def test_arenstorf():
"""
https://en.wikipedia.org/wiki/Richard_Arenstorf#The_Arenstorf_Orbit
https://commons.wikimedia.org/wiki/File:Arenstorf_Orbit.gif
Q: какие участки траектории наиболее быстрые?
"""
ode = Arenstorf()
t0, t1 = 0, 1 * ode.t_period
y0 = ode.y0
atol = 1e-6
rtol = 1e-3
tss = []
yss = []
methods = (
# (ExplicitEulerMethod(), AdaptType.RUNGE),
(RungeKuttaMethod(coeffs.rk4_coeffs), AdaptType.RUNGE),
(EmbeddedRungeKuttaMethod(coeffs.dopri_coeffs), AdaptType.EMBEDDED),
)
fig1, ax1 = plt.subplots(num='traj')
fig1.suptitle('Arenstorf orbit: trajectory')
ax1.set_xlabel('x1'), ax1.set_ylabel('x2')
fig2, ax2 = plt.subplots(num='dt(t)')
fig2.suptitle('Arenstorf orbit: step sizes')
ax2.set_xlabel('t'), ax2.set_ylabel('dt')
fig3, ax3 = plt.subplots(num='|f|')
fig3.suptitle('Arenstorf orbit: RHS analysis')
ax3.set_xlabel('t')
for method, adapt_type in methods:
ts, ys = adaptive_step_integration(method=method,
ode=ode,
y_start=y0,
t_span=(t0, t1),
adapt_type=adapt_type,
atol=atol, rtol=rtol)
tss.append(np.array(ts))
yss.append(ys)
for (m, _), ts, ys in zip(methods, tss, yss):
ax1.plot([y[0] for y in ys],
[y[1] for y in ys],
':', label=m.name)
ax2.plot(ts[:-1], ts[1:] - ts[:-1], '.-', label=m.name)
#derivatives = [np.linalg.norm(ode(t, y)) for t, y in zip(ts, ys)]
derivatives = [1/(np.linalg.norm(ode(t, y))) for t, y in zip(ts, ys)]
ax1.plot(0, 0, 'bo', label='Earth')
ax1.plot(1, 0, '.', color='grey', label='Moon')
ax3.plot(ts, derivatives, label='|f(t, y)|')
ax1.legend()
ax2.legend()
plt.show()
def test_arenstorf():
"""
https://en.wikipedia.org/wiki/Richard_Arenstorf#The_Arenstorf_Orbit
https://commons.wikimedia.org/wiki/File:Arenstorf_Orbit.gif
Q: which parts of the orbit are fastest?
"""
problem = Arenstorf()
t0, t1 = 0, 1 * problem.t_period
y0 = problem.y0
atol = 1e-6
rtol = 1e-3
tss = []
yss = []
methods = (
# (ExplicitEulerMethod(), AdaptType.RUNGE),
(RungeKuttaMethod(coeffs=collection.rk4_coeffs), AdaptType.RUNGE),
(EmbeddedRungeKuttaMethod(coeffs=collection.dopri_coeffs),
AdaptType.EMBEDDED),
)
plt.figure('traj'), plt.suptitle(
'Arenstorf orbit: trajectory'), plt.xlabel('x1'), plt.ylabel('x2')
plt.figure('dt(t)'), plt.suptitle(
'Arenstorf orbit: step sizes'), plt.xlabel('t'), plt.ylabel('dt')
for method, adapt_type in methods:
ts, ys = adaptive_step_integration(method=method,
func=problem,
y_start=y0,
t_span=(t0, t1),
adapt_type=adapt_type,
atol=atol,
rtol=rtol)
tss.append(np.array(ts))
yss.append(ys)
for (m, _), ts, ys in zip(methods, tss, yss):
plt.figure('traj'), plt.plot([y[0] for y in ys], [y[1] for y in ys],
':',
label=m.name)
plt.figure('dt(t)'), plt.plot(ts[:-1],
ts[1:] - ts[:-1],
'.-',
label=m.name)
plt.figure('traj')
plt.plot(0, 0, 'bo', label='Earth')
plt.plot(1, 0, '.', color='grey', label='Moon')
plt.legend()
plt.figure('dt(t)'), plt.legend()
plt.show()