Code:

Restricted Three Body Problem

Plotting x,y,dx,dy

Import

import numpy as np from scipy.integrate import odeint import matplotlib.pyplot as plt

Variables

a,x,y,u,v,xdot,ydot,udot,vdot = var('a,x,y,u,v,xdot,ydot,udot,vdot')

Sun-Jupiter Ratio

Em = 317.83 Ms = 5.9736*10^24 Sm = Em/Ms b = Sm/(1+Sm)

Restricted Three Body Problem

def r3bp(a,x,y,t): a = b x = x[0] y = y[0] u = u[0] v = v[0] xdot = u ydot = v udot = -(1-a)((x-a)/(sqrt((x-a)^2 + y^2))^3)-a((x+1-a)/(sqrt((x+1-a)^2 + y^2))^3)+x+2v vdot = -(1-a)(y/(sqrt((x-a)^2 + y^2))^3)-a(y/(sqrt((x+1-a)^2 + y^2))^3)+y-2u return[xdot,ydot,udot,vdot]

Initial conditions

x0 = -0.509 y0 = 0.883 u0 = 0.0259 v0 = 0.0149 t = np.linspace(0,100,num=1000) x,y,u,v = odeint(r3bp,x0,y0,u0,v0,t)

Data

x = x[:,0] y = y[:,0] u = u[:,0] v = v[:,0]

Plot functions

px = plt.plot(t,x) py = plt.plot(t,y) pu = plt.plot(t,u) pv = plt.plot(t,v) plot.show(px) plot.show(py) plot.show(pu) plot.show(pv)

TypeError Traceback (most recent call last) <ipython-input-37-2a6a37bd25e9> in <module>() 34 u0 = RealNumber('0.0259') 35 v0 = RealNumber('0.0149') ---> 36 t = np.linspace(Integer(0),Integer(100),num=Integer(1000)) 37 x,y,u,v = odeint(r3bp,x0,y0,u0,v0,t) 38

/opt/sagemath-9.0/local/lib/python3.7/site-packages/numpy/core/function_base.py in linspace(start, stop, num, endpoint, retstep, dtype, axis) 136 stop = asanyarray(stop) * 1.0 137 --> 138 dt = result_type(start, stop, float(num)) 139 if dtype is None: 140 dtype = dt

TypeError: data type not understood

Code:The following code:

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-37-2a6a37bd25e9> in <module>()
     34 u0 = RealNumber('0.0259')
     35 v0 = RealNumber('0.0149')
---> 36 t = np.linspace(Integer(0),Integer(100),num=Integer(1000))
     37 x,y,u,v = odeint(r3bp,x0,y0,u0,v0,t)
     38 
 
 /opt/sagemath-9.0/local/lib/python3.7/site-packages/numpy/core/function_base.py in linspace(start, stop, num, endpoint, retstep, dtype, axis)
    136     stop  = asanyarray(stop)  * 1.0
    137 
--> 138     dt = result_type(start, stop, float(num))
    139     if dtype is None:
    140         dtype = dt
 
dt

TypeError: data type not understoodunderstood

The following code:

# Restricted Three Body Problem
# Plotting x,y,dx,dy

# Import
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt

# Variables
a,x,y,u,v,xdot,ydot,udot,vdot = var('a,x,y,u,v,xdot,ydot,udot,vdot')

# Sun-Jupiter Ratio
Em = 317.83
Ms = 5.9736*10^24
Sm = Em/Ms
b = Sm/(1+Sm)

# Restricted Three Body Problem
def r3bp(a,x,y,t):
  a = b
  x = x[0]
  y = y[0]
  u = u[0]
  v = v[0]
  xdot = u
  ydot = v
  udot = -(1-a)*((x-a)/(sqrt((x-a)^2 + y^2))^3)-a*((x+1-a)/(sqrt((x+1-a)^2 + y^2))^3)+x+2*v
  vdot = -(1-a)*(y/(sqrt((x-a)^2 + y^2))^3)-a*(y/(sqrt((x+1-a)^2 + y^2))^3)+y-2*u
  return[xdot,ydot,udot,vdot]

# Initial conditions
x0 = -0.509
y0 = 0.883
u0 = 0.0259
v0 = 0.0149
t = np.linspace(0,100,num=1000)
x,y,u,v = odeint(r3bp,x0,y0,u0,v0,t)

# Data
x = x[:,0]
y = y[:,0]
u = u[:,0]
v = v[:,0]

# Plot functions
px = plt.plot(t,x)
py = plt.plot(t,y)
pu = plt.plot(t,u)
pv = plt.plot(t,v)
plot.show(px)
plot.show(py)
plot.show(pu)
plot.show(pv)

produces the following error:

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-37-2a6a37bd25e9> in <module>()
     34 u0 = RealNumber('0.0259')
     35 v0 = RealNumber('0.0149')
---> 36 t = np.linspace(Integer(0),Integer(100),num=Integer(1000))
     37 x,y,u,v = odeint(r3bp,x0,y0,u0,v0,t)
     38 

/opt/sagemath-9.0/local/lib/python3.7/site-packages/numpy/core/function_base.py in linspace(start, stop, num, endpoint, retstep, dtype, axis)
    136     stop  = asanyarray(stop)  * 1.0
    137 
--> 138     dt = result_type(start, stop, float(num))
    139     if dtype is None:
    140         dtype = dt

TypeError: data type not understood