def mag_oscillation(KE=.001):
# print(KE)
# p_phi1 = (KE/10.)**.5 #give half the KE to p_phi1
# p_phi2 = -p_phi1
# p_tht = 0.
# T_long = 2*numpy.pi/((5./3.)**.5)
p_phi1 = (KE / 18.)**.5
p_phi2 = p_phi1
p_tht = -2 * p_phi1
T_long = 2 * numpy.pi / ((7.)**.5)
calced_KE = p_phi1**2 * 5 + p_phi2**2 * 5 + 2 * p_tht**2
print(calced_KE, KE)
print(p_tht**2 / 2)
print(T_long)
init_state = numpy.array([0, 0, 0, 0, p_phi1, p_phi2, p_tht])
sim_path = utils.RK4_adapt(double_dipole_eqs,
init_state,
T_long * 2,
max_steps=10**6,
precision=10**-6)
t_vals = utils.read_column(sim_path, 0)
phi1_vals = numpy.array(utils.read_column(sim_path, 1))
phi2_vals = numpy.array(utils.read_column(sim_path, 2))
tht_vals = numpy.array(utils.read_column(sim_path, 3))
print(phi1_vals[-1] - tht_vals[-1])
pyplot.plot(t_vals, phi1_vals)
pyplot.plot(t_vals, phi2_vals)
pyplot.plot(t_vals, tht_vals)
pyplot.show()
def frame_gen(energy):
# del x_vals[:]
# del y_vals[:]
axes.clear()
sim_path = simulate_energy(energy)
t_vals = numpy.array(utils.read_column(sim_path, 0))
phi1_vals = numpy.array(utils.read_column(sim_path, 1))
phi2_vals = numpy.array(utils.read_column(sim_path, 2))
tht_vals = numpy.array(utils.read_column(sim_path, 3))
pyplot.plot(t_vals, phi1_vals)
pyplot.plot(t_vals, phi2_vals)
pyplot.plot(t_vals, tht_vals)
axes.set_ylim(-2., 2.)
axes.set_title('initial KE=%f' % energy)
def plot_all_variables(t, states):
figure, subplots = pyplot.subplots(2,4)
exp1 = 0.287723317652649
fits = []
figure.suptitle('residues of $\\phi_d$, $\\phi_t$, $\\theta$ and r. associated momenta plotted below. Green curve denotes expected curve from exponential growth.')
for ti in t:
row = []
for ind in range(len(states[0])):
row.append([states[0][ind]*numpy.exp(exp1*ti)])
fits.append(row)
# print(len(t), len(fits), utils.read_column(fits, 0))
for i in range(4):
subplots[0][i].plot(t, utils.read_column(states,i))
# subplots[0][i].plot(t, utils.read_column(fits,i))
subplots[1][i].plot(t, utils.read_column(states,i+4))
pyplot.show()
def plot_path_from_point(state0):
start = numpy.array(state0)
figure, subplots = pyplot.subplots(1, 2)
# print(start[-2:])
path = utils.RK4_adapt(reduced_double_dipole,
start,
6.,
max_steps=10**6,
precision=10**-7)
t_vals = utils.read_column(path, 0)
phid_vals = numpy.array(utils.read_column(path, 1))
phit_vals = numpy.array(utils.read_column(path, 2))
tht_vals = numpy.array(utils.read_column(path, 3))
pphid_vals = numpy.array(utils.read_column(path, 4))
pphit_vals = numpy.array(utils.read_column(path, 5))
ptht_vals = numpy.array(utils.read_column(path, 6))
force_r = numpy.array(map(rf_red, path))
ratio = numpy.array(map(lambda arr: arr[2] / arr[3], path))
# subplots[0].plot(t_vals ,phid_vals)
# subplots[0].plot(t_vals ,phit_vals)
# subplots[0].plot(t_vals ,tht_vals)
subplots[0].plot(t_vals, force_r)
# subplots[0].plot(t_vals ,ratio) #between phit and tht
subplots[1].plot(t_vals, pphid_vals)
subplots[1].plot(t_vals, pphit_vals)
subplots[1].plot(t_vals, ptht_vals)
pyplot.show()
def random_point_examine():
#phd, pht, tht, pd, pt, ptht
state0p, state0m = utils.reduced_state_gen()
figure, subplots = pyplot.subplots(2, 2)
states = [state0p, state0m]
print(state0p)
for state0_ind in range(2):
start = numpy.array(states[state0_ind])
print(start[-2:])
# print(start[-2:])
path = utils.RK4_adapt(reduced_double_dipole,
start,
20.,
max_steps=10**6,
precision=10**-7)
t_vals = utils.read_column(path, 0)
phid_vals = numpy.array(utils.read_column(path, 1))
phit_vals = numpy.array(utils.read_column(path, 2))
tht_vals = numpy.array(utils.read_column(path, 3))
pphid_vals = numpy.array(utils.read_column(path, 4))
pphit_vals = numpy.array(utils.read_column(path, 5))
ptht_vals = numpy.array(utils.read_column(path, 6))
force_r = numpy.array(map(rf_red, path))
subplots[state0_ind, 0].plot(t_vals, phid_vals)
subplots[state0_ind, 0].plot(t_vals, phit_vals)
subplots[state0_ind, 0].plot(t_vals, tht_vals)
subplots[state0_ind, 0].plot(t_vals, force_r)
subplots[state0_ind, 1].plot(t_vals, pphid_vals)
subplots[state0_ind, 1].plot(t_vals, pphit_vals)
subplots[state0_ind, 1].plot(t_vals, ptht_vals)
pyplot.show()
def plot_period_vs_energy():
# plot spinning periods
data_spinning = parse_file('./clean_spinnning_periods.txt')
p_vals = utils.read_column(data_spinning, 0)
sig_vals = utils.read_column(data_spinning, 1)
E_vals = utils.read_column(data_spinning, 2)
pyplot.plot(E_vals, p_vals, label='Large Amplitude Spinning Mode')
T_s = numpy.pi * 2 * (5. / 3.)**(-.5)
E_vals = numpy.linspace(-1. / 3., -1 / 5., 20)
ones = numpy.ones(20)
pyplot.plot(E_vals,
T_s * ones,
'b--',
label='Small Amplitude spinning mode')
#plot orbital periods
data_orbital = parse_file('./clean_orbital_periods.txt')
p_vals = utils.read_column(data_orbital, 0)
sig_vals = utils.read_column(data_orbital, 1)
E_vals = utils.read_column(data_orbital, 2)
p2_vals = map(lambda x: x * 2, p_vals)
pyplot.plot(E_vals, p_vals, label='Large Amplitude Orbital Mode')
# pyplot.plot(E_vals, p2_vals)
# plot pendulum periods
# E_p_vals_spin = spin_periods()
# pyplot.plot(E_p_vals_spin[0], E_p_vals_spin[1])
#plot analytic low-amplitude
T_o = numpy.pi * 2 * (7.)**(-.5)
E_vals = numpy.linspace(-1. / 3., -0.2, 20)
ones = numpy.ones(20)
pyplot.plot(E_vals,
T_o * ones,
'g--',
label='Small Amplitude orbital mode')
pyplot.xlabel('Energy $(U_0+T_0)$', fontsize=16)
pyplot.ylabel('Period ', fontsize=16)
pyplot.ylim(0, 12)
pyplot.xlim(-1. / 3., 1. / 6.)
pyplot.text((-0.3), 8, 'Spinning Mode')
pyplot.text((-0.3), 3.25, 'Orbital Mode')
# pyplot.text(
# x=(-1/3.+.005), y=6.,
# text='S', size=15
# )
# pyplot.legend(loc='upper right')
# pyplot.legend(handles = legend_elements, loc='upper right')
pyplot.title('Large Amplitude Period vs System Energy',
loc='left',
fontsize=18)
pyplot.savefig('plot.png')
pyplot.show()