In [37]:

    

import scipy.integrate as integrate
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np

def derivativesFunction(inputstate, timespan):
    x, y, z, xdot, ydot, zdot = inputstate
    
    mu = 398600.0  # km^3/sec^2
    
    rmag = np.sqrt(x**2.0 + y**2.0 + z**2.0)
    
    #print 'rmag, inputstate', rmag, inputstate
    
    derivs = [xdot,
              ydot,
              zdot,
              -mu*x/rmag**3.0,
              -mu*y/rmag**3.0,
              -mu*z/rmag**3.0]
    
    #print 'derivs', derivs
    
    return derivs

timespan = np.linspace(0, 10800.0, 10800.0)  # start, stop, numpoints  # seconds

stateinit = [-3410.673, 5950.957, -1788.627, 1.893006, -1.071993, -7.176346]  # km and km/s

statesOverTime = integrate.odeint(derivativesFunction, stateinit, timespan)

x, y, z, xdot, ydot, zdot = statesOverTime.T

#print statesOverTime

#print timespan, x

# plt.plot(phi, u)
afig, ax = plt.subplots()
ax.plot(timespan, x)
#ax.plot(x, y, z)
#ax.set_aspect('equal')
plt.grid(True)
plt.show()


fig3D = plt.figure()
ax3D = fig3D.add_subplot(111, projection='3d')
ax3D.plot(x, y, z)
ax3D.set_aspect('equal')


    

In [5]:

    

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

pi = np.pi
sqrt = np.sqrt
cos = np.cos
sin = np.sin

def deriv_z(z, phi):
    u, udot = z
    return [udot, -u + sqrt(u)]

phi = np.linspace(0, 7.0*pi, 2000)

zinit = [1.49907, 0]

z = integrate.odeint(deriv_z, zinit, phi)

u, udot = z.T

# plt.plot(phi, u)
afig, ax = plt.subplots()
ax.plot(1/u*cos(phi), 1/u*sin(phi))
ax.set_aspect('equal')
plt.grid(True)
plt.show()


    

In [16]:

    

import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt

mpl.rcParams['legend.fontsize'] = 10

fig = plt.figure()
ax = fig.gca(projection='3d')
theta = np.linspace(-4 * np.pi, 4 * np.pi, 100)
z = np.linspace(-2, 2, 100)
r = z**2 + 1
x = r * np.sin(theta)
y = r * np.cos(theta)
ax.plot(x, y, z, label='parametric curve')
ax.legend()

plt.show()


    

In [5]:

    




    

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