mirror of
https://git.freebsd.org/ports.git
synced 2025-06-15 09:40:35 -04:00
53 lines
1.3 KiB
Python
53 lines
1.3 KiB
Python
import heyoka as hy
|
|
import numpy as np
|
|
|
|
# Create the symbolic variables.
|
|
# from https://bluescarni.github.io/heyoka.py/notebooks/The%20restricted%20three-body%20problem.html
|
|
|
|
x, y, z, px, py, pz = hy.make_vars("x", "y", "z", "px", "py", "pz")
|
|
|
|
# Fix mu to 0.01.
|
|
mu = 0.01
|
|
|
|
rps_32 = ((x - mu)**2 + y**2 + z**2)**(-3/2.)
|
|
rpj_32 = ((x - mu + 1.)**2 + y**2 + z**2)**(-3/2.)
|
|
|
|
# The equations of motion.
|
|
dxdt = px + y
|
|
dydt = py - x
|
|
dzdt = pz
|
|
dpxdt = py - (1. - mu) * rps_32 * (x - mu) - mu * rpj_32 * (x - mu + 1.)
|
|
dpydt = -px -((1. - mu) * rps_32 + mu * rpj_32) * y
|
|
dpzdt = -((1. - mu) * rps_32 + mu * rpj_32) * z
|
|
|
|
# create the integrator object
|
|
ta = hy.taylor_adaptive(
|
|
# The ODEs.
|
|
[(x, dxdt), (y, dydt), (z, dzdt),
|
|
(px, dpxdt), (py, dpydt), (pz, dpzdt)],
|
|
# The initial conditions.
|
|
[-0.45, 0.80, 0.00, -0.80, -0.45, 0.58],
|
|
# Operate below machine precision
|
|
# and in high-accuracy mode.
|
|
tol = 1e-18, high_accuracy = True
|
|
)
|
|
|
|
# integrate the RTBP up to time unit
|
|
t_grid = np.linspace(0, 200, 2500)
|
|
out = ta.propagate_grid(t_grid)
|
|
print(out)
|
|
|
|
# plot
|
|
from matplotlib.pylab import plt
|
|
plt.rcParams["figure.figsize"] = (12,6)
|
|
|
|
plt.subplot(1,2,1)
|
|
plt.plot(out[4][:, 0], out[4][:, 1])
|
|
plt.xlabel("x")
|
|
plt.ylabel("y")
|
|
plt.subplot(1,2,2)
|
|
plt.plot(out[4][:, 0], out[4][:, 2])
|
|
plt.xlabel("x")
|
|
plt.ylabel("z");
|
|
|
|
plt.show();
|