Chris's Python Script (Simulation of Double Pendulum)

from numpy import sin, cos
import numpy as np
import matplotlib.pyplot as plt
import scipy.integrate as integrate
import matplotlib.animation as animation

G = 9.8  # acceleration due to gravity, in m/s^2
L1 = 1.0  # length of pendulum 1 in m
L2 = 1.0  # length of pendulum 2 in m
M1 = 1.0  # mass of pendulum 1 in kg
M2 = 1.0  # mass of pendulum 2 in kg

def derivs(state, t): # dynamics of system
    dydx = np.zeros_like(state)
    dydx[0] = state[1]
    del_ = state[2] - state[0]
    den1 = (M1 + M2)*L1 - M2*L1*cos(del_)*cos(del_)
    dydx[1] = (M2*L1*state[1]*state[1]*sin(del_)*cos(del_) +                  M2*G*sin(state[2])*cos(del_) +
              M2*L2*state[3]*state[3]*sin(del_) - (M1 +  M2)*G*sin(state[0]))/den1
    dydx[2] = state[3]
    den2 = (L2/L1)*den1
    dydx[3] = (-M2*L2*state[3]*state[3]*sin(del_)*cos(del_) + (M1 + M2)*G*sin(state[0])*cos(del_) -
               (M1 + M2)*L1*state[1]*state[1]*sin(del_) - (M1 + M2)*G*sin(state[2]))/den2

    return dydx

dt = 0.05
t = np.arange(0.0, 20, dt)

th1 = 90.0
w1 = 0.0
th2 = 0.0
w2 = 0.0

state = np.radians([th1, w1, th2, w2]) # initial state
y = integrate.odeint(derivs, state, t) # integrate  ODE using scipy.integrate.

x1 = L1*sin(y[:, 0])
y1 = -L1*cos(y[:, 0])

x2 = L2*sin(y[:, 2]) + x1
y2 = -L2*cos(y[:, 2]) + y1

fig = plt.figure()
ax = fig.add_subplot(111, autoscale_on=False, xlim=(-2, 2), ylim=(-2, 2))
ax.grid()

line, = ax.plot([], [], 'o-', lw=2)
time_template = 'time = %.1fs'
time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes)

def init():
    line.set_data([], [])
    time_text.set_text('')

    return line, time_text

def animate(i):
    thisx = [0, x1[i], x2[i]]  # x codrin of point making pendulum
    thisy = [0, y1[i], y2[i]]  # y cord of point
    line.set_data(thisx, thisy)
    time_text.set_text(time_template % (i*dt))

    return line, time_text

ani = animation.FuncAnimation(fig, animate, np.arange(1, len(y)),interval=25, blit=True, init_func=init)

plt.show()