1
1
Nilson123={{0.383972435,0.9340600},{0.41887902,0.8310000},{0.453785606,0.7447700},{0.488692191,0.6058400},{0.523598776,0.5309300},{0.558505361,0.4836000},{0.610865238,0.3308600},{0.698131701,0.1948600},{0.733038286,0.1418600},{0.785398163,0.0950760},{0.802851456,0.0689260},{0.837758041,0.0421590},{0.872664626,0.0219190},{0.872664626,0.0242300},{0.907571211,0.0092467},{0.959931089,0.0017368},{0.959931089,0.0019425},{1.047197551,0.0188800},{1.047197551,0.0192700},{1.134464014,0.0755400},{1.134464014,0.0692900},{1.221730476,0.1295000},{1.221730476,0.1435200},{1.308996939,0.2299500},{1.396263402,0.2972500},{1.483529864,0.3739100},{1.570796327,0.3994200},{1.745329252,0.3647600}}
2
2
k=7.6675*10^14,η=6.34963*10^-12,α0=0,α1=1.26993*10^-11,α2=1.90489*10^-11,α3=2.3282*10^-11,α4=2.64568*10^-11,P0=1.0,P2=1/2(-1+3Cos[θ^2),P4=1/8(3-30Cos[θ]^2+35Cos[θ]^4),Exp1=Exp[i*η*Log[(Csc[θ]/2])^2]],Exp2=Exp[i*η*Log[(Csc[[Pi]/2-θ/2])^2]]
3
3
y=Abs[(-η/(2k)*Csc[θ/2]^2*Exp1-η/(2k)*Csc[π/2-θ/2]^2*Exp2 +2/k*(Sin[δ0]*P0*Exp[I*(α0+δ0)]+5*Sin[δ2]*P2*Exp[I*(α2+δ2)]+9*Sin[δ4]*P4*Exp[I*(α4+δ4)]))]^2*10^28
4
4
FindFit[Nilson123,y,{δ0,δ2,δ4},θ]
5
5
{δ0->1.23497,δ2->0.381176,δ4->0.569623}
6
6
yFitValues=Abs[-η/(2k)Csc[θ/2]^2*Exp1-η/(2k)Csc[π/2-θ/2]^2*Exp2+2/k*(Sin[1.2349708950629241]*P0*Exp[I*(α0+1.2349708950629241)]+5*Sin[0.0×.3811763391934526]*P2*Exp[I*(α2+0.3811763391934526)]+9*Sin[0.5696227800485688]*P4*Exp[I*(α4+0.5696227800485688)])]^2*10^28
7
7
Show[ListPlot[Nilson123],Plot[yFitValues,{θ,0.1,1.8},PlotStyle->Orange]]
8
8
yManualValues=Abs[-(η/(2k))Csc[θ/2]^2*Exp1-(η/(2k))Csc[π/2-θ/2]^2*Exp2+2/k*(Sin[0.611]*P0*Exp[I*(α0+0.611)]+5*Sin[2]*P2*Exp[I*(α2+2)]+9*Sin[0.026]*P4*Exp[I*(α4+0.026)])]^2*10^28
9
9
Show[ListPlot[Nilson123],Plot[yManualValues,{θ,0.1,1.8},PlotStyle->Orange]]