In [48]:

    

# 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


    

In [49]:

    

import pickle
arquivo = open("../xyz", "r")

X = pickle.loads(arquivo.read())
print X.shape

joelho = X[0,:,:].T
trocanter = X[1,:,:].T
tibia = X[2,:,:].T

x_min = np.min(np.array([joelho[:, 0], trocanter[:, 0], tibia[:, 0]]))
x_max = np.max(np.array([joelho[:, 0], trocanter[:, 0], tibia[:, 0]]))

y_min = np.min(np.array([joelho[:, 1], trocanter[:, 1], tibia[:, 1]]))
y_max = np.max(np.array([joelho[:, 1], trocanter[:, 1], tibia[:, 1]]))

z_min = np.min(np.array([joelho[:, 2], trocanter[:, 2], tibia[:, 2]]))
z_max = np.max(np.array([joelho[:, 2], trocanter[:, 2], tibia[:, 2]]))

print joelho.shape


    

    




(3, 3, 66)
(66, 3)

In [50]:

    

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


    

In [51]:

    

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


    

In [52]:

    

# 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

rad = pi/180


    

In [53]:

    

# 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=(x_min, x_max), ylim=(z_min, z_max))
ax.grid()

line, = ax.plot([], [], 'o-', lw=2)
time_template = 'time = %.1fs'
time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes)


    

In [ ]:

    

def init():
    line.set_data([], [])
    time_text.set_text('')
    return line, time_text

def animate(i):
    thisx = [trocanter[i, 0], joelho[i, 0], tibia[i, 0]]
    thisy = [trocanter[i, 2], joelho[i, 1], tibia[i, 2]]

    line.set_data(thisx, thisy)
    
    return line, time_text

ani = animation.FuncAnimation(fig, animate, np.arange(1, 66),
    interval=25, blit=False, init_func=init)

#ani.save('double_pendulum.mp4', fps=15)
plt.show()


    

In [ ]: