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Q3
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Q3
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import numpy as np
import math
import matplotlib.pyplot as plt
from scipy.integrate import solve_ivp
miu = 3.003480575402412*10**(-6)
L1 = 0.990026593891877
alpha = 0.001
r1 = L1 + miu
r2 = -(L1 - 1 + miu)
c2 = (1 - miu) / (r1**3) + miu / (r2**3)
omega0 = pow((- c2 + 2 + pow(9 * c2**2 - 8*c2, 0.5))/2,0.5)
K = - 0.5 * (omega0 + (1+ 2*c2)/omega0)
x1 = L1 + alpha
x2 = 0
x3 = 0
x4 = 0
x5 = K * alpha * omega0
x6 = 0
def fun(t, y):
ydot = np.empty((42,))
ydot[:] = np.nan
rr1 = np.sqrt((y[0]+miu)**2 + y[1]**2 +y[2]**2)
rr2 = np.sqrt((y[0]+miu-1)**2 + y[1]**2 +y[2]**2)
ydot[0] = y[3]
ydot[1] = y[4]
ydot[2] = y[5]
ydot[3] = y[0]+2*y[4]-((1-miu)*(y[0]+miu))/(rr1**3)-(miu*(y[0]+miu-1))/(rr2**3)
ydot[4] = y[1]-2*y[3]-((1-miu)*y[1])/(rr1**3)-(miu*y[1])/(rr2**3)
ydot[5] = -((1-miu)*y[2])/(rr1**3)-(miu*y[2])/(rr2**3)
aa = (1 - (1-miu)/rr1**3 + (3*(y[0]+miu)**2*(1-miu))/rr1**5 -miu/rr2**3 +(3*miu*(y[0]+miu-1)**2)/rr2**5)
bb = (3*(1-miu)*(y[0]+miu)*y[1]/rr1**5 + 3*miu*y[1]*(y[0]+miu-1)/rr2**5)
cc = (3*(1-miu)*(y[0]+miu)*y[2]/rr1**5 + 3*miu*y[2]*(y[0]+miu-1)/rr2**5)
dd = (3*(1-miu)*(y[0]+miu)*y[1]/rr1**5 + 3*miu*(y[0]+miu-1)*y[1]/rr2**5)
ee = (1-(1-miu)/rr1**3+3*(1-miu)*y[1]**2/rr1**5 -miu/rr2**3+3*miu*y[1]**2/rr2**5)
ff = (3*(1-miu)*y[1]*y[2]/rr1**5 + 3*miu*y[1]*y[2]/rr2**5)
gg = ((3*y[2]*(1-miu)*(y[0]+miu))/(rr1**5) + (3*y[2]*miu*(y[0]+miu-1))/(rr2**5))
hh = ((3*y[2]*(1-miu)*y[1])/(rr1**5) + (3*y[2]*miu*y[1])/(rr2**5))
ii = (-(1-miu)/rr1**3 + 3*(1-miu)*y[2]**2/rr1**5-miu/rr2**3+3*miu*y[2]**2/rr2**5)
ydot[6] = y[24]
ydot[7] = y[25]
ydot[8] = y[26]
ydot[9] = y[27]
ydot[10] = y[28]
ydot[11] = y[29]
ydot[12] = y[30]
ydot[13] = y[31]
ydot[14] = y[32]
ydot[15] = y[33]
ydot[16] = y[34]
ydot[17] = y[35]
ydot[18] = y[36]
ydot[19] = y[37]
ydot[20] = y[38]
ydot[21] = y[39]
ydot[22] = y[40]
ydot[23] = y[41]
ydot[24] = aa*y[6]+bb*y[12]+cc*y[18]+2*y[30]
ydot[25] = aa*y[7]+bb*y[13]+cc*y[19]+2*y[31]
ydot[26] = aa*y[8]+bb*y[14]+cc*y[20]+2*y[32]
ydot[27] = aa*y[9]+bb*y[15]+cc*y[21]+2*y[33]
ydot[28] = aa*y[10]+bb*y[16]+cc*y[22]+2*y[34]
ydot[29] = aa*y[11]+bb*y[17]+cc*y[23]+2*y[35]
ydot[30] = dd*y[6]+ee*y[12]+ff*y[18]-2*y[24]
ydot[31] = dd*y[7]+ee*y[13]+ff*y[19]-2*y[25]
ydot[32] = dd*y[8]+ee*y[14]+ff*y[20]-2*y[26]
ydot[33] = dd*y[9]+ee*y[15]+ff*y[21]-2*y[27]
ydot[34] = dd*y[10]+ee*y[16]+ff*y[22]-2*y[28]
ydot[35] = dd*y[11]+ee*y[17]+ff*y[23]-2*y[29]
ydot[36] = gg*y[6]+ hh*y[12]+ ii*y[18]
ydot[37] = gg*y[7]+ hh*y[13]+ ii*y[19]
ydot[38] = gg*y[8]+ hh*y[14]+ ii*y[20]
ydot[39] = gg*y[9]+ hh*y[15]+ ii*y[21]
ydot[40] = gg*y[10]+hh*y[16]+ ii*y[22]
ydot[41] = gg*y[11]+hh*y[17]+ ii*y[23]
return ydot
def changeX(y0,tt):
t_span = (0, tt)
t_eval = np.linspace(t_span[0], t_span[1], 1000)
sol_rk = solve_ivp(fun, t_span, y0, method='DOP853', t_eval=t_eval)
xx = sol_rk.y[0][999]
yy = sol_rk.y[1][999]
zz = sol_rk.y[2][999]
xf = sol_rk.y[3][999]
yf = sol_rk.y[4][999]
zf = sol_rk.y[5][999]
rr1 = np.sqrt((xx+miu)**2 + yy**2 +zz**2)
rr2 = np.sqrt((xx+miu-1)**2 + yy**2 +zz**2)
x_n = np.array([y0[0] - xx, y0[1] - yy])
CX = np.array([[sol_rk.y[10][999], xf],
[sol_rk.y[16][999], yf]])
x_det = np.dot(np.linalg.inv(CX),x_n) #积分后的差值
orbit = sol_rk.y
#plt.plot(orbit[0], orbit[1])
#plt.show()
return x_det,orbit
def main():
x_c = [x1,x2,x3,x4,x5,x6,\
1,0,0,0,0,0,\
0,1,0,0,0,0,\
0,0,1,0,0,0,\
0,0,0,1,0,0,\
0,0,0,0,1,0,\
0,0,0,0,0,1]
x_x = np.empty((3,))
x_x[:] = 0.1
tt = 2*np.pi/omega0
while np.linalg.norm(x_x) > 10**(-12):
x_det,orbit = changeX(x_c,tt)
x_x = x_det
x_c[4] = x_c[4]+x_det[0]/(1+10*np.linalg.norm(x_x))
tt = tt+x_det[1]/(1+10*np.linalg.norm(x_x))
plt.plot(orbit[0], orbit[1])
plt.show()
for i in range(0,6):
print(orbit[i][999])
print(tt)
print(orbit[6][999],orbit[7][999], orbit[8][999], orbit[9][999], orbit[10][999],orbit[11][999])
print(orbit[12][999],orbit[13][999],orbit[14][999],orbit[15][999],orbit[16][999],orbit[17][999])
print(orbit[18][999],orbit[19][999],orbit[20][999],orbit[21][999],orbit[22][999],orbit[23][999])
print(orbit[24][999],orbit[25][999],orbit[26][999],orbit[27][999],orbit[28][999],orbit[29][999])
print(orbit[30][999],orbit[31][999],orbit[32][999],orbit[33][999],orbit[34][999],orbit[35][999])
print(orbit[36][999],orbit[37][999],orbit[38][999],orbit[39][999],orbit[40][999],orbit[41][999])
if __name__ == '__main__':
main()