# -*- coding: utf-8 -*-
import numpy as np
import scipy.integrate
import matplotlib.pyplot as plt
import matplotlib.animation as animation

w02 = 10
y0 = np.array([np.pi, 0])
frict = 0.5

# y' = f(y, t)
def f(y, t):
    # y[0] = angle, y[1] = vitesse angulaire
    # On renvoie : (vitesse, accélération)
    frottement = - frict * y[1]
    return np.array([y[1], -w02 * np.sin(y[0]) + frottement])

t = np.linspace(0, 100, 10000)
y = scipy.integrate.odeint(f, y0, t)

theta, thetadot = y[:, 0], y[:, 1]

fig = plt.figure()
ax = fig.add_subplot(111, autoscale_on=False,
            xlim=(-5, 5), ylim=(-5, 5))
ax.grid()

plt.title('Pendule : diagramme de phase')
plt.xlabel(r'$\theta$'); plt.ylabel(r"$\theta'$")

curves = plt.plot(theta, thetadot)

def animate(i):
    global frict
    frict = i / float(200)
    y = scipy.integrate.odeint(f, y0, t)
    theta, thetadot = y[:, 0], y[:, 1]
    plt.title('Pendule : diagramme de phase (frict = ' + str(frict) + ')')
    curves[0].set_data(theta, thetadot)

ani = animation.FuncAnimation(fig, animate, interval=10)

plt.show()