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06_pend.py
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06_pend.py
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#!/usr/bin/ python3
# -*- coding: utf-8 -*-
'''
Solution to pendulum exercise:
\dot{x} = y
\dot{y} = -\sin x
'''
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.integrate import odeint
def rhs_pend (y, t):
""" RHS equations for the pendulum system """
# Unpack both coordinates
X, Y = y
# Derivatives
dydt = [
Y,
np.sin(X)
]
return dydt
def integrate (y0, t, rhs_fun):
""" Given an initial condition x0 and a time vector structure, integrates
the system described by rhs_fun(y, t)i. Returns the solution array """
sol, info = odeint(rhs_fun, y0, t, full_output = True)
return sol
# Define a set of initial conditions
tp = np.linspace(0, 5, 50)
tn = np.linspace(0, -5, 50)
X, Y = np.meshgrid(np.linspace(-8, 8, 9), np.linspace(-3, 3, 9))
plt.figure()
for y0 in zip(X.ravel(), Y.ravel()):
solp = integrate(y0, tp, rhs_pend)
soln = integrate(y0, tn, rhs_pend)
plt.plot(solp[:, 0], solp[:, 1], 'k--')
plt.plot(soln[:, 0], soln[:, 1], 'k--')
plt.xlim([-8,8])
plt.ylim([-3,3])
plt.show()