:orphan: double_pendulum --------------- Animation of a double pendulum .. raw:: html ---- .. code-block:: python import numpy as np import time import gr try: from time import perf_counter except ImportError: from time import clock as perf_counter g = 9.8 # gravitational constant def rk4(x, h, y, f): k1 = h * f(x, y) k2 = h * f(x + 0.5 * h, y + 0.5 * k1) k3 = h * f(x + 0.5 * h, y + 0.5 * k2) k4 = h * f(x + h, y + k3) return x + h, y + (k1 + 2 * (k2 + k3) + k4) / 6.0 def pendulum_derivs(t, state): # The following derivation is from: # http://scienceworld.wolfram.com/physics/DoublePendulum.html t1, w1, t2, w2 = state a = (m1 + m2) * l1 b = m2 * l2 * np.cos(t1 - t2) c = m2 * l1 * np.cos(t1 - t2) d = m2 * l2 e = -m2 * l2 * w2**2 * np.sin(t1 - t2) - g * (m1 + m2) * np.sin(t1) f = m2 * l1 * w1**2 * np.sin(t1 - t2) - m2 * g * np.sin(t2) return np.array([w1, (e*d-b*f) / (a*d-c*b), w2, (a*f-c*e) / (a*d-c*b)]) def pendulum(theta, length, mass): l = length[0] + length[1] gr.clearws() gr.setviewport(0, 1, 0, 1) gr.setwindow(-l, l, -l, l) gr.setmarkertype(gr.MARKERTYPE_SOLID_CIRCLE) gr.setmarkercolorind(86) pivot = [0, 0.775] # draw pivot point gr.fillarea([-0.2, 0.2, 0.2, -0.2], [0.75, 0.75, 0.8, 0.8]) for i in range(2): x = [pivot[0], pivot[0] + np.sin(theta[i]) * length[i]] y = [pivot[1], pivot[1] - np.cos(theta[i]) * length[i]] gr.polyline(x, y) # draw rod gr.setmarkersize(3 * mass[i]) gr.polymarker([x[1]], [y[1]]) # draw bob pivot = [x[1], y[1]] gr.updatews() return l1 = 1.2 # length of rods l2 = 1.0 m1 = 1.0 # weights of bobs m2 = 1.5 t1 = 100.0 # inintial angles t2 = -20.0 w1 = 0.0 w2 = 0.0 t = 0 dt = 0.04 state = np.radians([t1, w1, t2, w2]) now = perf_counter() while t < 30: start = now t, state = rk4(t, dt, state, pendulum_derivs) t1, w1, t2, w2 = state pendulum([t1, t2], [l1, l2], [m1, m2]) now = perf_counter() if start + dt > now: time.sleep(start + dt - now)