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Copy pathpendulum_ode.py
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executable file
·188 lines (171 loc) · 7.65 KB
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#!/usr/bin/env python
import numpy as np
from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt
from matplotlib import animation
class PhaseSpaceAnim(object):
def __init__(self, figure, times, theta, omega, skip):
self._figure = figure
axes = figure.add_axes([0.1, 0.1, 0.8, 0.8])
axes.set_xlim(np.min(thetas), np.max(thetas))
axes.set_ylim(np.min(omegas), np.max(omegas))
axes.set_xlabel(r'$\theta$')
axes.set_ylabel(r'$\omega$')
self._line, = axes.plot([], [])
self._times = times
self._thetas = thetas
self._omegas = omegas
self._skip = skip
def create_init(self):
def init():
self._line.set_data([], [])
# self._figure.text(0.5, 0.9, r't = 0.000')
return self._line
return init
def create_animate(self):
def animate(i):
t = i*self._skip
self._line.set_data(self._thetas[:t], self._omegas[:t])
# self._figure.text(0.5, 0.9, r't = {0:.3f}'.format(t))
return self._line
return animate
def func(t, y, g, l, q, F_d, omega_d, phase_d, anharmonic):
theta, omega = y
if anharmonic:
return (
omega,
-(g/l)*np.sin(theta) - q*omega + F_d*np.sin(omega_d*t + phase_d)
)
return (
omega,
-(g/l)*theta - q*omega + F_d*np.sin(omega_d*t + phase_d)
)
def solve(func, t0=0.0, t_max=20.0, delta_t=0.01,
theta0=0.1, omega0=0.0, params={'g': 9.81, 'l': 9.81,
'q': 0.05, 'F_d': 0.0,
'omega_d': 0.5, 'phase_d': 0.0,
'anharmonic': False},
atol=1.0e-6, rtol=1.0e-6):
times = np.arange(t0, t_max, delta_t)
solution = solve_ivp(
func,
t_span=(t0, t_max),
y0=(theta0, omega0),
t_eval=times,
args=(params['g'], params['l'], params['q'],
params['F_d'], params['omega_d'],
params['phase_d'], params['anharmonic']),
method='RK45',
atol=atol,
rtol=rtol
)
if not solution.success:
raise RuntimeError(solution.message)
thetas = (solution.y[0] + np.pi) % (2.0*np.pi) - np.pi
return solution.t, thetas, solution.y[1]
def sample_poincare(times, thetas, omegas, omega_d, prec=1.0e-4):
p_times = []
p_thetas = []
p_omegas = []
cutoff = omega_d*prec/(4.0*np.pi)
for time, theta, omega in zip(times, thetas, omegas):
delta = omega_d*time/(2.0*np.pi)
if min(delta - np.floor(delta), np.ceil(delta) - delta) < cutoff:
p_times.append(time)
p_thetas.append(theta)
p_omegas.append(omega)
return np.array(p_times), np.array(p_thetas), np.array(p_omegas)
def plot_solution(times, thetas, omegas):
plt.subplot(3, 1, 1)
plt.plot(times, thetas, ',')
plt.subplot(3, 1, 2)
plt.plot(times, omegas, ',')
plt.subplot(3, 1, 3)
plt.plot(thetas, omegas, ',')
def animate_solution(mp4_file, times, thetas, omegas, skip):
figure = plt.figure()
thetaAnim = PhaseSpaceAnim(figure, times, thetas, omegas, skip)
init_f = thetaAnim.create_init()
anim_f = thetaAnim.create_animate()
anim = animation.FuncAnimation(figure, anim_f, init_func=init_f,
frames=len(times)//skip, interval=1,
blit=True)
anim.save(mp4_file, fps=15, writer=animation.AVConvFileWriter())
if __name__ == '__main__':
from argparse import ArgumentParser
arg_parser = ArgumentParser(description='solve ODE for a harmonic '
'damped pendulum')
arg_parser.add_argument('--l', type=float, default=9.81,
help='length of pendulum [m]')
arg_parser.add_argument('--g', type=float, default=9.81,
help='gravitational acceleration [rad/s**2]')
arg_parser.add_argument('--q', type=float, default=0.05,
help='damping factor [1/s]')
arg_parser.add_argument('--F_d', type=float, default=0.0,
help='amplitude of driving force')
arg_parser.add_argument('--omega_d', type=float, default=1.0,
help='frquency of driving force')
arg_parser.add_argument('--phase_d', type=float, default=0.0,
help='phase of driving force')
arg_parser.add_argument('--anharmonic', action='store_true',
help='do noet use harmonic approximation')
arg_parser.add_argument('--theta0', type=float, default=0.05,
help='initial theta value [rad]')
arg_parser.add_argument('--omega0', type=float, default=0.0,
help='initial omega value [rad/s]')
arg_parser.add_argument('--t0', type=float, default=0.0,
help='initial time value [s]')
arg_parser.add_argument('--t_max', type=float, default=10.0*2.0*np.pi,
help='maximum time value [s]')
arg_parser.add_argument('--delta_t', type=float, default=0.01,
help='time step [s]')
arg_parser.add_argument('--atol', type=float, default=1.0e-10,
help='absolute tolerance of integrator')
arg_parser.add_argument('--rtol', type=float, default=1.0e-10,
help='relative tolerance of integrator')
arg_parser.add_argument('--output', action='store_true',
help='write solutions to standrad output')
arg_parser.add_argument('--plot', action='store_true',
help='make plot')
arg_parser.add_argument('--poincare', action='store_true',
help='plot or print Poincare section')
arg_parser.add_argument('--only', action='store_true',
help='plot only Poincare section')
arg_parser.add_argument('--mp4', help='create MP4 animated plot')
arg_parser.add_argument('--skip', type=int, default=5,
help='number of skip points for animation')
options = arg_parser.parse_args()
times, thetas, omegas = solve(
func=func,
t0=options.t0, t_max=options.t_max, delta_t=options.delta_t,
theta0=options.theta0, omega0=options.omega0,
params={'g': options.g, 'l': options.l, 'q': options.q,
'F_d': options.F_d, 'omega_d': options.omega_d,
'phase_d': options.phase_d,
'anharmonic': options.anharmonic},
atol=options.atol, rtol=options.rtol
)
if options.poincare:
p_times, p_thetas, p_omegas = sample_poincare(
times=times, thetas=thetas, omegas=omegas,
omega_d=options.omega_d
)
if options.output:
if options.poincare:
for time, theta, omega in zip(p_times, p_thetas, p_omegas):
print('{0:.3f}\t{1:.10f}\t{2:.10f}'.format(time, theta,
omega))
else:
for time, theta, omega in zip(times, thetas, omegas):
print('{0:.3f}\t{1:.10f}\t{2:.10f}'.format(time, theta,
omega))
if options.plot:
if options.only:
plt.plot(p_thetas, p_omegas, '.')
else:
plot_solution(times, thetas, omegas)
if options.poincare:
plt.plot(p_thetas, p_omegas, 'r.')
plt.show()
if options.mp4:
animate_solution(options.mp4, times, thetas, omegas, options.skip)