The GIF below is assembled from a series of 3D plots that scan from -100 to -80 degrees azimuth. As it passes through -90 the Y and Z axis labels flip-flop between the left and right sides of the plot.
Q: Is there a way to stop this distracting flip-flopping without removing them completely?
I suppose one way would be to force them to remain visible on both sides all the time, and that might be an improvement. I don't know how to do that so I can't make the comparison.
If there is some aesthetically better way to do it than duplicating on both sides all the time, that would be great. Perhaps fading?
note: I made the GIF using ImageJ, which requires the step of conversion of the images to 8-bit color. The light gray shading of the sidewalls disappears at that point. It's not a big concern to me but just mentioning it in case one is surprised to see it go.
def deriv(X, t):
x, y, z, xdot, ydot, zdot = X
r1 = np.sqrt((x + mu)**2 + y**2 + z**2)
r2 = np.sqrt((x - 1. + mu)**2 + y**2 + z**2)
term_1 = x + 2. * ydot
term_2 = -(1.-mu) * (x + mu) / r1**3
term_3 = -mu * (x - 1. + mu) / r2**3
xddot = term_1 + term_2 + term_3
term_1 = -2. * xdot
term_2 = 1. - (1.-mu)/r1**3 - mu/r2**3
yddot = term_1 + y * term_2
term_1 = (1. - mu)/r1**3 + mu/r2**3 # should be plus???
zddot = -z * term_1
return np.array([xdot, ydot, zdot, xddot, yddot, zddot])
class Sat(object):
def __init__(self, X0, T0, nu12):
self.X0 = X0
self.pos0 = X0[:3]
self.v0 = X0[3:]
self.T0 = T0
self.nu1, self.nu2 = nu12
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint as ODEint
from mpl_toolkits.mplot3d import Axes3D
# From "Three-Dimensional, Periodic 'Halo' Orbits,
# Kathleen Connor Howell, Celestial Mechanics 32 (1984) 53-71
pi, twopi = np.pi, 2*np.pi
mu = 0.04
# starting points:
x0 = [0.723268, 0.729988, 0.753700, 0.777413, 0.801125, 0.817724]
y0 = 6*[0.0]
z0 = [0.040000, 0.215589, 0.267595, 0.284268, 0.299382, 0.313788]
xdot0 = 6*[0.0]
ydot0 = [0.198019, 0.397259, 0.399909, 0.361870, 0.312474, 0.271306]
zdot0 = 6*[0.0]
X0s = np.array(zip(x0, y0, z0, xdot0, ydot0, zdot0))
Thalf0s = [1.300177, 1.348532, 1.211253, 1.101099, 1.017241, 0.978653]
T0s = [2.0*x for x in Thalf0s]
nu1s = [1181.69, 51.07839, 4.95816, 1.101843, 0.94834, 1.10361]
nu2s = [ 0.98095, -0.90203, -0.40587, -0.420200, -1.58429, -2.09182]
nu12s = zip(nu1s, nu2s)
n_half = 200
fractional_times = np.linspace(0.0, 1.0, 2*n_half+1)
rtol, atol = 1E-12, 1E-12
sats = []
for X0, T0, nu12 in zip(X0s, T0s, nu12s):
sat = Sat(X0, T0, nu12)
sat.n_half = n_half
sat.t = sat.T0 * fractional_times
sat.rtol, sat.atol = rtol, atol
sats.append(sat)
for sat in sats:
answer, info = ODEint(deriv, sat.X0, sat.t,
rtol=sat.rtol, atol=sat.atol,
full_output = True )
sat.answer = answer
sat.mid = answer[sat.n_half]
sat.info = info
if 1 == 1:
xL2, xL1 = 0.74091, 1.21643 # lazy!
fig = plt.figure(figsize=[10, 8])
ax = fig.add_subplot(1, 1, 1, projection='3d')
for sat in sats:
x, y, z = sat.answer.T[:3]
ax.plot(x, y, z)
ax.plot([0.0-mu], [0], [0], 'ob', markersize=20)
ax.plot([1.0-mu], [0], [0], 'og', markersize=12)
ax.plot([xL2], [0], [0], 'ok', markersize=8)
ax.plot([xL1], [0], [0], 'ok', markersize=8)
ax.set_xlim(0.7, 1.25)
ax.set_ylim(-0.225, 0.225)
ax.set_zlim(-0.15, 0.40)
ax.text(xL1, 0, -0.05, "L1", fontsize=14, horizontalalignment='center')
ax.text(xL2, 0, -0.05, "L2", fontsize=14, horizontalalignment='center')
nplot = 80
thetas = np.linspace(0, twopi, nplot+1)[:-1]
azimuths = -90 + 10.0 * np.cos(thetas)
fnames = []
for i, azim in enumerate(azimuths):
fname = "haloz_3D_" + str(10000+i)[1:]
ax.elev, ax.azim = 0, azim
plt.savefig(fname)
fnames.append(fname)
# tight cropping
for i in range(len(fnames)):
fname_in = "haloz_3D_" + str(10000+i)[1:]
fname_out = "haloz_3D_crop_" + str(10000+i)[1:] + ".png"
img = plt.imread(fname_in + ".png")
plt.imsave(fname_out, img[200:-175, 240:-190])
