k12XLCGT,k12YLCGT,k12ZLCGT}

{f,
mass1LCGT,mass2LCGT,mass3LCGT,mass4LCGT,mass5LCGT,
g10HThermalLCGT,g10VThermalLCGT,g12HThermalLCGT,g12VThermalLCGT,g21HThermalLCGT,g21VThermalLCGT,g23HThermalLCGT,g23VThermalLCGT,g32HThermalLCGT,g32VThermalLCGT,g14HThermalLCGT,g14VThermalLCGT,g41HThermalLCGT,g41VThermalLCGT,g45HThermalLCGT,g45VThermalLCGT,g54HThermalLCGT,g54VThermalLCGT,
k10XThermalLCGT,k10YThermalLCGT,k10ZThermalLCGT,k12XThermalLCGT,k12YThermalLCGT,k12ZThermalLCGT,k21XThermalLCGT,k21YThermalLCGT,k21ZThermalLCGT,k14XThermalLCGT,k14YThermalLCGT,k14ZThermalLCGT,k41XThermalLCGT,k41YThermalLCGT,k41ZThermalLCGT
}

calculation for LCGT pendulum

trfLCGT[ll_,nn_,jj_,f_]:=trfAmpLCGT[ll,nn,jj,
nItemLCGT,f,
mass1LCGT,mass2LCGT,mass3LCGT,mass4LCGT,mass5LCGT,
g10HLCGT,g10VLCGT,g12HLCGT,g12VLCGT,g21HLCGT,g21VLCGT,g23HLCGT,g23VLCGT,g32HLCGT,g32VLCGT,g14HLCGT,g14VLCGT,g41HLCGT,g41VLCGT,g45HLCGT,g45VLCGT,g54HLCGT,g54VLCGT,
k10XLCGT,k10YLCGT,k10ZLCGT,k12XLCGT,k12YLCGT,k12ZLCGT,k21XLCGT,k21YLCGT,k21ZLCGT,k14XLCGT,k14YLCGT,k14ZLCGT,k41XLCGT,k41YLCGT,k41ZLCGT
]

noiseSeisLCGT[nn_,jj_,f_]:=Part[coupleMatLCGT,jj].seisLCGT[vibAmpLCGT,nn,jj,
nItemLCGT,f,
mass1LCGT,mass2LCGT,mass3LCGT,mass4LCGT,mass5LCGT,
g10HLCGT,g10VLCGT,g12HLCGT,g12VLCGT,g21HLCGT,g21VLCGT,g23HLCGT,g23VLCGT,g32HLCGT,g32VLCGT,g14HLCGT,g14VLCGT,g41HLCGT,g41VLCGT,g45HLCGT,g45VLCGT,g54HLCGT,g54VLCGT,
k10XLCGT,k10YLCGT,k10ZLCGT,k12XLCGT,k12YLCGT,k12ZLCGT,k21XLCGT,k21YLCGT,k21ZLCGT,k14XLCGT,k14YLCGT,k14ZLCGT,k41XLCGT,k41YLCGT,k41ZLCGT
]

noiseSeisCryoLCGT[nn_,jj_,f_] :=Part[coupleMatLCGT,jj].seisCryoLCGT[vibAmpLCGT,nn,jj,
nItemLCGT,f,
mass1LCGT,mass2LCGT,mass3LCGT,mass4LCGT,mass5LCGT,
g10HLCGT,g10VLCGT,g12HLCGT,g12VLCGT,g21HLCGT,g21VLCGT,g23HLCGT,g23VLCGT,g32HLCGT,g32VLCGT,g14HLCGT,g14VLCGT,g41HLCGT,g41VLCGT,g45HLCGT,g45VLCGT,g54HLCGT,g54VLCGT,
k10XLCGT,k10YLCGT,k10ZLCGT,k12XLCGT,k12YLCGT,k12ZLCGT,k21XLCGT,k21YLCGT,k21ZLCGT,k14XLCGT,k14YLCGT,k14ZLCGT,k41XLCGT,k41YLCGT,k41ZLCGT
]

noiseSeisRoomLCGT[nn_,jj_,f_] :=Part[coupleMatLCGT,jj].seisRoomLCGT[nn,jj,
nItemLCGT,f,
mass1LCGT,mass2LCGT,mass3LCGT,mass4LCGT,mass5LCGT,
g10HLCGT,g10VLCGT,g12HLCGT,g12VLCGT,g21HLCGT,g21VLCGT,g23HLCGT,g23VLCGT,g32HLCGT,g32VLCGT,g14HLCGT,g14VLCGT,g41HLCGT,g41VLCGT,g45HLCGT,g45VLCGT,g54HLCGT,g54VLCGT,
k10XLCGT,k10YLCGT,k10ZLCGT,k12XLCGT,k12YLCGT,k12ZLCGT,k21XLCGT,k21YLCGT,k21ZLCGT,k14XLCGT,k14YLCGT,k14ZLCGT,k41XLCGT,k41YLCGT,k41ZLCGT
]

dispTNoiseLCGT[ll_,nn_,f_]:=tNoiseLCGT[ll,nn,
f,
mass1LCGT,mass2LCGT,mass3LCGT,mass4LCGT,mass5LCGT,
g10HThermalLCGT,g10VThermalLCGT,g12HThermalLCGT,g12VThermalLCGT,g21HThermalLCGT,g21VThermalLCGT,g23HThermalLCGT,g23VThermalLCGT,g32HThermalLCGT,g32VThermalLCGT,g14HThermalLCGT,g14VThermalLCGT,g41HThermalLCGT,g41VThermalLCGT,g45HThermalLCGT,g45VThermalLCGT,g54HThermalLCGT,g54VThermalLCGT,
k10XThermalLCGT,k10YThermalLCGT,k10ZThermalLCGT,k12XThermalLCGT,k12YThermalLCGT,k12ZThermalLCGT,k21XThermalLCGT,k21YThermalLCGT,k21ZThermalLCGT,k14XThermalLCGT,k14YThermalLCGT,k14ZThermalLCGT,k41XThermalLCGT,k41YThermalLCGT,k41ZThermalLCGT
]

noiseTNoiseLCGT[ll_,nn_,jj_,f_] := {1}.coupleMatLCGT[[jj]]*trfLCGT[ll,nn,jj,f]*dispTNoiseLCGT[ll,nn,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)

seismic noise

noiseSeisSumLCGT[f_] := Sqrt[Sum[Sum[noiseSeisLCGT[nn,jj,f],{jj,1,3}]^2,{nn,1,3}]]

noiseSeisCryoSumLCGT[f_] := Sqrt[Sum[Sum[noiseSeisCryoLCGT[nn,jj,f],{jj,1,3}]^2,{nn,1,3}]]

noiseSeisRoomSumLCGT[f_] := Sqrt[Sum[Sum[noiseSeisRoomLCGT[nn,jj,f],{jj,1,3}]^2,{nn,1,3}]]

noiseSeisCompLCGT[jj_,f_] := Sqrt[Sum[noiseSeisLCGT[nn,jj,f]^2,{nn,1,3}]]

noiseSeisSumLCGT[17.63279198734363`]

noiseSeisCryoSumLCGT[100]

noiseSeisRoomSumLCGT[100]

suspension thermal noise (without violin mode)

noiseTNoiseSumLCGT[f_] := Sqrt[Sum[Sum[Sum[noiseTNoiseLCGT[ll,nn,jj,f],{jj,1,3}]^2,{ll,1,3}],{nn,1, nTotalLCGT}]]

noiseTNoiseCompDouble[jj_,f_] := Sqrt[Sum[Sum[noiseTNoiseLCGT[ll,nn,jj,f]^2,{ll,1,3}],{nn,1, nTotalLCGT}]] (*sum up of noise in "jj" direction*)

noiseTNoiseSumLCGT[100]

Q & resonant frequency

resLCGT=f  /. NSolve[Det[matLCGT[f,
mass1LCGT,mass2LCGT,mass3LCGT,mass4LCGT,mass5LCGT,
g10HLCGT,g10VLCGT,g12HLCGT,g12VLCGT,g21HLCGT,g21VLCGT,g23HLCGT,g23VLCGT,g32HLCGT,g32VLCGT,g14HLCGT,g14VLCGT,g41HLCGT,g41VLCGT,g45HLCGT,g45VLCGT,g54HLCGT,g54VLCGT,
k10XLCGT,k10YLCGT,k10ZLCGT,k12XLCGT,k12YLCGT,k12ZLCGT,k21XLCGT,k21YLCGT,k21ZLCGT,k14XLCGT,k14YLCGT,k14ZLCGT,k41XLCGT,k41YLCGT,k41ZLCGT]]==0,f];

Sort[resLCGT/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

Plots

Heat link diameter VS displacement noise at 3Hz

plotSeis3Hz =LogLogPlot[{ 2*noiseSeisSumLCGT[3],2*noiseSeisCryoSumLCGT[3],2*noiseSeisRoomSumLCGT[3]},{x,0.01,3},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotThermal3Hz = LogLogPlot[{ 2*noiseTNoiseSumLCGT[3]},{x,0.01,1}]

Show[plotThermal3Hz,plotSeis3Hz,PlotRange -> All]

Heat link diameter VS displacement noise at 10Hz

plotSeis10Hz = LogLogPlot[{ 2*noiseSeisSumLCGT[10],2*noiseSeisCryoSumLCGT[10],2*noiseSeisRoomSumLCGT[10]},{x,0.01,3},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotThermal10Hz = LogLogPlot[{ 2*noiseTNoiseSumLCGT[10]},{x,0.1,10}]

Show[plotSeis10Hz,plotThermal10Hz,PlotRange -> All]

all components of seismic noise 10Hz cross

2*noiseSeisSumLCGT[3]

plotSeis1LCGT = LogLogPlot[{ 2*noiseSeisSumLCGT[f],2*noiseSeisCryoSumLCGT[f],2*noiseSeisRoomSumLCGT[f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotSeis2LCGT = LogLogPlot[{2*noiseSeisSumLCGT[f],2*noiseSeisCryoSumLCGT[f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis3LCGT = LogLogPlot[{2*noiseSeisSumLCGT[f],2*noiseSeisCryoSumLCGT[f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeisLCGT=Show[plotSeis1LCGT,plotSeis2LCGT,plotLCGTmodel,PlotRange -> All]

all components of thermal noise 10Hz cross

plotTN1LCGT =LogLogPlot[2*noiseTNoiseSumLCGT[f]/l,{f,0.1,10},PlotStyle -> RGBColor[0,1,1]]

plotTN2LCGT =LogLogPlot[2*noiseTNoiseSumLCGT[f]/l,{f,10,100},PlotStyle -> RGBColor[0,1,1]]

plotTN3LCGT =LogLogPlot[2*noiseTNoiseSumLCGT[f]/l,{f,100,1000},PlotStyle -> RGBColor[0,1,1]]

plotTNLCGT = Show[plotTN1LCGT,plotTN2LCGT,plotTN3LCGT,PlotRange -> All]

Show[plotSeisLCGT,plotTNLCGT,plotLCGTmodel]

all components of seismic noise 3Hz cross

2*noiseSeisSumLCGT[3]

plotSeis1001LCGT = LogLogPlot[{ 2*noiseSeisSumLCGT[f],2*noiseSeisCryoSumLCGT[f],2*noiseSeisRoomSumLCGT[f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotSeis1002LCGT = LogLogPlot[{2*noiseSeisSumLCGT[f],2*noiseSeisCryoSumLCGT[f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis1003LCGT = LogLogPlot[{2*noiseSeisSumLCGT[f],2*noiseSeisCryoSumLCGT[f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis3HzLCGT=Show[plotSeis1001LCGT,plotSeis1002LCGT,plotLCGTmodel,PlotRange -> All]

all components of thermal noise 3Hz cross

plotTN1001LCGT =LogLogPlot[2*noiseTNoiseSumLCGT[f],{f,0.1,10},PlotStyle -> RGBColor[0,1,1]]

plotTN1002LCGT =LogLogPlot[2*noiseTNoiseSumLCGT[f],{f,10,100},PlotStyle -> RGBColor[0,1,1]]

plotTN1003LCGT =LogLogPlot[2*noiseTNoiseSumLCGT[f],{f,100,1000},PlotStyle -> RGBColor[0,1,1]]

plotTN3HzLCGT = Show[plotTN1001LCGT,plotTN1002LCGT,plotTN1003LCGT,PlotRange -> All]

Show[plotSeis3HzLCGT,plotTNLCGT,plotLCGTmodel]

all components 2

plotSeis101LCGT = LogLogPlot[2*noiseSeisSumLCGT[f],{f,0.1,10},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis102LCGT = LogLogPlot[2*noiseSeisSumLCGT[f],{f,10,100},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis103LCGT = LogLogPlot[2*noiseSeisSumLCGT[f],{f,100,1000},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeisLCGT2=Show[plotSeis101LCGT,plotSeis102LCGT,plotSeis103LCGT,PlotRange -> All]

plotTN101LCGT =LogLogPlot[2*noiseTNoiseSumLCGT[f],{f,0.1,10},PlotStyle -> RGBColor[0.5,0,1]]

plotTN102LCGT =LogLogPlot[2*noiseTNoiseSumLCGT[f],{f,10,100},PlotStyle -> RGBColor[0.5,0,1]]

plotTN103LCGT =LogLogPlot[2*noiseTNoiseSumLCGT[f],{f,100,1000},PlotStyle -> RGBColor[0.5,0,1]]

plotTNLCGT2 = Show[plotTN101LCGT,plotTN102LCGT,plotTN103LCGT,PlotRange -> All]

plotShotLCGT102=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0,0.5]]

Show[plotTN102LCGT,plotTN2LCGT,plotCLIO25model]

Show[plotTN102LCGT,plotSeis102LCGT,plotTN2LCGT,plotSeis2LCGT,plotCLIOmodel]

Show[plotSeis102LCGT,plotSeis2LCGT,plotCLIOmodel]

Show[plotTN102LCGT,plotTN2LCGT,plotCLIOmodel]

Show[plotSeisLCGT2,plotTNLCGT2,plotCLIOmodel,plotShotLCGT102]

Show[plotSeisLCGT2,plotTNLCGT2,plotCLIOmodel,plotShotLCGT102,plotLISM030320]

Show[plotSeisLCGT,plotTNLCGT,plotSeisLCGT2,plotTNLCGT2,plotShotLCGT102,plotCLIOmodel]

Show[plotSeisLCGT,plotSeisLCGT2,plotShotLCGT102,plotCLIOmodel]

Show[plotTNLCGT,plotTNLCGT2,plotShotLCGT102,plotCLIOmodel]

Show[plotShotLCGT,plotShotLCGT102,plotCLIOmodel]

seismic noise - each component

plot1= LogLogPlot[{noiseSeisLCGT[1,1,f],noiseSeisLCGT[2,2,f],noiseSeisLCGT[3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

plot2=LogLogPlot[{noiseSeisLCGT[1,1,f],noiseSeisLCGT[2,2,f],noiseSeisLCGT[3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

plot3=LogLogPlot[{noiseSeisLCGT[1,1,f],noiseSeisLCGT[2,2,f],noiseSeisLCGT[3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

Show[plot1,plot2,PlotRange -> All]

LogLogPlot[{f,2f,3f},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

thermal noise - each component

plot11= LogLogPlot[{noiseTNoiseLCGT[1,4,1,f],noiseTNoiseLCGT[5,4,1,f],noiseTNoiseLCGT[6,4,1,f],noiseTNoiseLCGT[3,4,3,f],noiseTNoiseLCGT[4,4,3,f],noiseTNoiseLCGT[5,4,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot12= LogLogPlot[{noiseTNoiseLCGT[1,4,1,f],noiseTNoiseLCGT[5,4,1,f],noiseTNoiseLCGT[6,4,1,f],noiseTNoiseLCGT[3,4,3,f],noiseTNoiseLCGT[4,4,3,f],noiseTNoiseLCGT[5,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot13= LogLogPlot[{noiseTNoiseLCGT[1,4,1,f],noiseTNoiseLCGT[5,4,1,f],noiseTNoiseLCGT[6,4,1,f],noiseTNoiseLCGT[3,4,3,f],noiseTNoiseLCGT[4,4,3,f],noiseTNoiseLCGT[5,4,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNLCGT,plot11,plot12,plot13,plotCLIOmodel]

Show[plot12,plotTNLCGT,plotCLIOmodel]

plot21= LogLogPlot[{noiseTNoiseLCGT[1,3,1,f],noiseTNoiseLCGT[5,3,1,f],noiseTNoiseLCGT[6,3,1,f],noiseTNoiseLCGT[3,3,3,f],noiseTNoiseLCGT[4,3,3,f],noiseTNoiseLCGT[5,3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot22= LogLogPlot[{noiseTNoiseLCGT[1,3,1,f],noiseTNoiseLCGT[5,3,1,f],noiseTNoiseLCGT[6,3,1,f],noiseTNoiseLCGT[3,3,3,f],noiseTNoiseLCGT[4,3,3,f],noiseTNoiseLCGT[5,3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot23= LogLogPlot[{noiseTNoiseLCGT[1,3,1,f],noiseTNoiseLCGT[5,3,1,f],noiseTNoiseLCGT[6,3,1,f],noiseTNoiseLCGT[3,3,3,f],noiseTNoiseLCGT[4,3,3,f],noiseTNoiseLCGT[5,3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNLCGT,plot21,plot22,plot23,plotCLIOmodel]

Show[plot22,plotTNLCGT,plotCLIOmodel]

Plot[{f,2 f,3 f,4 f,5 f,6 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot24= LogLogPlot[{noiseTNoiseLCGT[3,3,3,f],noiseTNoiseLCGT[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

plot25= LogLogPlot[{noiseTNoiseLCGT[3,3,3,f],noiseTNoiseLCGT[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

Show[plot24,plot24bc,plotCLIOmodel]

Show[plot25,plot24bc,plotCLIOmodel]

thermal noise - each direction

plot31= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1]}]

plot32= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1]}]

plot33= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1]}]

Show[plotTNLCGT,plot31,plot32,plot33,plotCLIOmodel,PlotRange -> All]

plot34 =Show[plot32,plot33,PlotRange -> All]

Show[plot34,plotCLIOmodel,plotTN2LCGT,plotTN3LCGT]

Plot[{f,2 f,3 f,4 f,5 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

thermal noise - each dissipation g4

plot41= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.8]}]

plot42= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.8]}]

plot43= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.8]}]

Show[plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

Show[plotTNbcLCGT,plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

thermal noise - each dissipation g3

plot51= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0.8]}]

plot52= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0.8]}]

plot53= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0.8]}]

plot54= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

Show[plotTNLCGT,plot51,plot52,plot53,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plotTNLCGT]

Show[plot54,plot52]

thermal noise - each dissipation magnet damping

plot61= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0]}]

plot62= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0]}]

plot63= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0]}]

Show[plotTNLCGT,plot61,plot62,plot63,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plot62,plotTNLCGT]

LCGT cryogenic suspension no VSPI (2004/04/26)

Parameters

intersting item

nItemLCGTb = 3;(*3:mirror*)

coupling & vibration amplification in cryostat

coupleZXLCGTb =1/1000;(*coupling Z -> X*)
coupleYXLCGTb = 1/1000;(*coupling Y -> X*)

SPIMatLCGTb = (({{1/100}, {1}, {1/1}}));

offset of beam centering

offsetRollLCGTb = 0 mm;
offsetPitchLCGTb = 0.1 mm;
offsetYawLCGTb = 0.1 mm;

vibration amplification factor in cryostat

vibAmpLCGTb = 10/10;

dimensions of mass for quad pendulum

m1

m1DensLCGTb = SpMassDens;
m1XLCGTb = SpMassX;
m1YLCGTb = SpMassY;
m1ZLCGTb = SpMassZ;
mCube[SpMassDens,SpMassX,SpMassY,SpMassZ]

m2

m2DensLCGTb = UMassDens;
m2rLCGTb = rUMass;
m2lLCGTb = lUMass;

m3

m3DensLCGTb = saDens;
m3rLCGTb = rMass;
m3lLCGTb = lMass;

mMassLCGTb=mCyl[m3DensLCGTb,m3rLCGTb,m3lLCGTb]

m4

m4DensLCGTb = RUMassDens;
m4rLCGTb = rRUMass;
m4lLCGTb = lRUMass;

m5

m5DensLCGTb = RMassDens;
m5rLCGTb = rRMass;
m5lLCGTb = lRMass;

spring for quad pendulum

g1

g1LengthLCGTb = lSpMassPend;
g1VFreqLCGTb = 0.5 Hz;

g2

g2LengthLCGTb = lUMassPend;
g2VFreqLCGTb = 0.7 Hz;

g3

g3LengthLCGTb = lSaPend;

finalYoungLCGTb = saYoung;

g4

g4LengthLCGTb = lUMassPend;
g4VFreqLCGTb =20 Hz;

g5

g5LengthLCGTb = lSaPend;
g5VFreqLCGTb =20 Hz;

kA

kAUYoungLCGTb = alYoung;
kAUShearLCGTb = alShear;
kAURadLCGTb = Pi;
kAURadMinLCGTb = 1.3 mm;
kAURadiusLCGTb = 25 cm;
kANumLCGTb = 8;
kANumLCGTb = Ceiling[kAURadMinLCGTb^2 /(kAUDiaLCGTb/2)^2];
kAUDiaLCGTb = 1 mm;
2*Sqrt[kAURadMinLCGTb^2/kANumLCGTb] 1000
Ceiling[kAURadMinLCGTb^2 /(kAUDiaLCGTb/2)^2]

kB

kBUYoungLCGTb = alYoung;
kBUShearLCGTb = alShear;
kBURadLCGTb = Pi;
kBURadMinLCGTb = 3.2 mm;
kBURadiusLCGTb = 20 cm;
kBNumLCGTb =Ceiling[ kBURadMinLCGTb^2 /(kBUDiaLCGTb/2)^2];
kBUDiaLCGTb =3 mm;
2*Sqrt[kBURadMinLCGTb^2/kBNumLCGTb] 1000
Ceiling[ kBURadMinLCGTb^2 /(kBUDiaLCGTb/2)^2]

kC

kCUYoungLCGTb = alYoung;
kCUShearLCGTb = alShear;
kCURadLCGTb = Pi;
kCUDiaLCGTb = kBUDiaLCGTb;
kCURadiusLCGTb = 20 cm;
kCNumLCGTb = 0 kBNumLCGTb;

dissipation

qRoomHLCGTb =10^6;
qCryoHLCGTb = 10^7;
qRoomVLCGTb = 10^3;
qCryoVLCGTb  = 10^5;
qUAlLCGTb =  10^3 ;

dillFactorLCGTb = dilutionFactor[mMassLCGTb,numSaPend,lSaPend,diaSaPend,finalYoungLCGTb]

qSaVLCGTb = 5*10^6/1;

qSaHLCGTb =qSaVLCGTb/dillFactorLCGTb

qg3VLCGTb = qCryoVLCGTb;

g3TempVLCGTb = m3TempLCGTb;(*縦防振の板ばねをcryoに入れるときはm3TempLCGTb,それ以外はm2TempLCGTb*)

in spring

g10HPhiLCGTb =  1/qRoomHLCGTb;
g10VPhiLCGTb =   1/qRoomVLCGTb;

g12HPhiLCGTb =   1/qCryoHLCGTb;
g12VPhiLCGTb =  1/qCryoVLCGTb/10^0;

g21HPhiLCGTb =  1/qCryoHLCGTb;
g21VPhiLCGTb =   1/qCryoVLCGTb/10^0;

g23HPhiLCGTb =   1/qSaVLCGTb*dillFactorLCGTb;
g23VPhiLCGTb =    1/qSaVLCGTb;

g32HPhiLCGTb =    1/qSaVLCGTb*dillFactorLCGTb;
g32VPhiLCGTb =    1/qSaVLCGTb;

g14HPhiLCGTb =  1/qCryoHLCGTb;
g14VPhiLCGTb =  1/qUAlLCGTb;

g41HPhiLCGTb =  1/qCryoHLCGTb;
g41VPhiLCGTb = 1/qUAlLCGTb;

g25HPhiLCGTb =  1/qSaHLCGTb;
g25VPhiLCGTb =  1/qSaVLCGTb/10^0;

g52HPhiLCGTb =  1/qSaHLCGTb;
g52VPhiLCGTb =  1/qSaVLCGTb/10^0;

kAPhiLCGTb =   1/qUAlLCGTb/10^0;
kBPhiLCGTb =   1/qUAlLCGTb;
kCPhiLCGTb =   1/qUAlLCGTb;

temperature for triple pendulum

tISCryoLCGTb = 8 K;

m1TempLCGTb = 14 K;
m2TempLCGTb = 15 K;
m3TempLCGTb = 20 K;
m4TempLCGTb = 14 K;
m5TempLCGTb = 15 K;

mk1TempLCGTb = tISCryoLCGTb;

Preparation

coupling matrix

coupleMatLCGTb=SPIMatLCGTb (({{1}, {coupleYXLCGTb}, {coupleZXLCGTb}}));

coupleMatTnoiseLCGTb= (({{1}, {coupleYXLCGTb}, {coupleZXLCGTb}}));

mass & moment inertia for LCGTb pendulum

m1

mass1LCGTb = mSpMass;

m2

mass2LCGTb = mUMass;

m3

mass3LCGTb = mMass;

m4

mass4LCGTb = mRUMass; (*see Parameters/Dimensions of final suspension/final mass*)

m5

mass5LCGTb =mRMass;

suspension wire for LCGTb pendulum

horizontal

g1HScLCGTb = scPend[mass1LCGTb+mass2LCGTb+mass3LCGTb+mass4LCGTb+mass5LCGTb,g1LengthLCGTb];
g2HScLCGTb = scPend[mass2LCGTb+mass3LCGTb+mass5LCGTb,g2LengthLCGTb];
g3HScLCGTb = scPend[mass3LCGTb,g3LengthLCGTb];
g4HScLCGTb = scPend[mass4LCGTb,g4LengthLCGTb];
g5HScLCGTb = scPend[mass5LCGTb,g5LengthLCGTb];

vertical

g1VScLCGTb = scFreq[mass1LCGTb+mass2LCGTb+mass3LCGTb+mass4LCGTb+mass5LCGTb,g1VFreqLCGTb];
g2VScLCGTb = scFreq[mass2LCGTb+mass3LCGTb+mass5LCGTb,g2VFreqLCGTb];
g3VScLCGTb = numSaPend*scVert[finalYoungLCGTb,diaSaPend,lSaPend];
g4VScLCGTb = scFreq[mass4LCGTb,g2VFreqLCGTb];
g5VScLCGTb = scFreq[mass5LCGTb,g5VFreqLCGTb];
(*g5VScLCGTb = numSaPend*scVert[saYoung,diaSaPend,lSaPend];*)

g10

g10HLCGTb = g1HScLCGTb(1 +I g10HPhiLCGTb);
g10VLCGTb = g1VScLCGTb(1 +I g10VPhiLCGTb);

g10HThermalLCGTb = g1HScLCGTb(1 +tRoom I g10HPhiLCGTb);
g10VThermalLCGTb = g1VScLCGTb(1 +tRoom I g10VPhiLCGTb);

g12

g12HLCGTb = g2HScLCGTb(1 +I g12HPhiLCGTb);
g12VLCGTb = g2VScLCGTb(1 +I g12VPhiLCGTb);

g12HThermalLCGTb = g2HScLCGTb(1 +m2TempLCGTb I g12HPhiLCGTb);
g12VThermalLCGTb = g2VScLCGTb(1 +m1TempLCGTb I g12VPhiLCGTb);

g21

g21HLCGTb = g2HScLCGTb(1 +I g21HPhiLCGTb);
g21VLCGTb = g2VScLCGTb(1 +I g21VPhiLCGTb);

g21HThermalLCGTb = g2HScLCGTb(1 +m1TempLCGTb I g21HPhiLCGTb);
g21VThermalLCGTb = g2VScLCGTb(1 +m1TempLCGTb I g21VPhiLCGTb);

g23

g23HLCGTb = g3HScLCGTb(1 +I g23HPhiLCGTb);
g23VLCGTb = g3VScLCGTb(1 +I g23VPhiLCGTb);

g23HThermalLCGTb = g3HScLCGTb(1 +m3TempLCGTb I g23HPhiLCGTb);
g23VThermalLCGTb = g3VScLCGTb(1 +m3TempLCGTb I g23VPhiLCGTb);

g32

g32HLCGTb = g3HScLCGTb(1 +I g32HPhiLCGTb);
g32VLCGTb = g3VScLCGTb(1 +I g32VPhiLCGTb);

g32HThermalLCGTb = g3HScLCGTb(1 +m2TempLCGTb I g32HPhiLCGTb);
g32VThermalLCGTb = g3VScLCGTb(1 +m3TempLCGTb I g32VPhiLCGTb);

g14

g14HLCGTb = g4HScLCGTb(1 +I g14HPhiLCGTb);
g14VLCGTb = g4VScLCGTb(1 +I g14VPhiLCGTb);

g14HThermalLCGTb = g4HScLCGTb(1 +m4TempLCGTb I g14HPhiLCGTb);
g14VThermalLCGTb = g4VScLCGTb(1 +m1TempLCGTb I g14VPhiLCGTb);

g41

g41HLCGTb = g4HScLCGTb(1 +I g41HPhiLCGTb);
g41VLCGTb = g4VScLCGTb(1 +I g41VPhiLCGTb);

g41HThermalLCGTb = g4HScLCGTb(1 +m1TempLCGTb I g41HPhiLCGTb);
g41VThermalLCGTb = g4VScLCGTb(1 +m1TempLCGTb I g41VPhiLCGTb);

g25

g25HLCGTb = g4HScLCGTb(1 +I g25HPhiLCGTb);
g25VLCGTb = g4VScLCGTb(1 +I g25VPhiLCGTb);

g25HThermalLCGTb = g5HScLCGTb(1 +m5TempLCGTb I g25HPhiLCGTb);
g25VThermalLCGTb = g5VScLCGTb(1 +m5TempLCGTb I g25VPhiLCGTb);

g54

g52HLCGTb = g5HScLCGTb(1 +I g52HPhiLCGTb);
g52VLCGTb = g5VScLCGTb(1 +I g52VPhiLCGTb);

g52HThermalLCGTb = g5HScLCGTb(1 +m4TempLCGTb I g52HPhiLCGTb);
g52VThermalLCGTb = g5VScLCGTb(1 +m5TempLCGTb I g52VPhiLCGTb);

heat link

kA

kAXscLCGTb = kANumLCGTb*scUX[kAUYoungLCGTb,kAURadLCGTb,kAUDiaLCGTb,kAURadiusLCGTb];
kAYscLCGTb = kANumLCGTb*scUY[kAUShearLCGTb,kAUDiaLCGTb,kAURadiusLCGTb];
kAZscLCGTb = kANumLCGTb*scUZ[kAUYoungLCGTb,kAURadLCGTb,kAUDiaLCGTb,kAURadiusLCGTb];

kB

kBXscLCGTb = kBNumLCGTb*scUZ[kBUYoungLCGTb,kBURadLCGTb,kBUDiaLCGTb,kBURadiusLCGTb];
kBYscLCGTb = kBNumLCGTb*scUY[kBUShearLCGTb,kBUDiaLCGTb,kBURadiusLCGTb];
kBZscLCGTb = kBNumLCGTb*scUX[kBUYoungLCGTb,kBURadLCGTb,kBUDiaLCGTb,kBURadiusLCGTb];

LogLogPlot[{kBXscLCGTb,kBYscLCGTb,kBZscLCGTb,g2HScLCGTb,g2VScLCGTb},{x,0.,7.2}]

kC

kCXscLCGTb = kCNumLCGTb*scUZ[kCUYoungLCGTb,kCURadLCGTb,kCUDiaLCGTb,kCURadiusLCGTb];
kCYscLCGTb = kCNumLCGTb*scUY[kCUShearLCGTb,kCUDiaLCGTb,kCURadiusLCGTb];
kCZscLCGTb = kCNumLCGTb*scUX[kCUYoungLCGTb,kCURadLCGTb,kCUDiaLCGTb,kCURadiusLCGTb];

k10

k10XLCGTb = kAXscLCGTb(1+ I kAPhiLCGTb);
k10YLCGTb = kAYscLCGTb(1+ I kAPhiLCGTb);
k10ZLCGTb = kAZscLCGTb(1+ I kAPhiLCGTb);

k10XThermalLCGTb = kAXscLCGTb(1+ tISCryoLCGTb I kAPhiLCGTb);
k10YThermalLCGTb = kAYscLCGTb(1+ tISCryoLCGTb I kAPhiLCGTb);
k10ZThermalLCGTb = kAZscLCGTb(1+ tISCryoLCGTb I kAPhiLCGTb);

k12

k12XLCGTb = kBXscLCGTb(1+ I kBPhiLCGTb);
k12YLCGTb = kBYscLCGTb(1+ I kBPhiLCGTb);
k12ZLCGTb = kBZscLCGTb(1+ I kBPhiLCGTb);

k12XThermalLCGTb = kBXscLCGTb(1+ m2TempLCGTb I kBPhiLCGTb);
k12YThermalLCGTb = kBYscLCGTb(1+ m2TempLCGTb I kBPhiLCGTb);
k12ZThermalLCGTb = kBZscLCGTb(1+ m2TempLCGTb I kBPhiLCGTb);

k21

k21XLCGTb = kBXscLCGTb(1+ I kBPhiLCGTb);
k21YLCGTb = kBYscLCGTb(1+ I kBPhiLCGTb);
k21ZLCGTb = kBZscLCGTb(1+ I kBPhiLCGTb);

k21XThermalLCGTb = kBXscLCGTb(1+ m2TempLCGTb I kBPhiLCGTb);
k21YThermalLCGTb = kBYscLCGTb(1+ m2TempLCGTb I kBPhiLCGTb);
k21ZThermalLCGTb = kBZscLCGTb(1+ m2TempLCGTb I kBPhiLCGTb);

k14

k14XLCGTb = kCXscLCGTb(1+ I kCPhiLCGTb);
k14YLCGTb = kCYscLCGTb(1+ I kCPhiLCGTb);
k14ZLCGTb = kCZscLCGTb(1+ I kCPhiLCGTb);

k14XThermalLCGTb = kCXscLCGTb(1+ m4TempLCGTb I kCPhiLCGTb);
k14YThermalLCGTb = kCYscLCGTb(1+ m4TempLCGTb I kCPhiLCGTb);
k14ZThermalLCGTb = kCZscLCGTb(1+ m4TempLCGTb I kCPhiLCGTb);

k14

k41XLCGTb = kCXscLCGTb(1+ I kCPhiLCGTb);
k41YLCGTb = kCYscLCGTb(1+ I kCPhiLCGTb);
k41ZLCGTb = kCZscLCGTb(1+ I kCPhiLCGTb);

k41XThermalLCGTb = kCXscLCGTb(1+ m4TempLCGTb I kCPhiLCGTb);
k41YThermalLCGTb = kCYscLCGTb(1+ m4TempLCGTb I kCPhiLCGTb);
k41ZThermalLCGTb = kCZscLCGTb(1+ m4TempLCGTb I kCPhiLCGTb);

parameter set for LCGTb pendulum

{f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx10_,hy10_,hz10_,hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_}

{nItemLCGTb,f,
mass1LCGTb,mass2LCGTb,mass3LCGTb,mass4LCGTb,mass5LCGTb,
g10HLCGTb,g10VLCGTb,g12HLCGTb,g12VLCGTb,g21HLCGTb,g21VLCGTb,g23HLCGTb,g23VLCGTb,g32HLCGTb,g32VLCGTb,g14HLCGTb,g14VLCGTb,g41HLCGTb,g41VLCGTb,g25HLCGTb,g25VLCGTb,g52HLCGTb,g52VLCGTb,
k10XLCGTb,k10YLCGTb,k10ZLCGTb,k12XLCGTb,k12YLCGTb,k12ZLCGTb,k21XLCGTb,k21YLCGTb,k21ZLCGTb,k14XLCGTb,k14YLCGTb,k14ZLCGTb,k41XLCGTb,k41YLCGTb,k41ZLCGTb
}

{g12HLCGTb,g12VLCGTb,g23HLCGTb,g23VLCGTb,k12XLCGTb,k12YLCGTb,k12ZLCGTb}

{f,
mass1LCGTb,mass2LCGTb,mass3LCGTb,mass4LCGTb,mass5LCGTb,
g10HThermalLCGTb,g10VThermalLCGTb,g12HThermalLCGTb,g12VThermalLCGTb,g21HThermalLCGTb,g21VThermalLCGTb,g23HThermalLCGTb,g23VThermalLCGTb,g32HThermalLCGTb,g32VThermalLCGTb,g14HThermalLCGTb,g14VThermalLCGTb,g41HThermalLCGTb,g41VThermalLCGTb,g25HThermalLCGTb,g25VThermalLCGTb,g52HThermalLCGTb,g52VThermalLCGTb,
k10XThermalLCGTb,k10YThermalLCGTb,k10ZThermalLCGTb,k12XThermalLCGTb,k12YThermalLCGTb,k12ZThermalLCGTb,k21XThermalLCGTb,k21YThermalLCGTb,k21ZThermalLCGTb,k14XThermalLCGTb,k14YThermalLCGTb,k14ZThermalLCGTb,k41XThermalLCGTb,k41YThermalLCGTb,k41ZThermalLCGTb
}

calculation for LCGTb pendulum

trfLCGTb[ll_,nn_,jj_,f_]:=trfAmpLCGTb[ll,nn,jj,
nItemLCGTb,f,
mass1LCGTb,mass2LCGTb,mass3LCGTb,mass4LCGTb,mass5LCGTb,
g10HLCGTb,g10VLCGTb,g12HLCGTb,g12VLCGTb,g21HLCGTb,g21VLCGTb,g23HLCGTb,g23VLCGTb,g32HLCGTb,g32VLCGTb,g14HLCGTb,g14VLCGTb,g41HLCGTb,g41VLCGTb,g25HLCGTb,g25VLCGTb,g52HLCGTb,g52VLCGTb,
k10XLCGTb,k10YLCGTb,k10ZLCGTb,k12XLCGTb,k12YLCGTb,k12ZLCGTb,k21XLCGTb,k21YLCGTb,k21ZLCGTb,k14XLCGTb,k14YLCGTb,k14ZLCGTb,k41XLCGTb,k41YLCGTb,k41ZLCGTb
]

noiseSeisLCGTb[nn_,jj_,f_]:=Part[coupleMatLCGTb,jj].seisLCGTb[vibAmpLCGTb,nn,jj,
nItemLCGTb,f,
mass1LCGTb,mass2LCGTb,mass3LCGTb,mass4LCGTb,mass5LCGTb,
g10HLCGTb,g10VLCGTb,g12HLCGTb,g12VLCGTb,g21HLCGTb,g21VLCGTb,g23HLCGTb,g23VLCGTb,g32HLCGTb,g32VLCGTb,g14HLCGTb,g14VLCGTb,g41HLCGTb,g41VLCGTb,g25HLCGTb,g25VLCGTb,g52HLCGTb,g52VLCGTb,
k10XLCGTb,k10YLCGTb,k10ZLCGTb,k12XLCGTb,k12YLCGTb,k12ZLCGTb,k21XLCGTb,k21YLCGTb,k21ZLCGTb,k14XLCGTb,k14YLCGTb,k14ZLCGTb,k41XLCGTb,k41YLCGTb,k41ZLCGTb
]

noiseSeisCryoLCGTb[nn_,jj_,f_] :=Part[coupleMatLCGTb,jj].seisCryoLCGTb[vibAmpLCGTb,nn,jj,
nItemLCGTb,f,
mass1LCGTb,mass2LCGTb,mass3LCGTb,mass4LCGTb,mass5LCGTb,
g10HLCGTb,g10VLCGTb,g12HLCGTb,g12VLCGTb,g21HLCGTb,g21VLCGTb,g23HLCGTb,g23VLCGTb,g32HLCGTb,g32VLCGTb,g14HLCGTb,g14VLCGTb,g41HLCGTb,g41VLCGTb,g25HLCGTb,g25VLCGTb,g52HLCGTb,g52VLCGTb,
k10XLCGTb,k10YLCGTb,k10ZLCGTb,k12XLCGTb,k12YLCGTb,k12ZLCGTb,k21XLCGTb,k21YLCGTb,k21ZLCGTb,k14XLCGTb,k14YLCGTb,k14ZLCGTb,k41XLCGTb,k41YLCGTb,k41ZLCGTb
]

noiseSeisRoomLCGTb[nn_,jj_,f_] :=Part[coupleMatLCGTb,jj].seisRoomLCGTb[nn,jj,
nItemLCGTb,f,
mass1LCGTb,mass2LCGTb,mass3LCGTb,mass4LCGTb,mass5LCGTb,
g10HLCGTb,g10VLCGTb,g12HLCGTb,g12VLCGTb,g21HLCGTb,g21VLCGTb,g23HLCGTb,g23VLCGTb,g32HLCGTb,g32VLCGTb,g14HLCGTb,g14VLCGTb,g41HLCGTb,g41VLCGTb,g25HLCGTb,g25VLCGTb,g52HLCGTb,g52VLCGTb,
k10XLCGTb,k10YLCGTb,k10ZLCGTb,k12XLCGTb,k12YLCGTb,k12ZLCGTb,k21XLCGTb,k21YLCGTb,k21ZLCGTb,k14XLCGTb,k14YLCGTb,k14ZLCGTb,k41XLCGTb,k41YLCGTb,k41ZLCGTb
]

dispTNoiseLCGTb[ll_,nn_,f_]:=tNoiseLCGTb[ll,nn,
f,
mass1LCGTb,mass2LCGTb,mass3LCGTb,mass4LCGTb,mass5LCGTb,
g10HThermalLCGTb,g10VThermalLCGTb,g12HThermalLCGTb,g12VThermalLCGTb,g21HThermalLCGTb,g21VThermalLCGTb,g23HThermalLCGTb,g23VThermalLCGTb,g32HThermalLCGTb,g32VThermalLCGTb,g14HThermalLCGTb,g14VThermalLCGTb,g41HThermalLCGTb,g41VThermalLCGTb,g25HThermalLCGTb,g25VThermalLCGTb,g52HThermalLCGTb,g52VThermalLCGTb,
k10XThermalLCGTb,k10YThermalLCGTb,k10ZThermalLCGTb,k12XThermalLCGTb,k12YThermalLCGTb,k12ZThermalLCGTb,k21XThermalLCGTb,k21YThermalLCGTb,k21ZThermalLCGTb,k14XThermalLCGTb,k14YThermalLCGTb,k14ZThermalLCGTb,k41XThermalLCGTb,k41YThermalLCGTb,k41ZThermalLCGTb
]

(*noiseTNoiseLCGTb[ll_,nn_,jj_,f_] := {1}.coupleMatLCGTb[[jj]]*trfLCGTb[ll,nn,jj,f]*dispTNoiseLCGTb[ll,nn,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)*)

noiseTNoiseLCGTb[ll_,f_] :={1}. coupleMatTnoiseLCGTb[[ll]]*dispTNoiseLCGTb[ll,nItemLCGTb,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)

seismic noise

noiseSeisSumLCGTb[f_] := Sqrt[Sum[Sum[noiseSeisLCGTb[nn,jj,f],{jj,1,3}]^2,{nn,1,3}]]

noiseSeisCryoSumLCGTb[f_] := Sqrt[Sum[Sum[noiseSeisCryoLCGTb[nn,jj,f],{jj,1,3}]^2,{nn,1,3}]]

noiseSeisRoomSumLCGTb[f_] := Sqrt[Sum[Sum[noiseSeisRoomLCGTb[nn,jj,f],{jj,1,3}]^2,{nn,1,3}]]

noiseSeisCompLCGTb[jj_,f_] := Sqrt[Sum[noiseSeisLCGTb[nn,jj,f]^2,{nn,1,3}]]

2*noiseSeisSumLCGTb[10]

noiseSeisCryoSumLCGTb[100]

noiseSeisRoomSumLCGTb[100]

suspension thermal noise (without violin mode)

(*noiseTNoiseSumLCGTb[f_] := Sqrt[Sum[Sum[Sum[noiseTNoiseLCGTb[ll,nn,jj,f],{jj,1,3}]^2,{ll,1,3}],{nn,1, nTotalLCGTb}]]*)

noiseTNoiseSumLCGTb[f_] := Sqrt[Sum[noiseTNoiseLCGTb[ll,f]^2,{ll,1,3}]]

noiseTNoiseCompDouble[jj_,f_] := Sqrt[Sum[Sum[noiseTNoiseLCGTb[ll,nn,jj,f]^2,{ll,1,3}],{nn,1, nTotalLCGTb}]] (*sum up of noise in "jj" direction*)

noiseTNoiseSumLCGTb[100]/l*2

dispLCGT[f_] := Sqrt[4*noiseSeisSumLCGTb[f]^2+4*noiseTNoiseSumLCGTb[f]^2+shotOriginal[f]^2+radiaOriginal[f]^2+dispThMass20[f]^2]

dispLCGT[10]

Q & resonant frequency

resLCGTb=f  /. NSolve[Det[matLCGTb[f,
mass1LCGTb,mass2LCGTb,mass3LCGTb,mass4LCGTb,mass5LCGTb,
g10HLCGTb,g10VLCGTb,g12HLCGTb,g12VLCGTb,g21HLCGTb,g21VLCGTb,g23HLCGTb,g23VLCGTb,g32HLCGTb,g32VLCGTb,g14HLCGTb,g14VLCGTb,g41HLCGTb,g41VLCGTb,g45HLCGTb,g45VLCGTb,g54HLCGTb,g54VLCGTb,
k10XLCGTb,k10YLCGTb,k10ZLCGTb,k12XLCGTb,k12YLCGTb,k12ZLCGTb,k21XLCGTb,k21YLCGTb,k21ZLCGTb,k14XLCGTb,k14YLCGTb,k14ZLCGTb,k41XLCGTb,k41YLCGTb,k41ZLCGTb]]==0,f];

Sort[resLCGTb/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

Plots

SPI

listFreqSPI=Table[10^x,{x,-1.0,3.0,0.01}];

listDispSeis=Table[2 noiseSeisSumLCGTb[10^x],{x,-1,3,0.01}];

listDispPlotSeis =Table[{Part[listFreqSPI,i],Part[listDispSeis,i]},{i,Length[listFreqSPI]}];

listDispOriginalLCGT = Table[dispLCGToriginal[10^x],{x,-1,3,0.01}];

listDispLCGT = Table[dispLCGT[10^x],{x,-1,3,0.01}];

listDispPlotOriginalLCGT =Table[{Part[listFreqSPI,i],Part[listDispOriginalLCGT,i]},{i,Length[listFreqSPI]}];

listDispPlotLCGT =Table[{Part[listFreqSPI,i],Part[listDispLCGT,i]},{i,Length[listFreqSPI]}];

Export["~/Study/CurrentProject/LCGT/calculatedList/061016/freqNoSPI.dat",Take[listDispPlotSeis,All,{1}]];

Export["~/Study/CurrentProject/LCGT/calculatedList/061016/dispNoSPI.dat",Take[listDispPlotSeis,All,{2}]];

Export["~/Study/CurrentProject/LCGT/calculatedList/061016/freqOriginalLCGT.dat",Take[listDispPlotOriginalLCGT,All,{1}]];

Export["~/Study/CurrentProject/LCGT/calculatedList/061016/dispOrigianlLCGT.dat",Take[listDispPlotOriginalLCGT,All,{2}]];

Put[listFreqSPI,"~/Study/CurrentProject/LCGT/calculatedList/061016/listFreq.txt"]

Put[listDispSPI,"~/Study/CurrentProject/LCGT/listDispNoSPI.txt"]

Put[listDispSPI,"~/Study/CurrentProject/LCGT/listDispSPI.txt"]

listDispPlotSPI =Table[{Part[listFreqSPI,i],Part[listDispSPI,i]},{i,Length[listFreqSPI]}];

listDispPlotLCGT =Table[{Part[listFreqSPI,i],Part[listDispLCGT,i]},{i,Length[listFreqSPI]}];

Put[listDispLCGT,"~/Study/CurrentProject/LCGT/listDispLCGT.txt"]

plotNoSPI=ListLogLogPlot[listDispPlotLCGT,PlotStyle->{RGBColor[0,0,1]}]

plotSPI=ListLogLogPlot[listDispPlotSPI,PlotStyle->{RGBColor[1,0,0]}]

plotLCGT=ListLogLogPlot[listDispPlotLCGT,PlotStyle->{RGBColor[0,1,0]}]

plotCompeSPI = Show[plotSPI,plotNoSPI,plotLCGT]

Heat link diameter VS displacement noise with cryo-mgas

2*noiseSeisSumLCGTb[10]/l

2*noiseTNoiseSumLCGTb[10]/l

plotSeismgas =LogLogPlot[{ 2*noiseSeisSumLCGTb[10],2*noiseSeisCryoSumLCGTb[10],2*noiseSeisRoomSumLCGTb[10]},{x,0.1,7.2},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotThermal10Hz = LogLogPlot[{ 2*noiseTNoiseSumLCGTb[10]/l},{x,0.1,10}]

2*noiseTNoiseSumLCGTb[10]/l

Show[plotThermal10Hz,plotSeismgas,PlotRange -> All]

Heat link diameter VS displacement noise without cryo-mgas

plotSeisNmgas = LogLogPlot[{ 2*noiseSeisSumLCGTb[10],2*noiseSeisCryoSumLCGTb[10],2*noiseSeisRoomSumLCGTb[10]},{x,0.003,1},PlotRange -> All,PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotThermal10Hz = LogLogPlot[{ 2*noiseTNoiseSumLCGTb[10]},{x,0.1,10}]

Show[plotSeis10Hz,plotThermal10Hz,PlotRange -> All]

all components of seismic noise 10Hz cross

2*noiseSeisSumLCGTb[10]

plotSeis1LCGTb = LogLogPlot[{ 2*noiseSeisSumLCGTb[f],2*noiseSeisCryoSumLCGTb[f],2*noiseSeisRoomSumLCGTb[f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotSeis2LCGTb = LogLogPlot[{2*noiseSeisSumLCGTb[f],2*noiseSeisCryoSumLCGTb[f],2*noiseSeisRoomSumLCGTb[f]},{f,10,30},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis3LCGTb = LogLogPlot[{2*noiseSeisSumLCGTb[f],2*noiseSeisCryoSumLCGTb[f],2*noiseSeisRoomSumLCGTb[f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

2*noiseSeisSumLCGTb[10]

plotSeisLCGTb=Show[plotSeis1LCGTb,plotLCGTmodel,PlotRange -> All]

plotSeis4LCGTb = LogLogPlot[2*noiseSeisSumLCGTb[f],{f,0.1,10},PlotStyle -> {RGBColor[1,0,0],Dashing[{0.01,0.01}]}]

plotSeis5LCGTb = LogLogPlot[2*noiseSeisSumLCGTb[f],{f,10,100},PlotStyle -> {RGBColor[1,0,0],Dashing[{0.01,0.01}]}]

plotSeis6LCGTb = LogLogPlot[2*noiseSeisSumLCGTb[f],{f,0.1,10},PlotStyle -> {RGBColor[0,1,0]}]

plotSeis7LCGTb = LogLogPlot[2*noiseSeisSumLCGTb[f],{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

plotSeisLCGTb=Show[plotSeis6LCGTb,plotSeis7LCGTb,plotLCGTmodel,plotSeis4LCGTb,plotSeis5LCGTb,PlotRange -> All]

all components of thermal noise 10Hz cross

2*noiseTNoiseSumLCGTb[10]

plotTN1LCGTb =LogLogPlot[2*noiseTNoiseSumLCGTb[f],{f,0.1,10},PlotStyle -> RGBColor[0,1,1]]

plotTN2LCGTb =LogLogPlot[2*noiseTNoiseSumLCGTb[f],{f,10,100},PlotStyle -> RGBColor[0,1,1]]

plotTN3LCGTb =LogLogPlot[2*noiseTNoiseSumLCGTb[f],{f,100,1000},PlotStyle -> RGBColor[0,1,1]]

plotTNLCGTb = Show[plotTN1LCGTb,plotTN2LCGTb,plotTN3LCGTb,PlotRange -> All]

Show[plotSeisLCGTb,plotTNLCGTb]

all components of seismic noise 3Hz cross

2*noiseSeisSumLCGTb[3]

plotSeis1001LCGTb = LogLogPlot[{ 2*noiseSeisSumLCGTb[f],2*noiseSeisCryoSumLCGTb[f],2*noiseSeisRoomSumLCGTb[f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotSeis1002LCGTb = LogLogPlot[{2*noiseSeisSumLCGTb[f],2*noiseSeisCryoSumLCGTb[f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis1003LCGTb = LogLogPlot[{2*noiseSeisSumLCGTb[f],2*noiseSeisCryoSumLCGTb[f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis3HzLCGTb=Show[plotSeis1001LCGTb,plotSeis1002LCGTb,plotLCGTbmodel,PlotRange -> All]

all components of thermal noise 3Hz cross

plotTN1001LCGTb =LogLogPlot[2*noiseTNoiseSumLCGTb[f],{f,0.1,10},PlotStyle -> RGBColor[0,1,1]]

plotTN1002LCGTb =LogLogPlot[2*noiseTNoiseSumLCGTb[f],{f,10,100},PlotStyle -> RGBColor[0,1,1]]

plotTN1003LCGTb =LogLogPlot[2*noiseTNoiseSumLCGTb[f],{f,100,1000},PlotStyle -> RGBColor[0,1,1]]

plotTN3HzLCGTb = Show[plotTN1001LCGTb,plotTN1002LCGTb,plotTN1003LCGTb,PlotRange -> All]

Show[plotSeis3HzLCGTb,plotTNLCGTb,plotLCGTbmodel]

all components 2

plotSeis101LCGTb = LogLogPlot[2*noiseSeisSumLCGTb[f],{f,0.1,10},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis102LCGTb = LogLogPlot[2*noiseSeisSumLCGTb[f],{f,10,100},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis103LCGTb = LogLogPlot[2*noiseSeisSumLCGTb[f],{f,100,1000},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeisLCGTb2=Show[plotSeis101LCGTb,plotSeis102LCGTb,plotSeis103LCGTb,PlotRange -> All]

plotTN101LCGTb =LogLogPlot[2*noiseTNoiseSumLCGTb[f],{f,0.1,10},PlotStyle -> RGBColor[0.5,0,1]]

plotTN102LCGTb =LogLogPlot[2*noiseTNoiseSumLCGTb[f],{f,10,100},PlotStyle -> RGBColor[0.5,0,1]]

plotTN103LCGTb =LogLogPlot[2*noiseTNoiseSumLCGTb[f],{f,100,1000},PlotStyle -> RGBColor[0.5,0,1]]

plotTNLCGTb2 = Show[plotTN101LCGTb,plotTN102LCGTb,plotTN103LCGTb,PlotRange -> All]

plotShotLCGTb102=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0,0.5]]

Show[plotTN102LCGTb,plotTN2LCGTb,plotCLIO25model]

Show[plotTN102LCGTb,plotSeis102LCGTb,plotTN2LCGTb,plotSeis2LCGTb,plotCLIOmodel]

Show[plotSeis102LCGTb,plotSeis2LCGTb,plotCLIOmodel]

Show[plotTN102LCGTb,plotTN2LCGTb,plotCLIOmodel]

Show[plotSeisLCGTb2,plotTNLCGTb2,plotCLIOmodel,plotShotLCGTb102]

Show[plotSeisLCGTb2,plotTNLCGTb2,plotCLIOmodel,plotShotLCGTb102,plotLISM030320]

Show[plotSeisLCGTb,plotTNLCGTb,plotSeisLCGTb2,plotTNLCGTb2,plotShotLCGTb102,plotCLIOmodel]

Show[plotSeisLCGTb,plotSeisLCGTb2,plotShotLCGTb102,plotCLIOmodel]

Show[plotTNLCGTb,plotTNLCGTb2,plotShotLCGTb102,plotCLIOmodel]

Show[plotShotLCGTb,plotShotLCGTb102,plotCLIOmodel]

seismic noise - each component

plot1= LogLogPlot[{noiseSeisLCGTb[1,1,f],noiseSeisLCGTb[2,2,f],noiseSeisLCGTb[3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

plot2=LogLogPlot[{noiseSeisLCGTb[1,1,f],noiseSeisLCGTb[2,2,f],noiseSeisLCGTb[3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

plot3=LogLogPlot[{noiseSeisLCGTb[1,1,f],noiseSeisLCGTb[2,2,f],noiseSeisLCGTb[3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

Show[plot1,plot2,plotLCGTmodel,PlotRange -> All]

LogLogPlot[{f,2f,3f},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

thermal noise - each component

plot11= LogLogPlot[{noiseTNoiseLCGTb[1,4,1,f],noiseTNoiseLCGTb[5,4,1,f],noiseTNoiseLCGTb[6,4,1,f],noiseTNoiseLCGTb[3,4,3,f],noiseTNoiseLCGTb[4,4,3,f],noiseTNoiseLCGTb[5,4,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot12= LogLogPlot[{noiseTNoiseLCGTb[1,4,1,f],noiseTNoiseLCGTb[5,4,1,f],noiseTNoiseLCGTb[6,4,1,f],noiseTNoiseLCGTb[3,4,3,f],noiseTNoiseLCGTb[4,4,3,f],noiseTNoiseLCGTb[5,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot13= LogLogPlot[{noiseTNoiseLCGTb[1,4,1,f],noiseTNoiseLCGTb[5,4,1,f],noiseTNoiseLCGTb[6,4,1,f],noiseTNoiseLCGTb[3,4,3,f],noiseTNoiseLCGTb[4,4,3,f],noiseTNoiseLCGTb[5,4,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNLCGTb,plot11,plot12,plot13,plotCLIOmodel]

Show[plot12,plotTNLCGTb,plotCLIOmodel]

plot21= LogLogPlot[{noiseTNoiseLCGTb[1,3,1,f],noiseTNoiseLCGTb[5,3,1,f],noiseTNoiseLCGTb[6,3,1,f],noiseTNoiseLCGTb[3,3,3,f],noiseTNoiseLCGTb[4,3,3,f],noiseTNoiseLCGTb[5,3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot22= LogLogPlot[{noiseTNoiseLCGTb[1,3,1,f],noiseTNoiseLCGTb[5,3,1,f],noiseTNoiseLCGTb[6,3,1,f],noiseTNoiseLCGTb[3,3,3,f],noiseTNoiseLCGTb[4,3,3,f],noiseTNoiseLCGTb[5,3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot23= LogLogPlot[{noiseTNoiseLCGTb[1,3,1,f],noiseTNoiseLCGTb[5,3,1,f],noiseTNoiseLCGTb[6,3,1,f],noiseTNoiseLCGTb[3,3,3,f],noiseTNoiseLCGTb[4,3,3,f],noiseTNoiseLCGTb[5,3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNLCGTb,plot21,plot22,plot23,plotCLIOmodel]

Show[plot22,plotTNLCGTb,plotCLIOmodel]

Plot[{f,2 f,3 f,4 f,5 f,6 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot24= LogLogPlot[{noiseTNoiseLCGTb[3,3,3,f],noiseTNoiseLCGTb[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

plot25= LogLogPlot[{noiseTNoiseLCGTb[3,3,3,f],noiseTNoiseLCGTb[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

Show[plot24,plot24bc,plotCLIOmodel]

Show[plot25,plot24bc,plotCLIOmodel]

thermal noise - each direction

plot31= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1]}]

plot32= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1]}]

plot33= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1]}]

Show[plotTNLCGTb,plot31,plot32,plot33,plotCLIOmodel,PlotRange -> All]

plot34 =Show[plot32,plot33,PlotRange -> All]

Show[plot34,plotCLIOmodel,plotTN2LCGTb,plotTN3LCGTb]

Plot[{f,2 f,3 f,4 f,5 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

thermal noise - each dissipation g4

plot41= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.8]}]

plot42= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.8]}]

plot43= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.8]}]

Show[plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

Show[plotTNbcLCGTb,plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

thermal noise - each dissipation g3

plot51= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0.8]}]

plot52= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0.8]}]

plot53= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0.8]}]

plot54= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

Show[plotTNLCGTb,plot51,plot52,plot53,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plotTNLCGTb]

Show[plot54,plot52]

thermal noise - each dissipation magnet damping

plot61= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0]}]

plot62= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0]}]

plot63= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0]}]

Show[plotTNLCGTb,plot61,plot62,plot63,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plot62,plotTNLCGTb]

LCGT cryogenic suspension no SPI (2008/07/07)

Parameters

intersting item

nItemLCGTc = 3;(*3:mirror*)

coupling & vibration amplification in cryostat

coupleZXLCGTc =1/1000;(*coupling Z -> X*)
coupleYXLCGTc = 1/1000;(*coupling Y -> X*)

SPIMatLCGTc = (({{1/1}, {1}, {1/1}}));

offset of beam centering

offsetRollLCGTc = 0 mm;
offsetPitchLCGTc = 0.1 mm;
offsetYawLCGTc = 0.1 mm;

vibration amplification factor in cryostat

vibAmpLCGTc = 10/10;

dimensions of mass for quad pendulum

m1

m1DensLCGTc = SpMassDens;
m1XLCGTc = SpMassX;
m1YLCGTc = SpMassY;
m1ZLCGTc = SpMassZ;
mCube[SpMassDens,SpMassX,SpMassY,SpMassZ]

m2

m2DensLCGTc = UMassDens;
m2rLCGTc = rUMass;
m2lLCGTc = lUMass;

m3

m3DensLCGTc = MassDens;
m3rLCGTc = rMass;
m3lLCGTc = lMass;

m4

m4DensLCGTc = RUMassDens;
m4rLCGTc = rRUMass;
m4lLCGTc = lRUMass;

m5

m5DensLCGTc = RMassDens;
m5rLCGTc = rRMass;
m5lLCGTc = lRMass;

spring for quad pendulum

g1

g1LengthLCGTc = lSpMassPend;
g1VFreqLCGTc = 0.5 Hz;

g2

g2LengthLCGTc = lUMassPend;
g2VFreqLCGTc = 0.7 Hz;

g3

g3LengthLCGTc = lSaPend;

g4

g4LengthLCGTc = lUMassPend;
g4VFreqLCGTc =20 Hz;

dilutionFactor[mMass,4,0.4m,2mm,alYoung]

g5

g5LengthLCGTc = lSaPend;
g5VFreqLCGTc =20 Hz;

kA

kAUYoungLCGTc = alYoung;
kAUShearLCGTc = alShear;
kAURadLCGTc = Pi;
kAURadMinLCGTc = 1.3 mm;
kAURadiusLCGTc = 25 cm;
kANumLCGTc = 7;
(*kANumLCGTc = Ceiling[kAURadMinLCGTc^2 /(kAUDiaLCGTc/2)^2];*)
kAUDiaLCGTc = 1 mm;
2*Sqrt[kAURadMinLCGTc^2/kANumLCGTc] 1000
Ceiling[kAURadMinLCGTc^2 /(kAUDiaLCGTc/2)^2]

kB

kBUYoungLCGTc = alYoung;
kBUShearLCGTc = alShear;
kBURadLCGTc = Pi;
kBURadMinLCGTc = 3.2 mm;
kBURadiusLCGTc = 20 cm;
kBNumLCGTc = 3;
(*kBNumLCGTc =Ceiling[ kBURadMinLCGTc^2 /(kBUDiaLCGTc/2)^2];*)
kBUDiaLCGTc =3 mm;
2*Sqrt[kBURadMinLCGTc^2/kBNumLCGTc] 1000
Ceiling[ kBURadMinLCGTc^2 /(kBUDiaLCGTc/2)^2]

kC

kCUYoungLCGTc = alYoung;
kCUShearLCGTc = alShear;
kCURadLCGTc = Pi;
kCUDiaLCGTc = kBUDiaLCGTc;
kCURadiusLCGTc = 20 cm;
kCNumLCGTc = 0 kBNumLCGTc;

dissipation

qRoomHLCGTc =10^6;
qCryoHLCGTc = 10^7;
qRoomVLCGTc = 10^3;
qCryoVLCGTc  = 10^5;
qUAlLCGTc =  10^3 ;

qSaHLCGTc =10^8;
qSaVLCGTc = 5*10^6;

qg3VLCGTc = qCryoVLCGTc;

g3TempVLCGTc = m3TempLCGTc;(*縦防振の板ばねをcryoに入れるときはm3TempLCGTc,それ以外はm2TempLCGTc*)

in spring

g10HPhiLCGTc =  1/qRoomHLCGTc;
g10VPhiLCGTc =   1/qRoomVLCGTc;

g12HPhiLCGTc =   1/qCryoHLCGTc;
g12VPhiLCGTc =  1/qCryoVLCGTc/10^0;

g21HPhiLCGTc =  1/qCryoHLCGTc;
g21VPhiLCGTc =   1/qCryoVLCGTc/10^0;

g23HPhiLCGTc =   1/qSaHLCGTc;
g23VPhiLCGTc =    1/qSaVLCGTc;

g32HPhiLCGTc =   1/qSaHLCGTc;
g32VPhiLCGTc =    1/qSaVLCGTc;

g14HPhiLCGTc =  1/qCryoHLCGTc;
g14VPhiLCGTc =  1/qUAlLCGTc;

g41HPhiLCGTc =  1/qCryoHLCGTc;
g41VPhiLCGTc = 1/qUAlLCGTc;

g25HPhiLCGTc =  1/qSaHLCGTc;
g25VPhiLCGTc =  1/qSaVLCGTc/10^0;

g52HPhiLCGTc =  1/qSaHLCGTc;
g52VPhiLCGTc =  1/qSaVLCGTc/10^0;

kAPhiLCGTc =   1/qUAlLCGTc/10^0;
kBPhiLCGTc =   1/qUAlLCGTc;
kCPhiLCGTc =   1/qUAlLCGTc;

temperature for triple pendulum

tISCryoLCGTc = 8 K;

m1TempLCGTc = 14 K;
m2TempLCGTc = 15 K;
m3TempLCGTc = 20 K;
m4TempLCGTc = 14 K;
m5TempLCGTc = 15 K;

mk1TempLCGTc = tISCryoLCGTc;

Preparation

coupling matrix

coupleMatLCGTc=SPIMatLCGTc (({{1}, {coupleYXLCGTc}, {coupleZXLCGTc}}));

coupleMatTnoiseLCGTc= (({{1}, {coupleYXLCGTc}, {coupleZXLCGTc}}));

mass & moment inertia for LCGTc pendulum

m1

mass1LCGTc = mSpMass;

m2

mass2LCGTc = mUMass;

m3

mass3LCGTc = mMass;

m4

mass4LCGTc = mRUMass; (*see Parameters/Dimensions of final suspension/final mass*)

m5

mass5LCGTc =mRMass;

suspension wire for LCGTc pendulum

horizontal

g1HScLCGTc = scPend[mass1LCGTc+mass2LCGTc+mass3LCGTc+mass4LCGTc+mass5LCGTc,g1LengthLCGTc];
g2HScLCGTc = scPend[mass2LCGTc+mass3LCGTc+mass5LCGTc,g2LengthLCGTc];
g3HScLCGTc = scPend[mass3LCGTc,g3LengthLCGTc];
g4HScLCGTc = scPend[mass4LCGTc,g4LengthLCGTc];
g5HScLCGTc = scPend[mass5LCGTc,g5LengthLCGTc];

vertical

g1VScLCGTc = scFreq[mass1LCGTc+mass2LCGTc+mass3LCGTc+mass4LCGTc+mass5LCGTc,g1VFreqLCGTc];
g2VScLCGTc = scFreq[mass2LCGTc+mass3LCGTc+mass5LCGTc,g2VFreqLCGTc];
g3VScLCGTc = numSaPend*scVert[saYoung,diaSaPend,lSaPend];
g4VScLCGTc = scFreq[mass4LCGTc,g2VFreqLCGTc];
g5VScLCGTc = scFreq[mass5LCGTc,g5VFreqLCGTc];
(*g5VScLCGTc = numSaPend*scVert[saYoung,diaSaPend,lSaPend];*)

g10

g10HLCGTc = g1HScLCGTc(1 +I g10HPhiLCGTc);
g10VLCGTc = g1VScLCGTc(1 +I g10VPhiLCGTc);

g10HThermalLCGTc = g1HScLCGTc(1 +tRoom I g10HPhiLCGTc);
g10VThermalLCGTc = g1VScLCGTc(1 +tRoom I g10VPhiLCGTc);

g12

g12HLCGTc = g2HScLCGTc(1 +I g12HPhiLCGTc);
g12VLCGTc = g2VScLCGTc(1 +I g12VPhiLCGTc);

g12HThermalLCGTc = g2HScLCGTc(1 +m2TempLCGTc I g12HPhiLCGTc);
g12VThermalLCGTc = g2VScLCGTc(1 +m1TempLCGTc I g12VPhiLCGTc);

g21

g21HLCGTc = g2HScLCGTc(1 +I g21HPhiLCGTc);
g21VLCGTc = g2VScLCGTc(1 +I g21VPhiLCGTc);

g21HThermalLCGTc = g2HScLCGTc(1 +m1TempLCGTc I g21HPhiLCGTc);
g21VThermalLCGTc = g2VScLCGTc(1 +m1TempLCGTc I g21VPhiLCGTc);

g23

g23HLCGTc = g3HScLCGTc(1 +I g23HPhiLCGTc);
g23VLCGTc = g3VScLCGTc(1 +I g23VPhiLCGTc);

g23HThermalLCGTc = g3HScLCGTc(1 +m3TempLCGTc I g23HPhiLCGTc);
g23VThermalLCGTc = g3VScLCGTc(1 +m3TempLCGTc I g23VPhiLCGTc);

g32

g32HLCGTc = g3HScLCGTc(1 +I g32HPhiLCGTc);
g32VLCGTc = g3VScLCGTc(1 +I g32VPhiLCGTc);

g32HThermalLCGTc = g3HScLCGTc(1 +m2TempLCGTc I g32HPhiLCGTc);
g32VThermalLCGTc = g3VScLCGTc(1 +m3TempLCGTc I g32VPhiLCGTc);

g14

g14HLCGTc = g4HScLCGTc(1 +I g14HPhiLCGTc);
g14VLCGTc = g4VScLCGTc(1 +I g14VPhiLCGTc);

g14HThermalLCGTc = g4HScLCGTc(1 +m4TempLCGTc I g14HPhiLCGTc);
g14VThermalLCGTc = g4VScLCGTc(1 +m1TempLCGTc I g14VPhiLCGTc);

g41

g41HLCGTc = g4HScLCGTc(1 +I g41HPhiLCGTc);
g41VLCGTc = g4VScLCGTc(1 +I g41VPhiLCGTc);

g41HThermalLCGTc = g4HScLCGTc(1 +m1TempLCGTc I g41HPhiLCGTc);
g41VThermalLCGTc = g4VScLCGTc(1 +m1TempLCGTc I g41VPhiLCGTc);

g25

g25HLCGTc = g4HScLCGTc(1 +I g25HPhiLCGTc);
g25VLCGTc = g4VScLCGTc(1 +I g25VPhiLCGTc);

g25HThermalLCGTc = g5HScLCGTc(1 +m5TempLCGTc I g25HPhiLCGTc);
g25VThermalLCGTc = g5VScLCGTc(1 +m5TempLCGTc I g25VPhiLCGTc);

g54

g52HLCGTc = g5HScLCGTc(1 +I g52HPhiLCGTc);
g52VLCGTc = g5VScLCGTc(1 +I g52VPhiLCGTc);

g52HThermalLCGTc = g5HScLCGTc(1 +m4TempLCGTc I g52HPhiLCGTc);
g52VThermalLCGTc = g5VScLCGTc(1 +m5TempLCGTc I g52VPhiLCGTc);

heat link

kA

kAXscLCGTc = kANumLCGTc*scUX[kAUYoungLCGTc,kAURadLCGTc,kAUDiaLCGTc,kAURadiusLCGTc];
kAYscLCGTc = kANumLCGTc*scUY[kAUShearLCGTc,kAUDiaLCGTc,kAURadiusLCGTc];
kAZscLCGTc = kANumLCGTc*scUZ[kAUYoungLCGTc,kAURadLCGTc,kAUDiaLCGTc,kAURadiusLCGTc];

kB

kBXscLCGTc = kBNumLCGTc*scUZ[kBUYoungLCGTc,kBURadLCGTc,kBUDiaLCGTc,kBURadiusLCGTc];
kBYscLCGTc = kBNumLCGTc*scUY[kBUShearLCGTc,kBUDiaLCGTc,kBURadiusLCGTc];
kBZscLCGTc = kBNumLCGTc*scUX[kBUYoungLCGTc,kBURadLCGTc,kBUDiaLCGTc,kBURadiusLCGTc];

LogLogPlot[{kBXscLCGTc,kBYscLCGTc,kBZscLCGTc,g2HScLCGTc,g2VScLCGTc},{x,0.,7.2}]

kC

kCXscLCGTc = kCNumLCGTc*scUZ[kCUYoungLCGTc,kCURadLCGTc,kCUDiaLCGTc,kCURadiusLCGTc];
kCYscLCGTc = kCNumLCGTc*scUY[kCUShearLCGTc,kCUDiaLCGTc,kCURadiusLCGTc];
kCZscLCGTc = kCNumLCGTc*scUX[kCUYoungLCGTc,kCURadLCGTc,kCUDiaLCGTc,kCURadiusLCGTc];

k10

(*k10XLCGTc = kAXscLCGTc(1+ I kAPhiLCGTc);
k10YLCGTc = kAYscLCGTc(1+ I kAPhiLCGTc);
k10ZLCGTc = kAZscLCGTc(1+ I kAPhiLCGTc);

k10XThermalLCGTc = kAXscLCGTc(1+ tISCryoLCGTc I kAPhiLCGTc);
k10YThermalLCGTc = kAYscLCGTc(1+ tISCryoLCGTc I kAPhiLCGTc);
k10ZThermalLCGTc = kAZscLCGTc(1+ tISCryoLCGTc I kAPhiLCGTc);*)

k12

k12XLCGTc = kBXscLCGTc(1+ I kBPhiLCGTc);
k12YLCGTc = kBYscLCGTc(1+ I kBPhiLCGTc);
k12ZLCGTc = kBZscLCGTc(1+ I kBPhiLCGTc);

k12XThermalLCGTc = kBXscLCGTc(1+ m2TempLCGTc I kBPhiLCGTc);
k12YThermalLCGTc = kBYscLCGTc(1+ m2TempLCGTc I kBPhiLCGTc);
k12ZThermalLCGTc = kBZscLCGTc(1+ m2TempLCGTc I kBPhiLCGTc);

k21

k21XLCGTc = kBXscLCGTc(1+ I kBPhiLCGTc);
k21YLCGTc = kBYscLCGTc(1+ I kBPhiLCGTc);
k21ZLCGTc = kBZscLCGTc(1+ I kBPhiLCGTc);

k21XThermalLCGTc = kBXscLCGTc(1+ m2TempLCGTc I kBPhiLCGTc);
k21YThermalLCGTc = kBYscLCGTc(1+ m2TempLCGTc I kBPhiLCGTc);
k21ZThermalLCGTc = kBZscLCGTc(1+ m2TempLCGTc I kBPhiLCGTc);

k14

k14XLCGTc = kCXscLCGTc(1+ I kCPhiLCGTc);
k14YLCGTc = kCYscLCGTc(1+ I kCPhiLCGTc);
k14ZLCGTc = kCZscLCGTc(1+ I kCPhiLCGTc);

k14XThermalLCGTc = kCXscLCGTc(1+ m4TempLCGTc I kCPhiLCGTc);
k14YThermalLCGTc = kCYscLCGTc(1+ m4TempLCGTc I kCPhiLCGTc);
k14ZThermalLCGTc = kCZscLCGTc(1+ m4TempLCGTc I kCPhiLCGTc);

k41

k41XLCGTc = kCXscLCGTc(1+ I kCPhiLCGTc);
k41YLCGTc = kCYscLCGTc(1+ I kCPhiLCGTc);
k41ZLCGTc = kCZscLCGTc(1+ I kCPhiLCGTc);

k41XThermalLCGTc = kCXscLCGTc(1+ m4TempLCGTc I kCPhiLCGTc);
k41YThermalLCGTc = kCYscLCGTc(1+ m4TempLCGTc I kCPhiLCGTc);
k41ZThermalLCGTc = kCZscLCGTc(1+ m4TempLCGTc I kCPhiLCGTc);

k40

k40XLCGTc = kAXscLCGTc(1+ I kAPhiLCGTc);
k40YLCGTc = kAYscLCGTc(1+ I kAPhiLCGTc);
k40ZLCGTc = kAZscLCGTc(1+ I kAPhiLCGTc);

k40XThermalLCGTc = kAXscLCGTc(1+ tISCryoLCGTc I kAPhiLCGTc);
k40YThermalLCGTc = kAYscLCGTc(1+ tISCryoLCGTc I kAPhiLCGTc);
k40ZThermalLCGTc = kAZscLCGTc(1+ tISCryoLCGTc I kAPhiLCGTc);

parameter set for LCGTc pendulum

{f_,
m1_,m2_,m3_,m4_,m5_,
gh10_,gv10_,gh12_,gv12_,gh21_,gv21_,gh23_,gv23_,gh32_,gv32_,gh14_,gv14_,gh41_,gv41_,gh45_,gv45_,gh54_,gv54_,
hx12_,hy12_,hz12_,hx21_,hy21_,hz21_,hx14_,hy14_,hz14_,hx41_,hy41_,hz41_,hx40_,hy40_,hz40_}

{nItemLCGTc,f,
mass1LCGTc,mass2LCGTc,mass3LCGTc,mass4LCGTc,mass5LCGTc,
g10HLCGTc,g10VLCGTc,g12HLCGTc,g12VLCGTc,g21HLCGTc,g21VLCGTc,g23HLCGTc,g23VLCGTc,g32HLCGTc,g32VLCGTc,g14HLCGTc,g14VLCGTc,g41HLCGTc,g41VLCGTc,g25HLCGTc,g25VLCGTc,g52HLCGTc,g52VLCGTc,
k12XLCGTc,k12YLCGTc,k12ZLCGTc,k21XLCGTc,k21YLCGTc,k21ZLCGTc,k14XLCGTc,k14YLCGTc,k14ZLCGTc,k41XLCGTc,k41YLCGTc,k41ZLCGTc,k40XLCGTc,k40YLCGTc,k40ZLCGTc
}

{g12HLCGTc,g12VLCGTc,g23HLCGTc,g23VLCGTc,k12XLCGTc,k12YLCGTc,k12ZLCGTc}

{f,
mass1LCGTc,mass2LCGTc,mass3LCGTc,mass4LCGTc,mass5LCGTc,
g10HThermalLCGTc,g10VThermalLCGTc,g12HThermalLCGTc,g12VThermalLCGTc,g21HThermalLCGTc,g21VThermalLCGTc,g23HThermalLCGTc,g23VThermalLCGTc,g32HThermalLCGTc,g32VThermalLCGTc,g14HThermalLCGTc,g14VThermalLCGTc,g41HThermalLCGTc,g41VThermalLCGTc,g25HThermalLCGTc,g25VThermalLCGTc,g52HThermalLCGTc,g52VThermalLCGTc,
k12XThermalLCGTc,k12YThermalLCGTc,k12ZThermalLCGTc,k21XThermalLCGTc,k21YThermalLCGTc,k21ZThermalLCGTc,k14XThermalLCGTc,k14YThermalLCGTc,k14ZThermalLCGTc,k41XThermalLCGTc,k41YThermalLCGTc,k41ZThermalLCGTc,k40XThermalLCGTc,k40YThermalLCGTc,k40ZThermalLCGTc
}

calculation for LCGTc pendulum

trfLCGTc[ll_,nn_,jj_,f_]:=trfAmpLCGTc[ll,nn,jj,
nItemLCGTc,f,
mass1LCGTc,mass2LCGTc,mass3LCGTc,mass4LCGTc,mass5LCGTc,
g10HLCGTc,g10VLCGTc,g12HLCGTc,g12VLCGTc,g21HLCGTc,g21VLCGTc,g23HLCGTc,g23VLCGTc,g32HLCGTc,g32VLCGTc,g14HLCGTc,g14VLCGTc,g41HLCGTc,g41VLCGTc,g25HLCGTc,g25VLCGTc,g52HLCGTc,g52VLCGTc,
k12XLCGTc,k12YLCGTc,k12ZLCGTc,k21XLCGTc,k21YLCGTc,k21ZLCGTc,k14XLCGTc,k14YLCGTc,k14ZLCGTc,k41XLCGTc,k41YLCGTc,k41ZLCGTc,k40XLCGTc,k40YLCGTc,k40ZLCGTc
]

noiseSeisLCGTc[nn_,jj_,f_]:=Part[coupleMatLCGTc,jj].seisLCGTc[vibAmpLCGTc,nn,jj,
nItemLCGTc,f,
mass1LCGTc,mass2LCGTc,mass3LCGTc,mass4LCGTc,mass5LCGTc,
g10HLCGTc,g10VLCGTc,g12HLCGTc,g12VLCGTc,g21HLCGTc,g21VLCGTc,g23HLCGTc,g23VLCGTc,g32HLCGTc,g32VLCGTc,g14HLCGTc,g14VLCGTc,g41HLCGTc,g41VLCGTc,g25HLCGTc,g25VLCGTc,g52HLCGTc,g52VLCGTc,
k12XLCGTc,k12YLCGTc,k12ZLCGTc,k21XLCGTc,k21YLCGTc,k21ZLCGTc,k14XLCGTc,k14YLCGTc,k14ZLCGTc,k41XLCGTc,k41YLCGTc,k41ZLCGTc,k40XLCGTc,k40YLCGTc,k40ZLCGTc
]

noiseSeisCryoLCGTc[nn_,jj_,f_] :=Part[coupleMatLCGTc,jj].seisCryoLCGTc[vibAmpLCGTc,nn,jj,
nItemLCGTc,f,
mass1LCGTc,mass2LCGTc,mass3LCGTc,mass4LCGTc,mass5LCGTc,
g10HLCGTc,g10VLCGTc,g12HLCGTc,g12VLCGTc,g21HLCGTc,g21VLCGTc,g23HLCGTc,g23VLCGTc,g32HLCGTc,g32VLCGTc,g14HLCGTc,g14VLCGTc,g41HLCGTc,g41VLCGTc,g25HLCGTc,g25VLCGTc,g52HLCGTc,g52VLCGTc,
k12XLCGTc,k12YLCGTc,k12ZLCGTc,k21XLCGTc,k21YLCGTc,k21ZLCGTc,k14XLCGTc,k14YLCGTc,k14ZLCGTc,k41XLCGTc,k41YLCGTc,k41ZLCGTc,k40XLCGTc,k40YLCGTc,k40ZLCGTc
]

noiseSeisRoomLCGTc[nn_,jj_,f_] :=Part[coupleMatLCGTc,jj].seisRoomLCGTc[nn,jj,
nItemLCGTc,f,
mass1LCGTc,mass2LCGTc,mass3LCGTc,mass4LCGTc,mass5LCGTc,
g10HLCGTc,g10VLCGTc,g12HLCGTc,g12VLCGTc,g21HLCGTc,g21VLCGTc,g23HLCGTc,g23VLCGTc,g32HLCGTc,g32VLCGTc,g14HLCGTc,g14VLCGTc,g41HLCGTc,g41VLCGTc,g25HLCGTc,g25VLCGTc,g52HLCGTc,g52VLCGTc,
k12XLCGTc,k12YLCGTc,k12ZLCGTc,k21XLCGTc,k21YLCGTc,k21ZLCGTc,k14XLCGTc,k14YLCGTc,k14ZLCGTc,k41XLCGTc,k41YLCGTc,k41ZLCGTc,k40XLCGTc,k40YLCGTc,k40ZLCGTc
]

dispTNoiseLCGTc[ll_,nn_,f_]:=tNoiseLCGTc[ll,nn,
f,
mass1LCGTc,mass2LCGTc,mass3LCGTc,mass4LCGTc,mass5LCGTc,
g10HThermalLCGTc,g10VThermalLCGTc,g12HThermalLCGTc,g12VThermalLCGTc,g21HThermalLCGTc,g21VThermalLCGTc,g23HThermalLCGTc,g23VThermalLCGTc,g32HThermalLCGTc,g32VThermalLCGTc,g14HThermalLCGTc,g14VThermalLCGTc,g41HThermalLCGTc,g41VThermalLCGTc,g25HThermalLCGTc,g25VThermalLCGTc,g52HThermalLCGTc,g52VThermalLCGTc,
k12XThermalLCGTc,k12YThermalLCGTc,k12ZThermalLCGTc,k21XThermalLCGTc,k21YThermalLCGTc,k21ZThermalLCGTc,k14XThermalLCGTc,k14YThermalLCGTc,k14ZThermalLCGTc,k41XThermalLCGTc,k41YThermalLCGTc,k41ZThermalLCGTc,k40XThermalLCGTc,k40YThermalLCGTc,k40ZThermalLCGTc
]

(*noiseTNoiseLCGTc[ll_,nn_,jj_,f_] := {1}.coupleMatLCGTc[[jj]]*trfLCGTc[ll,nn,jj,f]*dispTNoiseLCGTc[ll,nn,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)*)

noiseTNoiseLCGTc[ll_,f_] :={1}. coupleMatTnoiseLCGTc[[ll]]*dispTNoiseLCGTc[ll,nItemLCGTc,f] (*noise in "jj" direction by fluctuation force in "ll" direction of "nn" mass.*)

seismic noise

noiseSeisSumLCGTc[f_] := Sqrt[Sum[Sum[noiseSeisLCGTc[nn,jj,f],{jj,1,3}]^2,{nn,1,3}]]

noiseSeisCryoSumLCGTc[f_] := Sqrt[Sum[Sum[noiseSeisCryoLCGTc[nn,jj,f],{jj,1,3}]^2,{nn,1,3}]]

noiseSeisRoomSumLCGTc[f_] := Sqrt[Sum[Sum[noiseSeisRoomLCGTc[nn,jj,f],{jj,1,3}]^2,{nn,1,3}]]

noiseSeisCompLCGTc[jj_,f_] := Sqrt[Sum[noiseSeisLCGTc[nn,jj,f]^2,{nn,1,3}]]

2*noiseSeisSumLCGTc[10]

noiseSeisCryoSumLCGTc[100]

noiseSeisRoomSumLCGTc[100]

suspension thermal noise (without violin mode)

(*noiseTNoiseSumLCGTc[f_] := Sqrt[Sum[Sum[Sum[noiseTNoiseLCGTc[ll,nn,jj,f],{jj,1,3}]^2,{ll,1,3}],{nn,1, nTotalLCGTc}]]*)

noiseTNoiseSumLCGTc[f_] := Sqrt[Sum[noiseTNoiseLCGTc[ll,f]^2,{ll,1,3}]]

noiseTNoiseCompDouble[jj_,f_] := Sqrt[Sum[Sum[noiseTNoiseLCGTc[ll,nn,jj,f]^2,{ll,1,3}],{nn,1, nTotalLCGTc}]] (*sum up of noise in "jj" direction*)

noiseTNoiseSumLCGTc[100]/l*2

dispLCGT[f_] := Sqrt[4*noiseSeisSumLCGTc[f]^2+4*noiseTNoiseSumLCGTc[f]^2+shotOriginal[f]^2+radiaOriginal[f]^2+dispThMass20[f]^2]

dispLCGT[10]

Q & resonant frequency

resLCGTc=f  /. NSolve[Det[matLCGTc[f,
mass1LCGTc,mass2LCGTc,mass3LCGTc,mass4LCGTc,mass5LCGTc,
g10HLCGTc,g10VLCGTc,g12HLCGTc,g12VLCGTc,g21HLCGTc,g21VLCGTc,g23HLCGTc,g23VLCGTc,g32HLCGTc,g32VLCGTc,g14HLCGTc,g14VLCGTc,g41HLCGTc,g41VLCGTc,g45HLCGTc,g45VLCGTc,g54HLCGTc,g54VLCGTc,
k10XLCGTc,k10YLCGTc,k10ZLCGTc,k12XLCGTc,k12YLCGTc,k12ZLCGTc,k21XLCGTc,k21YLCGTc,k21ZLCGTc,k14XLCGTc,k14YLCGTc,k14ZLCGTc,k41XLCGTc,k41YLCGTc,k41ZLCGTc]]==0,f];

Sort[resLCGTc/.Complex[x_,y_]->{Sqrt[x^2+y^2],Sqrt[x^2+y^2]/2/y}]//MatrixForm

Plots

SPI

listFreqSPI=Table[10^x,{x,-1.0,3.0,0.01}];

listDispSeis=Table[2 noiseSeisSumLCGTc[10^x],{x,-1,3,0.01}];

listDispPlotSeis =Table[{Part[listFreqSPI,i],Part[listDispSeis,i]},{i,Length[listFreqSPI]}];

listDispOriginalLCGT = Table[dispLCGToriginal[10^x],{x,-1,3,0.01}];

listDispLCGT = Table[dispLCGT[10^x],{x,-1,3,0.01}];

listDispPlotOriginalLCGT =Table[{Part[listFreqSPI,i],Part[listDispOriginalLCGT,i]},{i,Length[listFreqSPI]}];

listDispPlotLCGT =Table[{Part[listFreqSPI,i],Part[listDispLCGT,i]},{i,Length[listFreqSPI]}];

Export["~/Study/CurrentProject/LCGT/calculatedList/061016/freqNoSPI.dat",Take[listDispPlotSeis,All,{1}]];

Export["~/Study/CurrentProject/LCGT/calculatedList/061016/dispNoSPI.dat",Take[listDispPlotSeis,All,{2}]];

Export["~/Study/CurrentProject/LCGT/calculatedList/061016/freqOriginalLCGT.dat",Take[listDispPlotOriginalLCGT,All,{1}]];

Export["~/Study/CurrentProject/LCGT/calculatedList/061016/dispOrigianlLCGT.dat",Take[listDispPlotOriginalLCGT,All,{2}]];

Put[listFreqSPI,"~/Study/CurrentProject/LCGT/calculatedList/061016/listFreq.txt"]

Put[listDispSPI,"~/Study/CurrentProject/LCGT/listDispNoSPI.txt"]

Put[listDispSPI,"~/Study/CurrentProject/LCGT/listDispSPI.txt"]

listDispPlotSPI =Table[{Part[listFreqSPI,i],Part[listDispSPI,i]},{i,Length[listFreqSPI]}];

listDispPlotLCGT =Table[{Part[listFreqSPI,i],Part[listDispLCGT,i]},{i,Length[listFreqSPI]}];

Put[listDispLCGT,"~/Study/CurrentProject/LCGT/listDispLCGT.txt"]

plotNoSPI=ListLogLogPlot[listDispPlotLCGT,PlotStyle->{RGBColor[0,0,1]}]

plotSPI=ListLogLogPlot[listDispPlotSPI,PlotStyle->{RGBColor[1,0,0]}]

plotLCGT=ListLogLogPlot[listDispPlotLCGT,PlotStyle->{RGBColor[0,1,0]}]

plotCompeSPI = Show[plotSPI,plotNoSPI,plotLCGT]

Heat link diameter VS displacement noise with cryo-mgas

2*noiseSeisSumLCGTc[10]/l

2*noiseTNoiseSumLCGTc[10]/l

plotSeismgas =LogLogPlot[{ 2*noiseSeisSumLCGTc[10],2*noiseSeisCryoSumLCGTc[10],2*noiseSeisRoomSumLCGTc[10]},{x,0.1,7.2},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotThermal10Hz = LogLogPlot[{ 2*noiseTNoiseSumLCGTc[10]/l},{x,0.1,10}]

2*noiseTNoiseSumLCGTc[10]/l

Show[plotThermal10Hz,plotSeismgas,PlotRange -> All]

Heat link diameter VS displacement noise without cryo-mgas

plotSeisNmgas = LogLogPlot[{ 2*noiseSeisSumLCGTc[10],2*noiseSeisCryoSumLCGTc[10],2*noiseSeisRoomSumLCGTc[10]},{x,0.003,1},PlotRange -> All,PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotThermal10Hz = LogLogPlot[{ 2*noiseTNoiseSumLCGTc[10]},{x,0.1,10}]

Show[plotSeis10Hz,plotThermal10Hz,PlotRange -> All]

all components of seismic noise 10Hz cross

2*noiseSeisSumLCGTc[10]

plotSeis1LCGTc = LogLogPlot[{ 2*noiseSeisSumLCGTc[f],2*noiseSeisCryoSumLCGTc[f],2*noiseSeisRoomSumLCGTc[f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotSeis2LCGTc = LogLogPlot[{2*noiseSeisSumLCGTc[f],2*noiseSeisCryoSumLCGTc[f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis3LCGTc = LogLogPlot[{2*noiseSeisSumLCGTc[f],2*noiseSeisCryoSumLCGTc[f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

2*noiseSeisSumLCGTc[10]

plotSeisLCGTc=Show[plotSeis1LCGTc,plotSeis2LCGTc,plotLCGTmodel,PlotRange -> All]

plotSeis4LCGTc = LogLogPlot[2*noiseSeisSumLCGTc[f],{f,0.1,10},PlotStyle -> {RGBColor[1,0,0],Dashing[{0.01,0.01}]}]

plotSeis5LCGTc = LogLogPlot[2*noiseSeisSumLCGTc[f],{f,10,100},PlotStyle -> {RGBColor[1,0,0],Dashing[{0.01,0.01}]}]

plotSeis6LCGTc = LogLogPlot[2*noiseSeisSumLCGTc[f],{f,0.1,10},PlotStyle -> {RGBColor[0,1,0]}]

plotSeis7LCGTc = LogLogPlot[2*noiseSeisSumLCGTc[f],{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

plotSeisLCGTc=Show[plotSeis6LCGTc,plotSeis7LCGTc,plotLCGTmodel,plotSeis4LCGTc,plotSeis5LCGTc,PlotRange -> All]

all components of thermal noise 10Hz cross

plotTN1LCGTc =LogLogPlot[2*noiseTNoiseSumLCGTc[f]/l,{f,0.1,10},PlotStyle -> RGBColor[0,1,1]]

plotTN2LCGTc =LogLogPlot[2*noiseTNoiseSumLCGTc[f]/l,{f,10,100},PlotStyle -> RGBColor[0,1,1]]

plotTN3LCGTc =LogLogPlot[2*noiseTNoiseSumLCGTc[f]/l,{f,100,1000},PlotStyle -> RGBColor[0,1,1]]

plotTNLCGTc = Show[plotTN1LCGTc,plotTN2LCGTc,plotTN3LCGTc,PlotRange -> All]

Sqrt[pThermal[100,20,30,100,10^6]]*2/l/100

plotDummy=LogLogPlot[Sqrt[pThermal[f,20,30,120,10^6]]*2/l/100,{f,30,300}]

Show[plotSeisLCGTc,plotTNLCGTc,plotLCGTHmodel,plotDummy]

all components of seismic noise 3Hz cross

2*noiseSeisSumLCGTc[3]

plotSeis1001LCGTc = LogLogPlot[{ 2*noiseSeisSumLCGTc[f],2*noiseSeisCryoSumLCGTc[f],2*noiseSeisRoomSumLCGTc[f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0],RGBColor[0,0,1]}]

plotSeis1002LCGTc = LogLogPlot[{2*noiseSeisSumLCGTc[f],2*noiseSeisCryoSumLCGTc[f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis1003LCGTc = LogLogPlot[{2*noiseSeisSumLCGTc[f],2*noiseSeisCryoSumLCGTc[f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0],RGBColor[1,0,0]}]

plotSeis3HzLCGTc=Show[plotSeis1001LCGTc,plotSeis1002LCGTc,plotLCGTcmodel,PlotRange -> All]

all components of thermal noise 3Hz cross

plotTN1001LCGTc =LogLogPlot[2*noiseTNoiseSumLCGTc[f],{f,0.1,10},PlotStyle -> RGBColor[0,1,1]]

plotTN1002LCGTc =LogLogPlot[2*noiseTNoiseSumLCGTc[f],{f,10,100},PlotStyle -> RGBColor[0,1,1]]

plotTN1003LCGTc =LogLogPlot[2*noiseTNoiseSumLCGTc[f],{f,100,1000},PlotStyle -> RGBColor[0,1,1]]

plotTN3HzLCGTc = Show[plotTN1001LCGTc,plotTN1002LCGTc,plotTN1003LCGTc,PlotRange -> All]

Show[plotSeis3HzLCGTc,plotTNLCGTc,plotLCGTcmodel]

all components 2

plotSeis101LCGTc = LogLogPlot[2*noiseSeisSumLCGTc[f],{f,0.1,10},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis102LCGTc = LogLogPlot[2*noiseSeisSumLCGTc[f],{f,10,100},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeis103LCGTc = LogLogPlot[2*noiseSeisSumLCGTc[f],{f,100,1000},PlotStyle -> RGBColor[1,0.5,0.5]]

plotSeisLCGTc2=Show[plotSeis101LCGTc,plotSeis102LCGTc,plotSeis103LCGTc,PlotRange -> All]

plotTN101LCGTc =LogLogPlot[2*noiseTNoiseSumLCGTc[f],{f,0.1,10},PlotStyle -> RGBColor[0.5,0,1]]

plotTN102LCGTc =LogLogPlot[2*noiseTNoiseSumLCGTc[f],{f,10,100},PlotStyle -> RGBColor[0.5,0,1]]

plotTN103LCGTc =LogLogPlot[2*noiseTNoiseSumLCGTc[f],{f,100,1000},PlotStyle -> RGBColor[0.5,0,1]]

plotTNLCGTc2 = Show[plotTN101LCGTc,plotTN102LCGTc,plotTN103LCGTc,PlotRange -> All]

plotShotLCGTc102=LogLogPlot[shot[f],{f,10,1000},PlotStyle -> RGBColor[1,0,0.5]]

Show[plotTN102LCGTc,plotTN2LCGTc,plotCLIO25model]

Show[plotTN102LCGTc,plotSeis102LCGTc,plotTN2LCGTc,plotSeis2LCGTc,plotCLIOmodel]

Show[plotSeis102LCGTc,plotSeis2LCGTc,plotCLIOmodel]

Show[plotTN102LCGTc,plotTN2LCGTc,plotCLIOmodel]

Show[plotSeisLCGTc2,plotTNLCGTc2,plotCLIOmodel,plotShotLCGTc102]

Show[plotSeisLCGTc2,plotTNLCGTc2,plotCLIOmodel,plotShotLCGTc102,plotLISM030320]

Show[plotSeisLCGTc,plotTNLCGTc,plotSeisLCGTc2,plotTNLCGTc2,plotShotLCGTc102,plotCLIOmodel]

Show[plotSeisLCGTc,plotSeisLCGTc2,plotShotLCGTc102,plotCLIOmodel]

Show[plotTNLCGTc,plotTNLCGTc2,plotShotLCGTc102,plotCLIOmodel]

Show[plotShotLCGTc,plotShotLCGTc102,plotCLIOmodel]

seismic noise - each component

plot1= LogLogPlot[{noiseSeisLCGTc[1,1,f],noiseSeisLCGTc[2,2,f],noiseSeisLCGTc[3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

plot2=LogLogPlot[{noiseSeisLCGTc[1,1,f],noiseSeisLCGTc[2,2,f],noiseSeisLCGTc[3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

plot3=LogLogPlot[{noiseSeisLCGTc[1,1,f],noiseSeisLCGTc[2,2,f],noiseSeisLCGTc[3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

Show[plot1,plot2,plotLCGTmodel,PlotRange -> All]

LogLogPlot[{f,2f,3f},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0],RGBColor[0.5,0,1],RGBColor[0.5,1,0.5]}]

thermal noise - each component

plot11= LogLogPlot[{noiseTNoiseLCGTc[1,4,1,f],noiseTNoiseLCGTc[5,4,1,f],noiseTNoiseLCGTc[6,4,1,f],noiseTNoiseLCGTc[3,4,3,f],noiseTNoiseLCGTc[4,4,3,f],noiseTNoiseLCGTc[5,4,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot12= LogLogPlot[{noiseTNoiseLCGTc[1,4,1,f],noiseTNoiseLCGTc[5,4,1,f],noiseTNoiseLCGTc[6,4,1,f],noiseTNoiseLCGTc[3,4,3,f],noiseTNoiseLCGTc[4,4,3,f],noiseTNoiseLCGTc[5,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot13= LogLogPlot[{noiseTNoiseLCGTc[1,4,1,f],noiseTNoiseLCGTc[5,4,1,f],noiseTNoiseLCGTc[6,4,1,f],noiseTNoiseLCGTc[3,4,3,f],noiseTNoiseLCGTc[4,4,3,f],noiseTNoiseLCGTc[5,4,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNLCGTc,plot11,plot12,plot13,plotCLIOmodel]

Show[plot12,plotTNLCGTc,plotCLIOmodel]

plot21= LogLogPlot[{noiseTNoiseLCGTc[1,3,1,f],noiseTNoiseLCGTc[5,3,1,f],noiseTNoiseLCGTc[6,3,1,f],noiseTNoiseLCGTc[3,3,3,f],noiseTNoiseLCGTc[4,3,3,f],noiseTNoiseLCGTc[5,3,3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot22= LogLogPlot[{noiseTNoiseLCGTc[1,3,1,f],noiseTNoiseLCGTc[5,3,1,f],noiseTNoiseLCGTc[6,3,1,f],noiseTNoiseLCGTc[3,3,3,f],noiseTNoiseLCGTc[4,3,3,f],noiseTNoiseLCGTc[5,3,3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot23= LogLogPlot[{noiseTNoiseLCGTc[1,3,1,f],noiseTNoiseLCGTc[5,3,1,f],noiseTNoiseLCGTc[6,3,1,f],noiseTNoiseLCGTc[3,3,3,f],noiseTNoiseLCGTc[4,3,3,f],noiseTNoiseLCGTc[5,3,3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

Show[plotTNLCGTc,plot21,plot22,plot23,plotCLIOmodel]

Show[plot22,plotTNLCGTc,plotCLIOmodel]

Plot[{f,2 f,3 f,4 f,5 f,6 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[1,1,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[0.5,1,1]}]

plot24= LogLogPlot[{noiseTNoiseLCGTc[3,3,3,f],noiseTNoiseLCGTc[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

plot25= LogLogPlot[{noiseTNoiseLCGTc[3,3,3,f],noiseTNoiseLCGTc[3,4,3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0],RGBColor[0,0,1]}]

Show[plot24,plot24bc,plotCLIOmodel]

Show[plot25,plot24bc,plotCLIOmodel]

thermal noise - each direction

plot31= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1]}]

plot32= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1]}]

plot33= LogLogPlot[{noiseTNoiseCompDouble[1,f],noiseTNoiseCompDouble[2,f],noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1]}]

Show[plotTNLCGTc,plot31,plot32,plot33,plotCLIOmodel,PlotRange -> All]

plot34 =Show[plot32,plot33,PlotRange -> All]

Show[plot34,plotCLIOmodel,plotTN2LCGTc,plotTN3LCGTc]

Plot[{f,2 f,3 f,4 f,5 f},{f,1,10},PlotStyle -> {RGBColor[1,0,0.5],RGBColor[1,0.5,0.5],RGBColor[0.5,0,1],RGBColor[0.5,0.5,1],RGBColor[1,1,0.5]}]

thermal noise - each dissipation g4

plot41= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0,0.8]}]

plot42= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0,0.8]}]

plot43= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0,0.8]}]

Show[plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

Show[plotTNbcLCGTc,plot41,plot42,plot43,plotCLIOmodel,PlotRange -> All]

thermal noise - each dissipation g3

plot51= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[0,1,0.8]}]

plot52= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0.8]}]

plot53= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[0,1,0.8]}]

plot54= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[0,1,0]}]

Show[plotTNLCGTc,plot51,plot52,plot53,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plotTNLCGTc]

Show[plot54,plot52]

thermal noise - each dissipation magnet damping

plot61= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,0.1,10},PlotStyle -> {RGBColor[1,0.5,0]}]

plot62= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,10,100},PlotStyle -> {RGBColor[1,0.5,0]}]

plot63= LogLogPlot[{noiseTNoiseCompDouble[3,f]},{f,100,1000},PlotStyle -> {RGBColor[1,0.5,0]}]

Show[plotTNLCGTc,plot61,plot62,plot63,plotCLIOmodel,PlotRange -> All]

Show[plot52,plot42,plot62,plotTNLCGTc]