.. _animation-double_pendulum_animated:

animation example code: double_pendulum_animated.py
===================================================

[`source code <double_pendulum_animated.py>`_]

::

    # Double pendulum formula translated from the C code at
    # http://www.physics.usyd.edu.au/~wheat/dpend_html/solve_dpend.c
    
    from numpy import sin, cos, pi, array
    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):
    
        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
    
    # create a time array from 0..100 sampled at 0.1 second steps
    dt = 0.05
    t = np.arange(0.0, 20, dt)
    
    # th1 and th2 are the initial angles (degrees)
    # w10 and w20 are the initial angular velocities (degrees per second)
    th1 = 120.0
    w1 = 0.0
    th2 = -10.0
    w2 = 0.0
    
    rad = pi/180
    
    # initial state
    state = np.array([th1, w1, th2, w2])*pi/180.
    
    # integrate your ODE using scipy.integrate.
    y = integrate.odeint(derivs, state, t)
    
    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]]
        thisy = [0, y1[i], y2[i]]
    
        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)
    
    #ani.save('double_pendulum.mp4', fps=15, clear_temp=True)
    plt.show()
    

Keywords: python, matplotlib, pylab, example, codex (see :ref:`how-to-search-examples`)