matplotlib & pandas

Python/matplotlab/gallery/animation/double_pendulum_sgskip.md

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+# 双摆问题
+
+这个动画说明了双摆问题。
+
+双摆公式从 http://www.physics.usyd.edu.au/~wheat/dpend_html/solve_dpend.c 的C代码翻译而来。 
+
+```python
+from numpy import sin, cos
+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 0.05 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
+
+# initial state
+state = np.radians([th1, w1, th2, w2])
+
+# 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.set_aspect('equal')
+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()
+```
+
+## 下载这个示例
+            
+- [下载python源码: double_pendulum_sgskip.py](https://matplotlib.org/_downloads/double_pendulum_sgskip.py)
+- [下载Jupyter notebook: double_pendulum_sgskip.ipynb](https://matplotlib.org/_downloads/double_pendulum_sgskip.ipynb)