create an animation and display it in iPython

iPythonAnim.py

## based on https://wakari.io/nb/url///wakari.io/static/notebooks/Lecture_4_Matplotlib.ipynb

## create double pendulum animation frames using matplotlib
from matplotlib import animation

from scipy.integrate import odeint


# solve the double pendulum motion
g = 9.82; L = 0.5; m = 0.1

def dx(x, t):
    x1, x2, x3, x4 = x[0], x[1], x[2], x[3]
    
    dx1 = 6.0/(m*L**2) * (2 * x3 - 3 * cos(x1-x2) * x4)/(16 - 9 * cos(x1-x2)**2)
    dx2 = 6.0/(m*L**2) * (8 * x4 - 3 * cos(x1-x2) * x3)/(16 - 9 * cos(x1-x2)**2)
    dx3 = -0.5 * m * L**2 * ( dx1 * dx2 * sin(x1-x2) + 3 * (g/L) * sin(x1))
    dx4 = -0.5 * m * L**2 * (-dx1 * dx2 * sin(x1-x2) + (g/L) * sin(x2))
    return [dx1, dx2, dx3, dx4]

x0 = [pi/2, pi/2, 0, 0]  # initial state
t = linspace(0, 10, 250) # time coordinates
x = odeint(dx, x0, t)    # solve the ODE problem


## animate the motion
fig, ax = plt.subplots(figsize=(5,5))

ax.set_ylim([-1.5, 0.5])
ax.set_xlim([1, -1])

pendulum1, = ax.plot([], [], color="red", lw=2)
pendulum2, = ax.plot([], [], color="blue", lw=2)

def init():
    pendulum1.set_data([], [])
    pendulum2.set_data([], [])

def update(n): 
    # n = frame counter
    # calculate the positions of the pendulums
    x1 = + L * sin(x[n, 0])
    y1 = - L * cos(x[n, 0])
    x2 = x1 + L * sin(x[n, 1])
    y2 = y1 - L * cos(x[n, 1])
    
    # update the line data
    pendulum1.set_data([0 ,x1], [0 ,y1])
    pendulum2.set_data([x1,x2], [y1,y2])

anim = animation.FuncAnimation(fig, update, init_func=init, frames=len(t), blit=True)

anim.save('animation.mp4', fps=20);

## and then display it
from IPython.display import HTML
video = open("animation.mp4", "rb").read()
video_encoded = video.encode("base64")
video_tag = '<video controls alt="test" src="data:video/x-m4v;base64,{0}">'.format(video_encoded)
HTML(video_tag)