from dyna import forced_pendulum
omega = 2./3
dt = 2*np.pi / omega / 25
tf = 1000
acc_factors = np.linspace(1, 1.5, 100)
fft_sig = []
t = np.arange(0, tf, dt)
mask = t > 400
hann = signal.hanning(mask.sum())
for i, acc in enumerate(acc_factors):
print i
t, theta, theta_dot = forced_pendulum(tf, dt, np.pi/3, 0,
q=0.5, acc=acc, omega=omega)
theta = theta[mask]
theta -= theta.mean()
theta /= np.sqrt((theta**2).mean())
theta *= hann
fft_sig.append(fftpack.fft(theta))
fft_sig = np.array(fft_sig)
np.save('fft_sig.npy', fft_sig)
import numpy as np
import matplotlib.pyplot as plt
from scipy import fftpack
from scipy import signal
from dyna import forced_pendulum
omega = 2.0 / 3
dt = 2 * np.pi / omega / 25
tf = 1000
acc = 1.17
eps = 1.0e-8
all_theta_signals = []
t, theta_0, theta_dot_0 = forced_pendulum(tf, dt, np.pi / 3, 0, q=0.5, acc=acc, omega=omega)
t, theta_1, theta_dot_1 = forced_pendulum(tf, dt, (1 + eps) * np.pi / 3, 0, q=0.5, acc=acc, omega=omega)
# Compute the distance between the two trajectories
dist = np.hypot(theta_1 - theta_0, theta_dot_1 - theta_dot_1)
plt.figure(figsize=(6, 4))
plt.semilogy(t, dist, lw=2)
plt.xlim(0, 400)
plt.xlabel(u"$t$", fontsize=22)
plt.ylabel("distance", fontsize=22)
plt.tight_layout()
plt.show()
import numpy as np
import matplotlib.pyplot as plt
from scipy import fftpack
from scipy import signal
from dyna import forced_pendulum
omega = 2./3
dt = 2*np.pi / omega / 25
tf = 1000
acc = 1.17
eps = 1.e-8
all_theta_signals = []
t, theta_0, theta_dot_0 = forced_pendulum(tf, dt, np.pi/3, 0,
q=0.5, acc=acc, omega=omega)
t, theta_1, theta_dot_1 = forced_pendulum(tf, dt, (1 + eps) * np.pi/3, 0,
q=0.5, acc=acc, omega=omega)
# Compute the distance between the two trajectories
dist = np.hypot(theta_1 - theta_0, theta_dot_1 - theta_dot_1)
plt.figure(figsize=(6, 4))
plt.semilogy(t, dist, lw=2)
plt.xlim(0, 400)
plt.xlabel(u'$t$', fontsize=22)
plt.ylabel('distance', fontsize=22)
plt.tight_layout()
plt.show()
omega = 2. / 3
dt = 2 * np.pi / omega / 25
tf = 1000
acc_factors = np.linspace(1, 1.5, 100)
acc_factors = acc_factors[[2, 15, 34]]
all_theta_signals = []
for i, acc in enumerate(acc_factors):
t, theta, theta_dot = forced_pendulum(tf,
dt,
np.pi / 3,
0,
q=0.5,
acc=acc,
omega=omega)
all_theta_signals.append(theta)
all_theta_signals = np.array(all_theta_signals)
mask = t > 400
theta_signals = all_theta_signals[:, mask]
theta_signals -= theta_signals.mean(axis=1)[:, np.newaxis]
theta_signals /= np.sqrt((theta_signals**2).mean(axis=1))[:, np.newaxis]
hann = signal.hanning(theta_signals.shape[1])
theta_signals *= hann
from mpl_toolkits.mplot3d import Axes3D
from dyna import forced_pendulum
fig = plt.figure()
ax = fig.gca(projection='3d')
omega = 2. / 3
dt = 2 * np.pi / omega / 100
tf = 10000
t, theta, theta_dot = forced_pendulum(1000,
dt,
np.pi / 3,
0,
q=0.5,
acc=1.07,
omega=omega)
mask = t > 400
ax.plot(np.mod(t[mask], 2 * np.pi / omega), theta[mask], theta_dot[mask])
ax.set_xlabel(u'$t$', fontsize=26)
ax.set_ylabel(u'$\\theta$', fontsize=26)
ax.set_zlabel(u'$\dot{\\theta}$', fontsize=26)
plt.show()
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from dyna import forced_pendulum
fig = plt.figure()
ax = fig.gca(projection='3d')
omega = 2./3
dt = 2*np.pi / omega / 100
tf = 10000
t, theta, theta_dot = forced_pendulum(1000, dt, np.pi/3, 0,
q=0.5, acc=1.07, omega=omega)
mask = t > 400
ax.plot(np.mod(t[mask], 2 * np.pi / omega), theta[mask],
theta_dot[mask])
ax.set_xlabel(u'$t$', fontsize=26)
ax.set_ylabel(u'$\\theta$', fontsize=26)
ax.set_zlabel(u'$\dot{\\theta}$', fontsize=26)
plt.show()
import matplotlib.pyplot as plt
from scipy import fftpack
from scipy import signal
from dyna import forced_pendulum
omega = 2./3
dt = 2*np.pi / omega / 100
tf = 1000
acc_factors = [1, 1.07]
t, theta_0, theta_dot_0 = forced_pendulum(tf, dt, np.pi/3, 0,
q=0.5, acc=acc_factors[0], omega=omega)
t, theta_1, theta_dot_1 = forced_pendulum(tf, dt, np.pi/3, 0,
q=0.5, acc=acc_factors[1], omega=omega)
time_mask = t > 400
theta_0 = theta_0[time_mask]
theta_1 = theta_1[time_mask]
theta_0 -= theta_0.mean()
theta_1 -= theta_1.mean()
hann = signal.hanning(len(theta_0))
theta_0 *= hann
theta_1 *= hann
