added double pendulum examples and linked in whats new

jdh2358 · jdh2358 · commit aef53adc8776 · 2011-09-30T08:07:01.000-05:00
diff --git a/doc/users/whats_new.rst b/doc/users/whats_new.rst
@@ -30,12 +30,12 @@ Kevin Davies has extended Yannick Copin's original Sankey example into a module
 Animation
 ---------
 
-Ryan May has written a backend-independent
-framework for creating animated figures. The :mod:`~matplotlib.animation`
-module is intended to replace the
-backend-specific examples formerly in the :ref:`examples-index`
-listings.  Examples using the new framework are in
-:ref:`animation-examples-index`.
+Ryan May has written a backend-independent framework for creating
+animated figures. The :mod:`~matplotlib.animation` module is intended
+to replace the backend-specific examples formerly in the
+:ref:`examples-index` listings.  Examples using the new framework are
+in :ref:`animation-examples-index`; see the entrancing :ref:`double
+pendulum <animation-double_pendulum_animated>` in action.
 
 This should be considered as a beta release of the framework;
 please try it and provide feedback.
diff --git a/examples/animation/double_pendulum_animated.py b/examples/animation/double_pendulum_animated.py
@@ -0,0 +1,87 @@
+# 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)
+
+plt.show()
