def plot_manifolds(self):
color_palette_green = sns.dark_palette('green', n_colors=self.numberOfOrbitsPerManifold)
color_palette_red = sns.dark_palette('red', n_colors=self.numberOfOrbitsPerManifold)
fig = plt.figure()
ax = fig.gca()
for i in range(self.numberOfOrbitsPerManifold):
plt.plot(self.WS.xs(i)['x'], self.WS.xs(i)['y'], color=color_palette_green[i])
plt.plot(self.WU.xs(i)['x'], self.WU.xs(i)['y'], color=color_palette_red[i])
C = 3.15
x_range = np.arange(0.7, 1.3, 0.001)
y_range = np.arange(-0.3, 0.3, 0.001)
X, Y = np.meshgrid(x_range, y_range)
Z = cr3bp_velocity(X, Y, C)
if Z.min() < 0:
plt.contourf(X, Y, Z, [Z.min(), 0], colors='black', alpha=0.2)
if self.U_section == (2 or 3):
ax.axvline(1 - self.massParameter, color='black')
bodies_df = load_bodies_location()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = bodies_df['Moon']['r'] * np.outer(np.cos(u), np.sin(v)) + bodies_df['Moon']['x']
y = bodies_df['Moon']['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df['Moon']['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
plt.scatter(x, y, color='black')
pass
def __init__(self, config, orbit_type):
self.orbit = []
self.config = config
self.orbitType = orbit_type
self.massParameter = 0.0121505810173
self.figSize = (20, 20)
self.titleSize = 20
self.suptitleSize = 30
orbit_ids = []
for orbit_id in list(self.config[self.orbitType].keys()):
ls = orbit_id.split('_')
if orbit_type == 'near_vertical':
orbit_ids.append(int(ls[2]))
if orbit_type == 'halo':
orbit_ids.append(int(ls[1]))
orbit_ids = [
self.orbitType + '_' + str(idx) for idx in sorted(orbit_ids)
]
for orbit_id in orbit_ids:
self.orbit.append(
load_orbit('../data/raw/' + orbit_id + '_final_orbit.txt'))
self.lagrangePoints = load_lagrange_points_location()
self.bodies = load_bodies_location()
sns.set_style("whitegrid")
pass
def plot_2d_shooting_conditions(self):
fig = plt.figure(figsize=self.figSize)
ax = fig.gca()
orbit_types = ['horizontal', 'vertical', 'halo']
lagrange_point_nrs = [1, 2]
x = []
z = []
ydot = []
c = []
for idx, orbit_type in enumerate(orbit_types):
for lagrange_point_nr in lagrange_point_nrs:
initial_conditions_file_path = '../../data/raw/orbits/L' + str(
lagrange_point_nr) + '_' + orbit_type + '_initial_conditions.txt'
initial_conditions_incl_m_df = load_initial_conditions_incl_M(initial_conditions_file_path)
plot_label = orbit_type.capitalize()
if plot_label == 'Horizontal' or plot_label == 'Vertical':
plot_label += ' Lyapunov'
x.extend(list(initial_conditions_incl_m_df[2].values))
z.extend(list(initial_conditions_incl_m_df[4].values))
c.extend(list(initial_conditions_incl_m_df[0].values))
sc = ax.scatter(x, z, c=c, cmap='viridis', s=20)
cb = plt.colorbar(sc)
cb.set_label('$C \enskip [-]$')
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
# Lagrange points and bodies
for lagrange_point_nr in lagrange_point_nrs:
ax.scatter(lagrange_points_df[lagrange_point_nr]['x'], lagrange_points_df[lagrange_point_nr]['z'], color='black', marker='x')
bodies_df = load_bodies_location()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
for body in bodies_df:
x = bodies_df[body]['r'] * np.outer(np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
ax.contourf(x, z, y, colors='black')
ax.legend(frameon=True, loc='upper right')
ax.set_xlabel('x [-]')
ax.set_ylabel('z [-]')
ax.grid(True, which='both', ls=':')
fig.tight_layout()
fig.subplots_adjust(top=0.9)
plt.suptitle('$L_1, L_2$ - Shooting conditions for H-L, halo, and V-L', size=self.suptitleSize)
if self.lowDPI:
fig.savefig('../../data/figures/orbits/orbit_shooting_conditions_2d.png', transparent=True, dpi=self.dpi)
else:
fig.savefig('../../data/figures/orbits/orbit_shooting_conditions_2d.pdf', transparent=True)
pass
def plot_3d_shooting_conditions(self):
fig = plt.figure(figsize=self.figSize)
ax = fig.gca(projection='3d')
orbit_types = ['horizontal', 'vertical', 'halo']
lagrange_point_nrs = [1, 2]
lines = []
linewidth = 2
for lagrange_point_nr in lagrange_point_nrs:
for idx, orbit_type in enumerate(orbit_types):
initial_conditions_file_path = '../../data/raw/orbits/L' + str(
lagrange_point_nr) + '_' + orbit_type + '_initial_conditions.txt'
initial_conditions_incl_m_df = load_initial_conditions_incl_M(initial_conditions_file_path)
plot_label = orbit_type.capitalize()
if plot_label == 'Horizontal' or plot_label == 'Vertical':
plot_label += ' Lyapunov'
line, = ax.plot(initial_conditions_incl_m_df[2].values, initial_conditions_incl_m_df[6].values,
initial_conditions_incl_m_df[4].values, label=plot_label, linewidth=linewidth,
color=self.plottingColors['tripleLine'][idx])
lines.append(line)
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
# Lagrange points and bodies
for lagrange_point_nr in lagrange_point_nrs:
ax.scatter(lagrange_points_df[lagrange_point_nr]['x'], lagrange_points_df[lagrange_point_nr]['z'],
color='black', marker='x')
bodies_df = load_bodies_location()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
for body in bodies_df:
x = bodies_df[body]['r'] * np.outer(np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
ax.plot_surface(x, y, z, color='black')
# print(ax.elev)
# print(ax.azim)
# ax.view_init(20, -75)
plt.plot(ax.get_xlim(), [0, 0], 'black', linewidth=0.5)
ax.legend(frameon=True, loc='upper right', handles=lines[:3])
ax.set_xlabel('x [-]')
ax.set_ylabel('$\dot{y}$ [-]')
ax.set_zlabel('z [-]')
ax.grid(True, which='both', ls=':')
fig.tight_layout()
fig.subplots_adjust(top=0.9)
plt.suptitle('$L_1, L_2$ - Shooting conditions', size=self.suptitleSize)
fig.savefig('../../data/figures/orbits/orbit_shooting_conditions_3d.pdf', transparent=True)
pass
def plot_manifolds(self):
# Plot: subplots
fig = plt.figure(figsize=self.figSize)
ax = fig.gca()
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
# Lagrange points and bodies
for lagrange_point_nr in lagrange_point_nrs:
ax.scatter(lagrange_points_df[lagrange_point_nr]['x'], lagrange_points_df[lagrange_point_nr]['y'], color='black', marker='x')
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
bodies_df = load_bodies_location()
for body in bodies_df:
x = bodies_df[body]['r'] * np.outer(np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
ax.contourf(x, y, z, colors='black')
# Determine color for plot
plot_alpha = 1
line_width = 1
for manifold_orbit_number in range(self.numberOfOrbitsPerManifold):
ax.plot(self.W_S_plus.xs(manifold_orbit_number)['x'], self.W_S_plus.xs(manifold_orbit_number)['y'], color=self.colorPaletteStable[manifold_orbit_number], alpha=plot_alpha, linewidth=line_width)
ax.plot(self.W_S_min.xs(manifold_orbit_number)['x'], self.W_S_min.xs(manifold_orbit_number)['y'], color=self.colorPaletteStable[manifold_orbit_number], alpha=plot_alpha, linewidth=line_width)
ax.plot(self.W_U_plus.xs(manifold_orbit_number)['x'], self.W_U_plus.xs(manifold_orbit_number)['y'], color=self.colorPaletteUnstable[manifold_orbit_number], alpha=plot_alpha, linewidth=line_width)
ax.plot(self.W_U_min.xs(manifold_orbit_number)['x'], self.W_U_min.xs(manifold_orbit_number)['y'], color=self.colorPaletteUnstable[manifold_orbit_number], alpha=plot_alpha, linewidth=line_width)
ax.set_xlabel('x [-]')
ax.set_ylabel('y [-]')
ax.grid(True, which='both', ls=':')
fig.tight_layout()
fig.subplots_adjust(top=0.9)
plt.suptitle('$L_' + str(self.lagrangePointNr) + '$ ' + self.orbitTypeForTitle + ' $\{ \mathcal{W}^{S \pm}, \mathcal{W}^{U \pm} \}$ - Spatial overview', size=self.suptitleSize)
plt.savefig('../../data/figures/manifolds/refined_for_c/L' + str(self.lagrangePointNr) + '_' + self.orbitType + '_' + str(self.orbitId) + '_manifold.pdf',
transparent=True)
plt.close()
pass
def plot_manifolds(self):
# Plot: subplots
if self.orbitType == 'horizontal':
figsize = (self.figSize[0], self.figSize[1] / 2)
fig = plt.figure(figsize=figsize)
ax00 = fig.add_subplot(2, 3, 1, projection='3d')
ax01 = fig.add_subplot(2, 3, 2, projection='3d')
ax02 = fig.add_subplot(2, 3, 3, projection='3d')
ax10 = fig.add_subplot(2, 3, 4)
ax11 = fig.add_subplot(2, 3, 5)
ax12 = fig.add_subplot(2, 3, 6)
else:
figsize = self.figSize
fig = plt.figure(figsize=figsize)
ax00 = fig.add_subplot(4, 3, 1, projection='3d')
ax01 = fig.add_subplot(4, 3, 2, projection='3d')
ax02 = fig.add_subplot(4, 3, 3, projection='3d')
ax10 = fig.add_subplot(4, 3, 4)
ax11 = fig.add_subplot(4, 3, 5)
ax12 = fig.add_subplot(4, 3, 6)
ax20 = fig.add_subplot(4, 3, 7)
ax21 = fig.add_subplot(4, 3, 8)
ax22 = fig.add_subplot(4, 3, 9)
ax30 = fig.add_subplot(4, 3, 10)
ax31 = fig.add_subplot(4, 3, 11)
ax32 = fig.add_subplot(4, 3, 12)
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
# Lagrange points and bodies
for lagrange_point_nr in lagrange_point_nrs:
ax00.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax01.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax02.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax10.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
color='black',
marker='x')
ax11.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
color='black',
marker='x')
ax12.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
color='black',
marker='x')
if self.orbitType != 'horizontal':
ax20.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax21.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax22.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax30.scatter(lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax31.scatter(lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax32.scatter(lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
bodies_df = load_bodies_location()
for body in bodies_df:
x = bodies_df[body]['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
ax00.plot_surface(x, y, z, color='black')
ax01.plot_surface(x, y, z, color='black')
ax02.plot_surface(x, y, z, color='black')
ax10.contourf(x, y, z, colors='black')
ax11.contourf(x, y, z, colors='black')
ax12.contourf(x, y, z, colors='black')
if self.orbitType != 'horizontal':
ax20.contourf(x, z, y, colors='black')
ax21.contourf(x, z, y, colors='black')
ax22.contourf(x, z, y, colors='black')
ax30.contourf(y, z, x, colors='black')
ax31.contourf(y, z, x, colors='black')
ax32.contourf(y, z, x, colors='black')
# Determine color for plot
plot_alpha = 1
line_width = 0.5
for manifold_orbit_number in range(self.numberOfOrbitsPerManifold):
ax00.plot(self.W_S_plus[0].xs(manifold_orbit_number)['x'],
self.W_S_plus[0].xs(manifold_orbit_number)['y'],
self.W_S_plus[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax01.plot(self.W_S_plus[1].xs(manifold_orbit_number)['x'],
self.W_S_plus[1].xs(manifold_orbit_number)['y'],
self.W_S_plus[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax02.plot(self.W_S_plus[2].xs(manifold_orbit_number)['x'],
self.W_S_plus[2].xs(manifold_orbit_number)['y'],
self.W_S_plus[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax10.plot(self.W_S_plus[0].xs(manifold_orbit_number)['x'],
self.W_S_plus[0].xs(manifold_orbit_number)['y'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax11.plot(self.W_S_plus[1].xs(manifold_orbit_number)['x'],
self.W_S_plus[1].xs(manifold_orbit_number)['y'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax12.plot(self.W_S_plus[2].xs(manifold_orbit_number)['x'],
self.W_S_plus[2].xs(manifold_orbit_number)['y'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
if self.orbitType != 'horizontal':
ax20.plot(self.W_S_plus[0].xs(manifold_orbit_number)['x'],
self.W_S_plus[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax21.plot(self.W_S_plus[1].xs(manifold_orbit_number)['x'],
self.W_S_plus[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax22.plot(self.W_S_plus[2].xs(manifold_orbit_number)['x'],
self.W_S_plus[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax30.plot(self.W_S_plus[0].xs(manifold_orbit_number)['y'],
self.W_S_plus[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax31.plot(self.W_S_plus[1].xs(manifold_orbit_number)['y'],
self.W_S_plus[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax32.plot(self.W_S_plus[2].xs(manifold_orbit_number)['y'],
self.W_S_plus[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax00.plot(self.W_S_min[0].xs(manifold_orbit_number)['x'],
self.W_S_min[0].xs(manifold_orbit_number)['y'],
self.W_S_min[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax01.plot(self.W_S_min[1].xs(manifold_orbit_number)['x'],
self.W_S_min[1].xs(manifold_orbit_number)['y'],
self.W_S_min[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax02.plot(self.W_S_min[2].xs(manifold_orbit_number)['x'],
self.W_S_min[2].xs(manifold_orbit_number)['y'],
self.W_S_min[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax10.plot(self.W_S_min[0].xs(manifold_orbit_number)['x'],
self.W_S_min[0].xs(manifold_orbit_number)['y'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax11.plot(self.W_S_min[1].xs(manifold_orbit_number)['x'],
self.W_S_min[1].xs(manifold_orbit_number)['y'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax12.plot(self.W_S_min[2].xs(manifold_orbit_number)['x'],
self.W_S_min[2].xs(manifold_orbit_number)['y'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
if self.orbitType != 'horizontal':
ax20.plot(self.W_S_min[0].xs(manifold_orbit_number)['x'],
self.W_S_min[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax21.plot(self.W_S_min[1].xs(manifold_orbit_number)['x'],
self.W_S_min[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax22.plot(self.W_S_min[2].xs(manifold_orbit_number)['x'],
self.W_S_min[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax30.plot(self.W_S_min[0].xs(manifold_orbit_number)['y'],
self.W_S_min[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax31.plot(self.W_S_min[1].xs(manifold_orbit_number)['y'],
self.W_S_min[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax32.plot(self.W_S_min[2].xs(manifold_orbit_number)['y'],
self.W_S_min[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteStable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax00.plot(self.W_U_plus[0].xs(manifold_orbit_number)['x'],
self.W_U_plus[0].xs(manifold_orbit_number)['y'],
self.W_U_plus[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax01.plot(self.W_U_plus[1].xs(manifold_orbit_number)['x'],
self.W_U_plus[1].xs(manifold_orbit_number)['y'],
self.W_U_plus[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax02.plot(self.W_U_plus[2].xs(manifold_orbit_number)['x'],
self.W_U_plus[2].xs(manifold_orbit_number)['y'],
self.W_U_plus[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax10.plot(self.W_U_plus[0].xs(manifold_orbit_number)['x'],
self.W_U_plus[0].xs(manifold_orbit_number)['y'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax11.plot(self.W_U_plus[1].xs(manifold_orbit_number)['x'],
self.W_U_plus[1].xs(manifold_orbit_number)['y'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax12.plot(self.W_U_plus[2].xs(manifold_orbit_number)['x'],
self.W_U_plus[2].xs(manifold_orbit_number)['y'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
if self.orbitType != 'horizontal':
ax20.plot(
self.W_U_plus[0].xs(manifold_orbit_number)['x'],
self.W_U_plus[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax21.plot(
self.W_U_plus[1].xs(manifold_orbit_number)['x'],
self.W_U_plus[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax22.plot(
self.W_U_plus[2].xs(manifold_orbit_number)['x'],
self.W_U_plus[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax30.plot(
self.W_U_plus[0].xs(manifold_orbit_number)['y'],
self.W_U_plus[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax31.plot(
self.W_U_plus[1].xs(manifold_orbit_number)['y'],
self.W_U_plus[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax32.plot(
self.W_U_plus[2].xs(manifold_orbit_number)['y'],
self.W_U_plus[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax00.plot(self.W_U_min[0].xs(manifold_orbit_number)['x'],
self.W_U_min[0].xs(manifold_orbit_number)['y'],
self.W_U_min[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax01.plot(self.W_U_min[1].xs(manifold_orbit_number)['x'],
self.W_U_min[1].xs(manifold_orbit_number)['y'],
self.W_U_min[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax02.plot(self.W_U_min[2].xs(manifold_orbit_number)['x'],
self.W_U_min[2].xs(manifold_orbit_number)['y'],
self.W_U_min[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax10.plot(self.W_U_min[0].xs(manifold_orbit_number)['x'],
self.W_U_min[0].xs(manifold_orbit_number)['y'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax11.plot(self.W_U_min[1].xs(manifold_orbit_number)['x'],
self.W_U_min[1].xs(manifold_orbit_number)['y'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax12.plot(self.W_U_min[2].xs(manifold_orbit_number)['x'],
self.W_U_min[2].xs(manifold_orbit_number)['y'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
if self.orbitType != 'horizontal':
ax20.plot(
self.W_U_min[0].xs(manifold_orbit_number)['x'],
self.W_U_min[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax21.plot(
self.W_U_min[1].xs(manifold_orbit_number)['x'],
self.W_U_min[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax22.plot(
self.W_U_min[2].xs(manifold_orbit_number)['x'],
self.W_U_min[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax30.plot(
self.W_U_min[0].xs(manifold_orbit_number)['y'],
self.W_U_min[0].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax31.plot(
self.W_U_min[1].xs(manifold_orbit_number)['y'],
self.W_U_min[1].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
ax32.plot(
self.W_U_min[2].xs(manifold_orbit_number)['y'],
self.W_U_min[2].xs(manifold_orbit_number)['z'],
color=self.colorPaletteUnstable[manifold_orbit_number],
alpha=plot_alpha,
linewidth=line_width)
plot_alpha = 1
line_width = 2
ax00.plot(self.orbitDf[0]['x'],
self.orbitDf[0]['y'],
self.orbitDf[0]['z'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
ax01.plot(self.orbitDf[1]['x'],
self.orbitDf[1]['y'],
self.orbitDf[1]['z'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
ax02.plot(self.orbitDf[2]['x'],
self.orbitDf[2]['y'],
self.orbitDf[2]['z'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
ax10.plot(self.orbitDf[0]['x'],
self.orbitDf[0]['y'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
ax11.plot(self.orbitDf[1]['x'],
self.orbitDf[1]['y'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
ax12.plot(self.orbitDf[2]['x'],
self.orbitDf[2]['y'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
if self.orbitType != 'horizontal':
ax20.plot(self.orbitDf[0]['x'],
self.orbitDf[0]['z'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
ax21.plot(self.orbitDf[1]['x'],
self.orbitDf[1]['z'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
ax22.plot(self.orbitDf[2]['x'],
self.orbitDf[2]['z'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
ax30.plot(self.orbitDf[0]['y'],
self.orbitDf[0]['z'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
ax31.plot(self.orbitDf[1]['y'],
self.orbitDf[1]['z'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
ax32.plot(self.orbitDf[2]['y'],
self.orbitDf[2]['z'],
color=self.plottingColors['orbit'],
alpha=plot_alpha,
linewidth=line_width)
ax00.set_xlabel('x [-]')
ax00.set_ylabel('y [-]')
ax00.set_zlabel('z [-]')
ax00.grid(True, which='both', ls=':')
ax00.view_init(30, -120)
ax00.set_title('C = ' + str(self.C[0]))
ax01.set_xlabel('x [-]')
ax01.set_ylabel('y [-]')
ax01.set_zlabel('z [-]')
ax01.grid(True, which='both', ls=':')
ax01.view_init(30, -120)
ax01.set_title('C = ' + str(self.C[1]))
ax02.set_xlabel('x [-]')
ax02.set_ylabel('y [-]')
ax02.set_zlabel('z [-]')
if self.orbitType == 'horizontal':
ax00.set_zlim([-0.4, 0.4])
ax01.set_zlim([-0.4, 0.4])
ax02.set_zlim([-0.4, 0.4])
ax02.grid(True, which='both', ls=':')
ax02.view_init(30, -120)
ax02.set_title('C = ' + str(self.C[2]))
xlim = [
min(ax00.get_xlim()[0],
ax01.get_xlim()[0],
ax02.get_xlim()[0]),
max(ax00.get_xlim()[1],
ax01.get_xlim()[1],
ax02.get_xlim()[1])
]
ylim = [
min(ax00.get_ylim()[0],
ax01.get_ylim()[0],
ax02.get_ylim()[0]),
max(ax00.get_ylim()[1],
ax01.get_ylim()[1],
ax02.get_ylim()[1])
]
zlim = [
min(ax00.get_zlim()[0],
ax01.get_zlim()[0],
ax02.get_zlim()[0]),
max(ax00.get_zlim()[1],
ax01.get_zlim()[1],
ax02.get_zlim()[1])
]
ax00.set_xlim(xlim)
ax01.set_xlim(xlim)
ax02.set_xlim(xlim)
ax00.set_ylim(ylim)
ax01.set_ylim(ylim)
ax02.set_ylim(ylim)
ax00.set_zlim(zlim)
ax01.set_zlim(zlim)
ax02.set_zlim(zlim)
ax10.set_xlabel('x [-]')
ax11.set_xlabel('x [-]')
ax12.set_xlabel('x [-]')
ax10.set_ylabel('y [-]')
xlim = [
min(ax10.get_xlim()[0],
ax11.get_xlim()[0],
ax12.get_xlim()[0]),
max(ax10.get_xlim()[1],
ax11.get_xlim()[1],
ax12.get_xlim()[1])
]
ylim = [
min(ax10.get_ylim()[0],
ax11.get_ylim()[0],
ax12.get_ylim()[0]),
max(ax10.get_ylim()[1],
ax11.get_ylim()[1],
ax12.get_ylim()[1])
]
ax10.set_xlim(xlim)
ax11.set_xlim(xlim)
ax12.set_xlim(xlim)
ax10.set_ylim(ylim)
ax11.set_ylim(ylim)
ax12.set_ylim(ylim)
ax10.grid(True, which='both', ls=':')
ax11.grid(True, which='both', ls=':')
ax12.grid(True, which='both', ls=':')
# Plot zero velocity surface
x_range = np.arange(-6.0, 4.0, 0.001)
y_range = np.arange(-3.0, 3.0, 0.001)
x_mesh, y_mesh = np.meshgrid(x_range, y_range)
z_mesh0 = cr3bp_velocity(x_mesh, y_mesh, 3.15)
z_mesh1 = cr3bp_velocity(x_mesh, y_mesh, 3.1)
z_mesh2 = cr3bp_velocity(x_mesh, y_mesh, 3.05)
if z_mesh0.min() < 0:
ax10.contourf(x_mesh,
y_mesh,
z_mesh0,
list(np.linspace(z_mesh0.min(), 0, 10)),
cmap='gist_gray_r',
alpha=0.5)
if z_mesh1.min() < 0:
ax11.contourf(x_mesh,
y_mesh,
z_mesh1,
list(np.linspace(z_mesh1.min(), 0, 10)),
cmap='gist_gray_r',
alpha=0.5)
if z_mesh2.min() < 0:
ax12.contourf(x_mesh,
y_mesh,
z_mesh2,
list(np.linspace(z_mesh2.min(), 0, 10)),
cmap='gist_gray_r',
alpha=0.5)
if self.orbitType != 'horizontal':
ax20.set_xlabel('x [-]')
ax21.set_xlabel('x [-]')
ax22.set_xlabel('x [-]')
ax20.set_ylabel('z [-]')
xlim = [
min(ax20.get_xlim()[0],
ax21.get_xlim()[0],
ax22.get_xlim()[0]),
max(ax20.get_xlim()[1],
ax21.get_xlim()[1],
ax22.get_xlim()[1])
]
ylim = [
min(ax20.get_ylim()[0],
ax21.get_ylim()[0],
ax22.get_ylim()[0]),
max(ax20.get_ylim()[1],
ax21.get_ylim()[1],
ax22.get_ylim()[1])
]
ax20.set_xlim(xlim)
ax21.set_xlim(xlim)
ax22.set_xlim(xlim)
ax20.set_ylim(ylim)
ax21.set_ylim(ylim)
ax22.set_ylim(ylim)
ax20.grid(True, which='both', ls=':')
ax21.grid(True, which='both', ls=':')
ax22.grid(True, which='both', ls=':')
ax30.set_xlabel('y [-]')
ax31.set_xlabel('y [-]')
ax32.set_xlabel('y [-]')
ax30.set_ylabel('z [-]')
xlim = [
min(ax30.get_xlim()[0],
ax31.get_xlim()[0],
ax32.get_xlim()[0]),
max(ax30.get_xlim()[1],
ax31.get_xlim()[1],
ax32.get_xlim()[1])
]
ylim = [
min(ax30.get_ylim()[0],
ax31.get_ylim()[0],
ax32.get_ylim()[0]),
max(ax30.get_ylim()[1],
ax31.get_ylim()[1],
ax32.get_ylim()[1])
]
ax30.set_xlim(xlim)
ax31.set_xlim(xlim)
ax32.set_xlim(xlim)
ax30.set_ylim(ylim)
ax31.set_ylim(ylim)
ax32.set_ylim(ylim)
ax30.grid(True, which='both', ls=':')
ax31.grid(True, which='both', ls=':')
ax32.grid(True, which='both', ls=':')
fig.tight_layout()
if self.orbitType == 'horizontal':
fig.subplots_adjust(top=0.9)
else:
fig.subplots_adjust(top=0.95)
plt.suptitle(
'$L_' + str(self.lagrangePointNr) + '$ ' + self.orbitTypeForTitle +
' $\{ \mathcal{W}^{S \pm}, \mathcal{W}^{U \pm} \}$ - Spatial comparison',
size=self.suptitleSize)
fig.savefig('../../data/figures/manifolds/refined_for_c/L' +
str(self.lagrangePointNr) + '_' + self.orbitType +
'_manifold_comparison.pdf',
transparent=True)
# fig.savefig('/Users/koen/Documents/Courses/AE5810 Thesis Space/Meetings/0901/L' + str(self.lagrangePointNr) + '_' + self.orbitType + '_' + str(self.orbitId) + '_manifold_subplots.png')
plt.close()
pass
def animate(self):
fig = plt.figure()
self.ax = fig.gca()
self.lines = [
plt.plot([], [],
color=self.orbitColor,
alpha=self.orbitAlpha,
marker='o',
markevery=[-1])[0] for idx in range(6)
]
# Text object to display absolute normalized time of trajectories within the manifolds
self.timeText = self.ax.text2D(0.05,
0.95,
s='$\|t\| \\approx 0$',
transform=self.ax.transAxes,
size=self.timeTextSize)
# Plot zero velocity surface
x_range = np.arange(-5, 5, 0.001)
y_range = np.arange(-5, 5, 0.001)
x_mesh, y_mesh = np.meshgrid(x_range, y_range)
z_mesh = cr3bp_velocity(x_mesh, y_mesh, self.cLevel)
# self.ax.plot_surface(x_mesh, y_mesh, -z_mesh, alpha=0.1, linewidth=0,
# cmap=matplotlib.colors.ListedColormap(sns.color_palette("Blues", n_colors=100)),
# vmin=self.zLim[0], vmax=-z_mesh.min(), rstride=50, cstride=50)
self.ax.plot_surface(x_mesh,
y_mesh,
-z_mesh,
alpha=0.2,
linewidth=0,
color='black')
self.ax.plot_wireframe(x_mesh,
y_mesh,
-z_mesh,
alpha=1,
linewidth=0.5,
color='black',
rstride=50,
cstride=50)
# Plot both primaries
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
bodies_df = load_bodies_location()
for body in bodies_df:
x = self.orbitalBodiesEnlargementFactor * bodies_df[body][
'r'] * np.outer(np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = self.orbitalBodiesEnlargementFactor * bodies_df[body][
'r'] * np.outer(np.sin(u), np.sin(v))
z = self.orbitalBodiesEnlargementFactor * bodies_df[body][
'r'] * np.outer(np.ones(np.size(u)), np.cos(v))
self.ax.plot_surface(x, y, z, color='black', zorder=3)
# Plot Lagrange points 1 and 2
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
for lagrange_point_nr in lagrange_point_nrs:
self.ax.scatter3D(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x',
s=self.lagrangePointMarkerSize,
zorder=1)
title = 'Rotating reference frame - Spatial overview at C = ' + str(
self.cLevel)
self.ax.set_xlim3d(self.xLim)
self.ax.set_ylim3d(self.yLim)
self.ax.set_zlim3d(self.zLim)
fig.tight_layout()
fig.subplots_adjust(top=0.9)
plt.suptitle(title, size=self.suptitleSize)
# self.ax.elev = 60
self.initialElevation = self.ax.elev
self.initialAzimuth = self.ax.azim
self.ax.set_aspect('equal')
# plt.show()
plt.axis('off')
# Determine the maximum value of t
t_max = 1
print('Maximum value for t = ' + str(t_max) + ', animation t: = ')
# Introduce a new time-vector for linearly spaced time throughout the animation
# self.t = np.linspace(0, t_max, np.round(t_max / 0.05) + 1)
self.t = np.linspace(0, t_max, np.round(t_max / 0.005) + 1)
animation_function = animation.FuncAnimation(
fig,
self.update_lines,
init_func=self.initiate_lines,
frames=len(self.t),
interval=1,
blit=True)
empty_writer_object = animation.writers['ffmpeg']
animation_writer = empty_writer_object(
fps=30, metadata=dict(artist='Koen Langemeijer'))
file_name = '../../../data/animations/reference_frame/spatial_rotating_reference_frame_' + str(
self.cLevel) + '.mp4'
animation_function.save(file_name, writer=animation_writer)
def animate(self):
print(
'\nProducing a HorizontalLyapunovBifurcationToAxialAnimation at L'
+ str(self.librationPointNr) + '\n')
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
self.lines = [
plt.plot([], [], color=self.orbitColor, alpha=self.orbitAlpha)[0]
]
# Text object to display absolute normalized time of trajectories within the manifolds
self.jacobiEnergyText = ax.text2D(
0.05,
0.05,
s='Horizontal Lyapunov family \n $C \\approx$ {:.4f}'.format(
round(self.jacobiEnergyHorizontalLyapunov[0], 4)),
transform=ax.transAxes,
size=self.timeTextSize)
# Plot the first orbit
orbit_df = load_orbit('../../../data/raw/orbits/L' +
str(self.librationPointNr) + '_horizontal_' +
str(0) + '.txt')
plt.plot(orbit_df['x'],
orbit_df['y'],
orbit_df['z'],
color='orange',
alpha=self.orbitAlpha,
linewidth=self.orbitLinewidth)
# Plot the Moon
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
bodies_df = load_bodies_location()
x = bodies_df['Moon']['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df['Moon']['x']
y = bodies_df['Moon']['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df['Moon']['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
ax.plot_surface(x, y, z, color='black')
# Plot Lagrange points 1 and 2
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
for lagrange_point_nr in lagrange_point_nrs:
ax.scatter3D(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x',
s=self.lagrangePointMarkerSize)
title = 'Bifurcation from horizontal Lyapunov to axial and vertical Lyapunov families at $L_' + str(
self.librationPointNr) + '$'
ax.set_xlim3d(self.xLim)
ax.set_ylim3d(self.yLim)
ax.set_zlim3d(self.zLim)
ax.set_xlabel('x [-]')
ax.set_ylabel('y [-]')
ax.set_zlabel('z [-]')
plt.show()
ax.grid(True, which='both', ls=':')
fig.tight_layout()
fig.subplots_adjust(top=0.9)
plt.suptitle(title, size=self.suptitleSize)
# Fix overlap between labels and ticks
ax.xaxis._axinfo['label']['space_factor'] = 2.0
ax.yaxis._axinfo['label']['space_factor'] = 2.0
ax.zaxis._axinfo['label']['space_factor'] = 2.0
# ax.elev = 10
# ax.azim = -80
# Determine number of frames
number_of_frames = int(
self.orbitIdBifurcationsFromHorizontalLyapunov[1] + 1 +
self.numberOfAxialOrbits + len(self.verticalLyapunovIndices))
print('Number of frames equals ' + str(number_of_frames))
animation_function = animation.FuncAnimation(
fig,
self.update_lines,
init_func=self.initiate_lines,
frames=number_of_frames,
interval=1,
blit=True)
empty_writer_object = animation.writers['ffmpeg']
animation_writer = empty_writer_object(
fps=30, metadata=dict(artist='Koen Langemeijer'))
file_name = '../../../data/animations/bifurcations/L' + str(
self.librationPointNr
) + '_horizontal_lyapunov_bifurcation_to_axial_family.mp4'
animation_function.save(file_name, writer=animation_writer)
def plot_saddle(self):
fig = plt.figure(figsize=self.figSize)
ax = fig.add_subplot(111, projection='3d')
# azim=150
# elev=25
# print(ax.azim)
# ax.view_init(elev=elev, azim=azim)
ax.view_init(elev=25, azim=17)
# Plot zero velocity surface
# x_range = np.arange(self.xlim[0], self.xlim[1], 0.01)
# y_range = np.arange(self.ylim[0], self.ylim[1], 0.01)
x_range = np.arange(self.crange[0], self.crange[1], 0.01)
y_range = np.arange(self.crange[0], self.crange[1], 0.01)
x_mesh, y_mesh = np.meshgrid(x_range, y_range)
z_mesh = cr3bp_velocity(x_mesh, y_mesh, self.cLevel)
self.zlim = [-0.5, -min([min(i) for i in z_mesh])]
print(z_mesh)
threshold_z = 0.3
for idx1, row in enumerate(z_mesh):
for idx2, item in enumerate(row):
if item > threshold_z:
z_mesh[idx1][idx2] = threshold_z
# print(max([max(i) for i in z_mesh]))
# print(min([min(i) for i in z_mesh]))
if z_mesh.min() < 0:
# plt.contour(x_mesh, y_mesh, z_mesh, [z_mesh.min(), 0], colors='black', alpha=0.3)
# ax.contour(x_mesh, y_mesh, z_mesh, list(np.linspace(z_mesh.min(), 0, 10)), cmap='gist_gray_r',
# alpha=0.5)
ax.plot_surface(x_mesh,
y_mesh,
-z_mesh,
alpha=1,
linewidth=0,
cmap='viridis',
zorder=-1,
vmin=self.zlim[0],
vmax=self.zlim[1],
rstride=1,
cstride=1)
# ax.plot_wireframe(x_mesh, y_mesh, -z_mesh, alpha=1, linewidth=0.05, color='black', rstride=1, cstride=1)
pass
# Lagrange points and bodies
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
for idx, lagrange_point_nr in enumerate(lagrange_point_nrs):
ax.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x',
zorder=idx)
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
bodies_df = load_bodies_location()
for idx, body in enumerate(bodies_df):
x = bodies_df[body]['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
ax.plot_surface(x, y, z, color='black', zorder=2 + idx)
ax.plot([-self.massParameter, 1 - self.massParameter], [0, 0],
color='black')
ax.set_xlim(self.xlim)
ax.set_ylim(self.ylim)
ax.set_zlim(self.zlim)
# ax.set_title(str(azim))
plt.axis('off')
plt.show()
pass
def plot(self):
colors = sns.color_palette("Blues", n_colors=6)
# Plot: 3d overview
fig = plt.figure(figsize=(7 * (1 + np.sqrt(5)) / 2, 7))
ax = fig.gca(projection='3d')
# Plot both primaries
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
bodies_df = load_bodies_location()
for body in bodies_df:
x = bodies_df[body]['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
ax.plot_surface(x, y, z, color='black')
# Plot Lagrange points 1 and 2
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
for lagrange_point_nr in lagrange_point_nrs:
ax.scatter3D(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x',
s=50)
# ax.annotate('Moon', xy=(-0.002,0.004),
# xytext=(-0.002, 0.04), fontsize=20, ha = 'center', va = 'top',
# arrowprops=dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'),
# )
# ax.annotate('$L_1$', xy=(-0.023, 0.012),
# xytext=(-0.023, 0.04), fontsize=20, ha='center', va='top',
# arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0'),
# )
# ax.annotate('$L_2$', xy=(0.023, -0.004),
# xytext=(0.023, 0.04), fontsize=20, ha='center', va='top',
# arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0'),
# )
# params = {'legend.fontsize': 16}
# plt.rcParams.update(params)
C = 3.1
# x_range = np.arange(0.7, 1.3, 0.001)
# y_range = np.arange(-0.3, 0.3, 0.001)
x_range = np.arange(0.8, 1.2, 0.001)
y_range = np.arange(-0.2, 0.2, 0.001)
X, Y = np.meshgrid(x_range, y_range)
Z = cr3bp_velocity(X, Y, C)
if Z.min() < 0:
plt.contourf(X, Y, Z, 0, colors='black', alpha=0.05, zorder=1000)
linewidth = 2
df = load_orbit('../../data/raw_equal_energy/horizontal_L1_577.txt')
ax.plot(df['x'],
df['y'],
df['z'],
color=sns.color_palette("viridis", 3)[0],
alpha=0.75,
linestyle='-',
label='Horizontal Lyapunov',
linewidth=linewidth)
df = load_orbit('../../data/raw_equal_energy/halo_L1_799.txt')
ax.plot(df['x'],
df['y'],
df['z'],
color=sns.color_palette("viridis", 3)[2],
alpha=0.75,
linestyle='-',
label='Halo',
linewidth=linewidth)
df = load_orbit('../../data/raw_equal_energy/vertical_L1_1163.txt')
ax.plot(df['x'],
df['y'],
df['z'],
color=sns.color_palette("viridis", 3)[1],
alpha=0.75,
linestyle='-',
label='Vertical Lyapunov',
linewidth=linewidth)
ax.legend(frameon=True, loc='lower right')
df = load_orbit('../../data/raw_equal_energy/horizontal_L2_760.txt')
ax.plot(df['x'],
df['y'],
df['z'],
color=sns.color_palette("viridis", 3)[0],
alpha=0.75,
linestyle='-',
linewidth=linewidth)
df = load_orbit('../../data/raw_equal_energy/vertical_L2_1299.txt')
ax.plot(df['x'],
df['y'],
df['z'],
color=sns.color_palette("viridis", 3)[1],
alpha=0.75,
linestyle='-',
linewidth=linewidth)
df = load_orbit('../../data/raw_equal_energy/halo_L2_651.txt')
ax.plot(df['x'],
df['y'],
df['z'],
color=sns.color_palette("viridis", 3)[2],
alpha=0.75,
linestyle='-',
linewidth=linewidth)
ax.set_xlabel('x [-]')
ax.set_ylabel('y [-]')
ax.set_zlabel('z [-]')
ax.grid(True, which='both', ls=':')
# ax.view_init(25, -60)
ax.view_init(20, -60)
# ax.set_xlim([0.7, 1.3])
# ax.set_ylim([-0.3, 0.3])
# ax.set_zlim([-0.3, 0.3])
ax.set_xlim([0.8, 1.2])
ax.set_ylim([-0.2, 0.2])
ax.set_zlim([-0.2, 0.2])
plt.tight_layout()
# plt.show()
# fig.savefig('../../../data/figures/family_of_equal_energy.png')
if self.lowDPI:
fig.savefig('../../data/figures/new_family_of_equal_energy.png',
transparent=True,
dpi=self.dpi)
else:
fig.savefig('../../data/figures/new_family_of_equal_energy.pdf',
transparent=True)
# tikz_save('../../../data/figures/family_of_equal_energy.tex')
plt.close()
pass
def plot_image_trajectories_with_angle(self, theta):
line_width_near_heteroclinic = 2
print('Theta:')
# for theta in self.thetaRangeList:
print(theta)
df_s = load_manifold_refactored('../../data/raw/poincare_sections/' +
str(self.numberOfOrbitsPerManifold) +
'/L2_' + self.orbitType +
'_W_S_min_3.1_' + str(int(theta)) +
'_full.txt')
df_u = load_manifold_refactored('../../data/raw/poincare_sections/' +
str(self.numberOfOrbitsPerManifold) +
'/L1_' + self.orbitType +
'_W_U_plus_3.1_' + str(int(theta)) +
'_full.txt')
fig = plt.figure(figsize=self.figSize)
ax0 = fig.add_subplot(111, projection='3d')
plot_alpha = 1
# Plot near-heteroclinic connection
index_near_heteroclinic_s = int(
self.minimumImpulse.loc[theta]['taus'] *
self.numberOfOrbitsPerManifold)
index_near_heteroclinic_u = int(
self.minimumImpulse.loc[theta]['tauu'] *
self.numberOfOrbitsPerManifold)
portrait_s = []
portrait_u = []
for i in range(0, 5000, 10):
portrait_s.append(df_s.xs(i).head(1))
portrait_u.append(df_u.xs(i).tail(1))
pass
portrait_s = pd.concat(portrait_s)
portrait_u = pd.concat(portrait_u)
plt.plot(portrait_s['x'],
portrait_s['y'],
portrait_s['z'],
color='g',
linewidth=0.5)
plt.plot(portrait_u['x'],
portrait_u['y'],
portrait_u['z'],
color='r',
linewidth=0.5)
# for i in range(0, 5000, 10):
# ax0.scatter(df_s.xs(i).head(1)['x'], df_s.xs(i).head(1)['y'],
# df_s.xs(i).head(1)['z'], color='g', s=0.1)
# ax0.scatter(df_u.xs(i).tail(1)['x'], df_u.xs(i).tail(1)['y'],
# df_u.xs(i).tail(1)['z'], color='r', s=0.1)
# (T1)
ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'],
df_s.xs(index_near_heteroclinic_s)['y'],
df_s.xs(index_near_heteroclinic_s)['z'],
color='g',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'],
df_u.xs(index_near_heteroclinic_u)['y'],
df_u.xs(index_near_heteroclinic_u)['z'],
color='r',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
# # (T4)
# ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'], -df_s.xs(index_near_heteroclinic_s)['y'], df_s.xs(index_near_heteroclinic_s)['z'], color='r', alpha=plot_alpha, linewidth=line_width_near_heteroclinic)
# ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'], -df_u.xs(index_near_heteroclinic_u)['y'], df_u.xs(index_near_heteroclinic_u)['z'], color='g', alpha=plot_alpha, linewidth=line_width_near_heteroclinic)
#
# # (T3)
# ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'], df_s.xs(index_near_heteroclinic_s)['y'],
# -df_s.xs(index_near_heteroclinic_s)['z'], color='g', alpha=plot_alpha,
# linewidth=line_width_near_heteroclinic)
# ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'], df_u.xs(index_near_heteroclinic_u)['y'],
# -df_u.xs(index_near_heteroclinic_u)['z'], color='r', alpha=plot_alpha,
# linewidth=line_width_near_heteroclinic)
# # (T2)
# ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'], -df_s.xs(index_near_heteroclinic_s)['y'],
# -df_s.xs(index_near_heteroclinic_s)['z'], color='r', alpha=plot_alpha,
# linewidth=line_width_near_heteroclinic)
# ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'], -df_u.xs(index_near_heteroclinic_u)['y'],
# -df_u.xs(index_near_heteroclinic_u)['z'], color='g', alpha=plot_alpha,
# linewidth=line_width_near_heteroclinic)
bodies_df = load_bodies_location()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
# for body in ['Moon']:
for body in ['Earth', 'Moon']:
x = bodies_df[body]['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
ax0.plot_surface(x, y, z, color='black')
# Lagrange points and bodies
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
for lagrange_point_nr in lagrange_point_nrs:
ax0.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
# Create cubic bounding box to simulate equal aspect ratio
max_range = np.array([
max(df_s['x'].max(), df_u['x'].max()) -
min(df_s['x'].min(), df_u['x'].min()),
max(df_s['y'].max(), df_u['y'].max()) -
min(df_s['y'].min(), df_u['y'].min()),
max(df_s['z'].max(), df_u['z'].max()) -
min(df_s['z'].min(), df_u['z'].min())
]).max()
Xb = 0.3 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][0].flatten(
) + 0.2 * (max(df_s['x'].max(), df_u['x'].max()) +
min(df_s['x'].min(), df_u['x'].min()))
Yb = 0.3 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][1].flatten(
) + 0.5 * (max(df_s['y'].max(), df_u['y'].max()) +
min(df_s['y'].min(), df_u['y'].min()))
Zb = 0.3 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][2].flatten(
) + 0.5 * (max(df_s['z'].max(), df_u['z'].max()) +
min(df_s['z'].min(), df_u['z'].min()))
# Comment or uncomment following both lines to test the fake bounding box:
if self.orbitType != 'halo':
for xb, yb, zb in zip(Xb, Yb, Zb):
ax0.plot([xb], [yb], [zb], 'w')
arc_length = 0.2
surface_alpha = 0.1
surface_color = 'black'
x_range = np.arange(1 - self.massParameter - arc_length * 0.75,
1 - self.massParameter, 0.001)
z_range = np.arange(-arc_length * 0.75, arc_length * 0.75, 0.001)
x_mesh, z_mesh = np.meshgrid(x_range, z_range)
y_mesh = -abs(x_mesh -
(1 - self.massParameter)) / np.tan(35 * np.pi / 180)
# Plot poincare plane
ax0.plot_surface(x_mesh,
y_mesh,
z_mesh,
alpha=surface_alpha,
color=surface_color)
ax0.plot_wireframe(x_mesh,
y_mesh,
z_mesh,
color=surface_color,
rstride=500,
cstride=500,
linewidth=1)
# Plot line at angle
plt.plot(
[1 - self.massParameter, np.min(x_mesh)], [0, np.min(y_mesh)],
[0, 0],
color='k',
linestyle=':',
linewidth=1)
# Plot line orthogonal to collinear points
plt.plot([1 - self.massParameter, 1 - self.massParameter],
[0, np.min(y_mesh)], [0, 0],
color='k',
linestyle=':',
linewidth=1)
# Plot line from primary to L2
plt.plot([-self.massParameter, lagrange_points_df['L2']['x']], [0, 0],
[0, 0],
color='k',
linestyle=':',
linewidth=1)
# Indicate connection on plane
ax0.scatter(df_u.xs(index_near_heteroclinic_u).tail(1)['x'],
df_u.xs(index_near_heteroclinic_u).tail(1)['y'],
df_u.xs(index_near_heteroclinic_u).tail(1)['z'],
s=20,
linewidth=line_width_near_heteroclinic,
facecolors='none',
edgecolors='r')
# Set viewpoint
ax0.set_xlim(lagrange_points_df['L1']['x'],
lagrange_points_df['L2']['x'])
ax0.set_ylim(-0.15, 0.05)
ax0.set_zlim(-0.1, 0.1)
print(ax0.azim)
print(ax0.elev)
# ax0.view_init(elev=15, azim=220) # Single line
ax0.view_init(elev=5, azim=220) # View from Earth
# ax0.view_init(elev=5, azim=340) # View from outside
plt.tight_layout()
fig.subplots_adjust(right=1.1)
plt.axis('off')
# plt.show()
plt.savefig('../../data/figures/cover_page_angle.pdf',
transparent=True)
plt.close()
pass
def plot_image_trajectories(self, theta):
line_width_near_heteroclinic = 3
print('Theta:')
# for theta in self.thetaRangeList:
print(theta)
df_s = load_manifold_refactored('../../data/raw/poincare_sections/' +
str(self.numberOfOrbitsPerManifold) +
'/L2_' + self.orbitType +
'_W_S_min_3.1_' + str(int(theta)) +
'_full.txt')
df_u = load_manifold_refactored('../../data/raw/poincare_sections/' +
str(self.numberOfOrbitsPerManifold) +
'/L1_' + self.orbitType +
'_W_U_plus_3.1_' + str(int(theta)) +
'_full.txt')
print(df_s)
fig = plt.figure(figsize=self.figSize)
ax0 = fig.add_subplot(111, projection='3d')
plot_alpha = 1
# Plot near-heteroclinic connection
index_near_heteroclinic_s = int(
self.minimumImpulse.loc[theta]['taus'] *
self.numberOfOrbitsPerManifold)
index_near_heteroclinic_u = int(
self.minimumImpulse.loc[theta]['tauu'] *
self.numberOfOrbitsPerManifold)
# for i in range(0, 5000, 50):
# ax0.plot(df_s.xs(i)['x'], df_s.xs(i)['y'],
# df_s.xs(i)['z'], color='g', alpha=plot_alpha,
# linewidth=0.5)
# ax0.plot(df_u.xs(i)['x'], df_u.xs(i)['y'],
# df_u.xs(i)['z'], color='r', alpha=plot_alpha,
# linewidth=0.5)
# (T1)
ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'],
df_s.xs(index_near_heteroclinic_s)['y'],
df_s.xs(index_near_heteroclinic_s)['z'],
color='g',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'],
df_u.xs(index_near_heteroclinic_u)['y'],
df_u.xs(index_near_heteroclinic_u)['z'],
color='r',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
# # (T4)
# ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'], -df_s.xs(index_near_heteroclinic_s)['y'], df_s.xs(index_near_heteroclinic_s)['z'], color='r', alpha=plot_alpha, linewidth=line_width_near_heteroclinic)
# ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'], -df_u.xs(index_near_heteroclinic_u)['y'], df_u.xs(index_near_heteroclinic_u)['z'], color='g', alpha=plot_alpha, linewidth=line_width_near_heteroclinic)
#
# # (T3)
# ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'], df_s.xs(index_near_heteroclinic_s)['y'],
# -df_s.xs(index_near_heteroclinic_s)['z'], color='g', alpha=plot_alpha,
# linewidth=line_width_near_heteroclinic)
# ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'], df_u.xs(index_near_heteroclinic_u)['y'],
# -df_u.xs(index_near_heteroclinic_u)['z'], color='r', alpha=plot_alpha,
# linewidth=line_width_near_heteroclinic)
# # (T2)
# ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'], -df_s.xs(index_near_heteroclinic_s)['y'],
# -df_s.xs(index_near_heteroclinic_s)['z'], color='r', alpha=plot_alpha,
# linewidth=line_width_near_heteroclinic)
# ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'], -df_u.xs(index_near_heteroclinic_u)['y'],
# -df_u.xs(index_near_heteroclinic_u)['z'], color='g', alpha=plot_alpha,
# linewidth=line_width_near_heteroclinic)
bodies_df = load_bodies_location()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
# for body in ['Earth', 'Moon']:
for body in ['Moon']:
x = bodies_df[body]['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
ax0.plot_surface(x, y, z, color='black')
# Lagrange points and bodies
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
for lagrange_point_nr in lagrange_point_nrs:
ax0.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
# Create cubic bounding box to simulate equal aspect ratio
max_range = np.array([
max(df_s['x'].max(), df_u['x'].max()) -
min(df_s['x'].min(), df_u['x'].min()),
max(df_s['y'].max(), df_u['y'].max()) -
min(df_s['y'].min(), df_u['y'].min()),
max(df_s['z'].max(), df_u['z'].max()) -
min(df_s['z'].min(), df_u['z'].min())
]).max()
Xb = 0.3 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][0].flatten(
) + 0.2 * (max(df_s['x'].max(), df_u['x'].max()) +
min(df_s['x'].min(), df_u['x'].min()))
Yb = 0.3 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][1].flatten(
) + 0.5 * (max(df_s['y'].max(), df_u['y'].max()) +
min(df_s['y'].min(), df_u['y'].min()))
Zb = 0.3 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][2].flatten(
) + 0.5 * (max(df_s['z'].max(), df_u['z'].max()) +
min(df_s['z'].min(), df_u['z'].min()))
# Comment or uncomment following both lines to test the fake bounding box:
if self.orbitType != 'halo':
for xb, yb, zb in zip(Xb, Yb, Zb):
ax0.plot([xb], [yb], [zb], 'w')
# azim=150
# elev=25
print(ax0.azim)
print(ax0.elev)
ax0.view_init(elev=15, azim=220) # Single line
# ax0.view_init(elev=20, azim=240) # Manifold lines
plt.tight_layout()
plt.axis('off')
# plt.show()
plt.savefig('../../data/figures/cover_page.pdf', transparent=True)
plt.close()
pass
def animate(self):
fig = plt.figure()
self.ax = fig.add_subplot(111, projection='3d')
self.horizontalLyapunov = [
load_orbit('../../../data/raw/orbits/L' + str(1) + '_horizontal_' +
str(self.orbitIds['horizontal'][1][self.cLevel]) +
'_100.txt'),
load_orbit('../../../data/raw/orbits/L' + str(2) + '_horizontal_' +
str(self.orbitIds['horizontal'][2][self.cLevel]) +
'_100.txt')
]
self.verticalLyapunov = [
load_orbit('../../../data/raw/orbits/L' + str(1) + '_vertical_' +
str(self.orbitIds['vertical'][1][self.cLevel]) +
'_100.txt'),
load_orbit('../../../data/raw/orbits/L' + str(2) + '_vertical_' +
str(self.orbitIds['vertical'][2][self.cLevel]) +
'_100.txt')
]
self.halo = [
load_orbit('../../../data/raw/orbits/L' + str(1) + '_halo_' +
str(self.orbitIds['halo'][1][self.cLevel]) +
'_100.txt'),
load_orbit('../../../data/raw/orbits/L' + str(2) + '_halo_' +
str(self.orbitIds['halo'][2][self.cLevel]) + '_100.txt')
]
self.lines = [
plt.plot([], [],
color=self.orbitColor,
alpha=self.orbitAlpha,
marker='o',
markevery=[-1])[0] for idx in range(6)
]
# Text object to display absolute normalized time of trajectories within the manifolds
self.timeText = self.ax.text2D(0.05,
0.05,
s='$\|t\| \\approx 0$',
transform=self.ax.transAxes,
size=self.timeTextSize)
# Plot zero velocity surface
x_range = np.arange(self.xLim[0], self.xLim[1], 0.001)
y_range = np.arange(self.yLim[0], self.yLim[1], 0.001)
x_mesh, y_mesh = np.meshgrid(x_range, y_range)
z_mesh = cr3bp_velocity(x_mesh, y_mesh, c_level)
if z_mesh.min() < 0:
plt.contour(x_mesh,
y_mesh,
z_mesh, [z_mesh.min(), 0],
colors='black',
alpha=0.3)
# Plot both orbits
for k in range(2):
plt.plot(self.horizontalLyapunov[k]['x'],
self.horizontalLyapunov[k]['y'],
self.horizontalLyapunov[k]['z'],
color=self.orbitColor,
alpha=self.orbitAlpha,
linewidth=self.orbitLinewidth,
linestyle=':')
plt.plot(self.verticalLyapunov[k]['x'],
self.verticalLyapunov[k]['y'],
self.verticalLyapunov[k]['z'],
color=self.orbitColor,
alpha=self.orbitAlpha,
linewidth=self.orbitLinewidth,
linestyle=':')
plt.plot(self.halo[k]['x'],
self.halo[k]['y'],
self.halo[k]['z'],
color=self.orbitColor,
alpha=self.orbitAlpha,
linewidth=self.orbitLinewidth,
linestyle=':')
# Plot both primaries
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
bodies_df = load_bodies_location()
for body in bodies_df:
x = bodies_df[body]['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
self.ax.plot_surface(x, y, z, color='black')
# Plot Lagrange points 1 and 2
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
for lagrange_point_nr in lagrange_point_nrs:
self.ax.scatter3D(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x',
s=self.lagrangePointMarkerSize)
title = 'Types of periodic libration point motion - Rotating spatial overview at C = ' + str(
c_level)
self.ax.set_xlim3d(self.xLim)
self.ax.set_ylim3d(self.yLim)
self.ax.set_zlim3d(self.zLim)
self.ax.set_xlabel('x [-]')
self.ax.set_ylabel('y [-]')
self.ax.set_zlabel('z [-]')
self.ax.grid(True, which='both', ls=':')
fig.tight_layout()
fig.subplots_adjust(top=0.9)
plt.suptitle(title, size=self.suptitleSize)
# Fix overlap between labels and ticks
self.ax.xaxis._axinfo['label']['space_factor'] = 2.0
self.ax.yaxis._axinfo['label']['space_factor'] = 2.0
self.ax.zaxis._axinfo['label']['space_factor'] = 2.0
self.initialElevation = self.ax.elev
self.initialAzimuth = self.ax.azim
# Determine the maximum value of t
t_max = 0
for lagrange_point_idx in [0, 1]:
t_max = max(
t_max, self.horizontalLyapunov[lagrange_point_idx].tail(1)
['time'].values[0])
t_max = max(
t_max, self.verticalLyapunov[lagrange_point_idx].tail(1)
['time'].values[0])
t_max = max(
t_max, self.halo[lagrange_point_idx].tail(1)['time'].values[0])
print('Maximum value for t = ' + str(t_max) + ', animation t: = ')
# Introduce a new time-vector for linearly spaced time throughout the animation
self.t = np.linspace(0, t_max, np.round(t_max / 0.005) + 1)
animation_function = animation.FuncAnimation(
fig,
self.update_lines,
init_func=self.initiate_lines,
frames=len(self.t),
interval=1,
blit=True)
empty_writer_object = animation.writers['ffmpeg']
animation_writer = empty_writer_object(
fps=30, metadata=dict(artist='Koen Langemeijer'))
file_name = '../../../data/animations/orbits/spatial_orbits_rotating_' + str(
c_level) + '.mp4'
animation_function.save(file_name, writer=animation_writer)
def plot_image_trajectories(self):
line_width_near_heteroclinic = 1.5
print('Theta:')
for theta in self.thetaRangeList:
print(theta)
df_s = load_manifold_refactored(
'../../data/raw/poincare_sections/' +
str(self.numberOfOrbitsPerManifold) + '/L2_' + self.orbitType +
'_W_S_min_3.1_' + str(int(theta)) + '_full.txt')
df_u = load_manifold_refactored(
'../../data/raw/poincare_sections/' +
str(self.numberOfOrbitsPerManifold) + '/L1_' + self.orbitType +
'_W_U_plus_3.1_' + str(int(theta)) + '_full.txt')
fig = plt.figure(figsize=self.figSize)
ax0 = fig.add_subplot(111, projection='3d')
if self.numberOfOrbitsPerManifold > 100:
# Plot at max 100 lines
range_step_size = int(self.numberOfOrbitsPerManifold / 100)
else:
range_step_size = 1
plot_alpha = 1
line_width = 0.5
# Plot near-heteroclinic connection
try:
index_near_heteroclinic_s = int(
self.minimumImpulse.loc[theta]['tau1'] *
self.numberOfOrbitsPerManifold)
index_near_heteroclinic_u = int(
self.minimumImpulse.loc[theta]['tau2'] *
self.numberOfOrbitsPerManifold)
# (T1)
ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'],
df_s.xs(index_near_heteroclinic_s)['y'],
df_s.xs(index_near_heteroclinic_s)['z'],
color='g',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'],
df_u.xs(index_near_heteroclinic_u)['y'],
df_u.xs(index_near_heteroclinic_u)['z'],
color='r',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
# (T4)
ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'],
-df_s.xs(index_near_heteroclinic_s)['y'],
df_s.xs(index_near_heteroclinic_s)['z'],
color='r',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'],
-df_u.xs(index_near_heteroclinic_u)['y'],
df_u.xs(index_near_heteroclinic_u)['z'],
color='g',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
if orbit_type != 'horizontal':
# (T3)
ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'],
df_s.xs(index_near_heteroclinic_s)['y'],
-df_s.xs(index_near_heteroclinic_s)['z'],
color='g',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'],
df_u.xs(index_near_heteroclinic_u)['y'],
-df_u.xs(index_near_heteroclinic_u)['z'],
color='r',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
# (T2)
ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'],
-df_s.xs(index_near_heteroclinic_s)['y'],
-df_s.xs(index_near_heteroclinic_s)['z'],
color='r',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'],
-df_u.xs(index_near_heteroclinic_u)['y'],
-df_u.xs(index_near_heteroclinic_u)['z'],
color='g',
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
pass
connection_text = '$min(\Delta r) \quad \\forall \enskip \Delta V < 0.5$ \n' + \
'$\Delta V = \enskip $' + str(np.round(self.minimumImpulse.loc[theta]['dv'], 1)) + '\n' + \
'$\Delta r = \enskip $' + str(np.round(self.minimumImpulse.loc[theta]['dr'], 1))
ax0.text2D(0.0,
0.8,
s=connection_text,
horizontalalignment='left',
verticalalignment='bottom',
transform=ax0.transAxes,
bbox=dict(boxstyle="round", fc="w"))
except KeyError:
pass
bodies_df = load_bodies_location()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = bodies_df['Moon']['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df['Moon']['x']
y = bodies_df['Moon']['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df['Moon']['r'] * np.outer(np.ones(np.size(u)),
np.cos(v))
ax0.plot_surface(x, y, z, color='black')
# Create cubic bounding box to simulate equal aspect ratio
max_range = np.array([
max(df_s['x'].max(), df_u['x'].max()) -
min(df_s['x'].min(), df_u['x'].min()),
max(df_s['y'].max(), df_u['y'].max()) -
min(df_s['y'].min(), df_u['y'].min()),
max(df_s['z'].max(), df_u['z'].max()) -
min(df_s['z'].min(), df_u['z'].min())
]).max()
Xb = 0.5 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][0].flatten(
) + 0.5 * (max(df_s['x'].max(), df_u['x'].max()) +
min(df_s['x'].min(), df_u['x'].min()))
Yb = 0.5 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][1].flatten(
) + 0.5 * (max(df_s['y'].max(), df_u['y'].max()) +
min(df_s['y'].min(), df_u['y'].min()))
Zb = 0.5 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][2].flatten(
) + 0.5 * (max(df_s['z'].max(), df_u['z'].max()) +
min(df_s['z'].min(), df_u['z'].min()))
# Comment or uncomment following both lines to test the fake bounding box:
for xb, yb, zb in zip(Xb, Yb, Zb):
ax0.plot([xb], [yb], [zb], 'w')
ax0.set_xlabel('x [-]')
ax0.set_ylabel('y [-]')
ax0.set_zlabel('z [-]')
ax0.grid(True, which='both', ls=':')
fig.tight_layout()
fig.subplots_adjust(top=0.9)
plt.suptitle(
self.orbitTypeForTitle +
' near-heteroclinic cycle $\mathcal{W}^{U+} \cup \mathcal{W}^{S-}$ (C = 3.1, $\\theta$ = '
+ str(theta) + '$^\circ$)',
size=self.suptitleSize)
# plt.show()
plt.savefig('../../data/figures/poincare_sections/' +
str(self.numberOfOrbitsPerManifold) + '/' +
self.orbitType + '_3.1_heteroclinic_cycle_' +
str(theta) + '.pdf',
transparent=True)
plt.close()
pass
def plot_family(self):
c_normalized = [(value - min(self.C)) / (max(self.C) - min(self.C))
for value in self.C]
colors = matplotlib.colors.ListedColormap(
sns.color_palette("viridis_r"))(c_normalized)
# colors = matplotlib.colors.ListedColormap(sns.dark_palette("blue", reverse=True))(c_normalized)
sm = plt.cm.ScalarMappable(cmap=matplotlib.colors.ListedColormap(
sns.color_palette("viridis", len(self.C))),
norm=plt.Normalize(vmin=min(self.C),
vmax=max(self.C)))
# sm = plt.cm.ScalarMappable(cmap=sns.dark_palette("blue", as_cmap=True, reverse=True), norm=plt.Normalize(vmin=min(self.C), vmax=max(self.C)))
# clean the array of the scalar mappable
sm._A = []
# Plot 1: 3d overview
fig1 = plt.figure(figsize=self.figSize)
ax1 = fig1.gca()
# Plot 2: subplots
if self.orbitType == 'horizontal':
fig2 = plt.figure(figsize=(self.figSize[0], self.figSize[1] / 2))
ax2 = fig2.add_subplot(1, 2, 1, projection='3d')
ax5 = fig2.add_subplot(1, 2, 2)
else:
fig2 = plt.figure(figsize=self.figSize)
ax2 = fig2.add_subplot(2, 2, 1, projection='3d')
ax3 = fig2.add_subplot(2, 2, 4)
ax4 = fig2.add_subplot(2, 2, 3)
ax5 = fig2.add_subplot(2, 2, 2)
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
# Lagrange points and bodies
for lagrange_point_nr in lagrange_point_nrs:
ax1.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
color='black',
marker='x')
ax2.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax5.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
color='black',
marker='x')
if self.orbitType != 'horizontal':
ax3.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax4.scatter(lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
bodies_df = load_bodies_location()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = bodies_df['Moon']['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df['Moon']['x']
y = bodies_df['Moon']['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df['Moon']['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
ax1.contourf(x, y, z, colors='black')
ax2.plot_surface(x, y, z, color='black')
ax5.contourf(x, y, z, colors='black')
if self.orbitType != 'horizontal':
ax3.contourf(x, z, y, colors='black')
ax4.contourf(y, z, x, colors='black')
# Determine color for plot
# colorOrderOfLinearInstability = ['whitesmoke', 'silver', 'dimgrey']
plot_alpha = 1
line_width = 0.5
# Plot every 100th member, including the ultimate member of the family
spacing_factor = 100
orbitIdsPlot = list(range(0, len(self.C) - 1, spacing_factor))
if orbitIdsPlot[-1] != len(self.C) - 1:
orbitIdsPlot.append(len(self.C) - 1)
# Plot orbits
for i in orbitIdsPlot:
# plot_color = colorOrderOfLinearInstability[self.orderOfLinearInstability[i]]
nan_correction = sum(
[1 for nan in self.indexNanEntries if nan < i])
plot_color = colors[self.plotColorIndexBasedOnC[i -
nan_correction]]
df = load_orbit('../../data/raw/orbits/extended/L' +
str(self.lagrangePointNr) + '_' + self.orbitType +
'_' + str(i) + '.txt')
ax1.plot(df['x'],
df['y'],
color=plot_color,
alpha=plot_alpha,
linewidth=line_width)
ax2.plot(df['x'],
df['y'],
df['z'],
color=plot_color,
alpha=plot_alpha,
linewidth=line_width)
ax5.plot(df['x'],
df['y'],
color=plot_color,
alpha=plot_alpha,
linewidth=line_width)
if self.orbitType != 'horizontal':
ax3.plot(df['x'],
df['z'],
color=plot_color,
alpha=plot_alpha,
linewidth=line_width)
ax4.plot(df['y'],
df['z'],
color=plot_color,
alpha=plot_alpha,
linewidth=line_width)
# # Plot the bifurcations
# for i in self.orbitIdBifurcations:
# # plot_color = 'b'
# nan_correction = sum([1 for nan in self.indexNanEntries if nan < i])
# plot_color = colors[self.plotColorIndexBasedOnC[i - nan_correction]]
# df = load_orbit('../../data/raw/orbits/extended/L' + str(self.lagrangePointNr) + '_' + self.orbitType + '_' + str(i) + '.txt')
# ax1.plot(df['x'], df['y'], color=plot_color, linewidth=3)
# ax2.plot(df['x'], df['y'], df['z'], color=plot_color, linewidth=3)
# ax5.plot(df['x'], df['y'], color=plot_color, linewidth=3)
# if self.orbitType != 'horizontal':
# ax3.plot(df['x'], df['z'], color=plot_color, linewidth=3)
# ax4.plot(df['y'], df['z'], color=plot_color, linewidth=3)
ax1.set_xlabel('x [-]')
ax1.set_ylabel('y [-]')
ax1.grid(True, which='both', ls=':')
ax2.set_xlabel('x [-]')
ax2.set_ylabel('y [-]')
ax2.set_zlabel('z [-]')
ax2.set_zlim([-1.2, 1.2])
ax2.grid(True, which='both', ls=':')
ax2.view_init(30, -120)
if self.orbitType != 'horizontal':
ax3.set_xlabel('x [-]')
ax3.set_ylabel('z [-]')
ax3.set_ylim([-1.2, 1.2])
ax3.grid(True, which='both', ls=':')
ax4.set_xlabel('y [-]')
ax4.set_ylabel('z [-]')
ax4.set_ylim([-1.2, 1.2])
ax4.grid(True, which='both', ls=':')
ax5.set_xlabel('x [-]')
ax5.set_ylabel('y [-]')
ax5.grid(True, which='both', ls=':')
fig2.tight_layout()
if self.orbitType == 'horizontal':
fig2.subplots_adjust(top=0.8)
else:
fig2.subplots_adjust(top=0.9)
if self.orbitType != 'horizontal':
cax, kw = matplotlib.colorbar.make_axes([ax2, ax3, ax4, ax5])
else:
cax, kw = matplotlib.colorbar.make_axes([ax2, ax5])
cbar = plt.colorbar(sm, cax=cax, label='C [-]', **kw)
plt.suptitle('$L_' + str(self.lagrangePointNr) + '$ ' +
self.orbitTypeForTitle + ' - Orthographic projection',
size=self.suptitleSize)
fig1.suptitle('$L_' + str(self.lagrangePointNr) + '$ ' +
self.orbitTypeForTitle + ': family',
size=self.suptitleSize)
fig2.savefig('../../data/figures/orbits/extended/L' +
str(self.lagrangePointNr) + '_' + self.orbitType +
'_family_subplots.pdf',
transparent=True)
plt.close(fig2)
plt.close()
pass
def plot_manifolds(self):
line_width_near_heteroclinic = 2
color_near_heteroclinic = 'k'
print('Theta:')
for theta in self.thetaRangeList:
print(theta)
df_s = load_manifold_refactored(
'../../data/raw/poincare_sections/' +
str(self.numberOfOrbitsPerManifold) + '/L2_' + self.orbitType +
'_W_S_min_3.1_' + str(int(theta)) + '_full.txt')
df_u = load_manifold_refactored(
'../../data/raw/poincare_sections/' +
str(self.numberOfOrbitsPerManifold) + '/L1_' + self.orbitType +
'_W_U_plus_3.1_' + str(int(theta)) + '_full.txt')
fig = plt.figure(figsize=self.figSize)
ax0 = fig.add_subplot(2, 2, 1, projection='3d')
ax1 = fig.add_subplot(2, 2, 2)
ax3 = fig.add_subplot(2, 2, 3)
ax2 = fig.add_subplot(2, 2, 4)
# ax0.set_aspect('equal')
# ax1.set_aspect('equal')
# ax2.set_aspect('equal')
# ax3.set_aspect('equal')
if self.numberOfOrbitsPerManifold > 100:
# Plot at max 100 lines
range_step_size = int(self.numberOfOrbitsPerManifold / 100)
else:
range_step_size = 1
plot_alpha = 1
line_width = 0.5
for i in range(0, self.numberOfOrbitsPerManifold, range_step_size):
# Plot manifolds
ax0.plot(df_u.xs(i)['x'],
df_u.xs(i)['y'],
df_u.xs(i)['z'],
color=self.colorPaletteUnstable[i],
alpha=plot_alpha,
linewidth=line_width)
ax0.plot(df_s.xs(i)['x'],
df_s.xs(i)['y'],
df_s.xs(i)['z'],
color=self.colorPaletteStable[i],
alpha=plot_alpha,
linewidth=line_width)
ax1.plot(df_s.xs(i)['x'],
df_s.xs(i)['y'],
color=self.colorPaletteStable[i],
alpha=plot_alpha,
linewidth=line_width)
ax1.plot(df_u.xs(i)['x'],
df_u.xs(i)['y'],
color=self.colorPaletteUnstable[i],
alpha=plot_alpha,
linewidth=line_width)
ax2.plot(df_s.xs(i)['x'],
df_s.xs(i)['z'],
color=self.colorPaletteStable[i],
alpha=plot_alpha,
linewidth=line_width)
ax2.plot(df_u.xs(i)['x'],
df_u.xs(i)['z'],
color=self.colorPaletteUnstable[i],
alpha=plot_alpha,
linewidth=line_width)
ax3.plot(df_s.xs(i)['y'],
df_s.xs(i)['z'],
color=self.colorPaletteStable[i],
alpha=plot_alpha,
linewidth=line_width)
ax3.plot(df_u.xs(i)['y'],
df_u.xs(i)['z'],
color=self.colorPaletteUnstable[i],
alpha=plot_alpha,
linewidth=line_width)
# Plot near-heteroclinic connection
try:
index_near_heteroclinic_s = int(
self.minimumImpulse.loc[theta]['tau1'] *
self.numberOfOrbitsPerManifold)
index_near_heteroclinic_u = int(
self.minimumImpulse.loc[theta]['tau2'] *
self.numberOfOrbitsPerManifold)
ax0.plot(df_s.xs(index_near_heteroclinic_s)['x'],
df_s.xs(index_near_heteroclinic_s)['y'],
df_s.xs(index_near_heteroclinic_s)['z'],
color=color_near_heteroclinic,
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax0.plot(df_u.xs(index_near_heteroclinic_u)['x'],
df_u.xs(index_near_heteroclinic_u)['y'],
df_u.xs(index_near_heteroclinic_u)['z'],
color=color_near_heteroclinic,
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax1.plot(df_s.xs(index_near_heteroclinic_s)['x'],
df_s.xs(index_near_heteroclinic_s)['y'],
color=color_near_heteroclinic,
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax1.plot(df_u.xs(index_near_heteroclinic_u)['x'],
df_u.xs(index_near_heteroclinic_u)['y'],
color=color_near_heteroclinic,
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax2.plot(df_s.xs(index_near_heteroclinic_s)['x'],
df_s.xs(index_near_heteroclinic_s)['z'],
color=color_near_heteroclinic,
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax2.plot(df_u.xs(index_near_heteroclinic_u)['x'],
df_u.xs(index_near_heteroclinic_u)['z'],
color=color_near_heteroclinic,
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax3.plot(df_s.xs(index_near_heteroclinic_s)['y'],
df_s.xs(index_near_heteroclinic_s)['z'],
color=color_near_heteroclinic,
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
ax3.plot(df_u.xs(index_near_heteroclinic_u)['y'],
df_u.xs(index_near_heteroclinic_u)['z'],
color=color_near_heteroclinic,
alpha=plot_alpha,
linewidth=line_width_near_heteroclinic)
connection_text = '$\Delta \mathbf{V} = $' + str(np.round(self.minimumImpulse.loc[theta]['dv'], 1)) + 'm/s \n' + \
'$\Delta \mathbf{r} = $' + str(np.round(self.minimumImpulse.loc[theta]['dr'], 1)) + 'km'
ax1.text(0.975,
0.075,
connection_text,
horizontalalignment='right',
verticalalignment='bottom',
transform=ax1.transAxes,
bbox={
'facecolor': 'navy',
'alpha': 0.1,
'pad': 3
})
except KeyError:
pass
bodies_df = load_bodies_location()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = bodies_df['Moon']['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df['Moon']['x']
y = bodies_df['Moon']['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df['Moon']['r'] * np.outer(np.ones(np.size(u)),
np.cos(v))
ax0.plot_surface(x, y, z, color='black')
ax1.contourf(x, y, z, colors='black')
ax2.contourf(x, z, y, colors='black')
# ax3.contourf(y, z, x, colors='black')
# Create cubic bounding box to simulate equal aspect ratio
max_range = np.array([
max(df_s['x'].max(), df_u['x'].max()) -
min(df_s['x'].min(), df_u['x'].min()),
max(df_s['y'].max(), df_u['y'].max()) -
min(df_s['y'].min(), df_u['y'].min()),
max(df_s['z'].max(), df_u['z'].max()) -
min(df_s['z'].min(), df_u['z'].min())
]).max()
Xb = 0.5 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][0].flatten(
) + 0.5 * (max(df_s['x'].max(), df_u['x'].max()) +
min(df_s['x'].min(), df_u['x'].min()))
Yb = 0.5 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][1].flatten(
) + 0.5 * (max(df_s['y'].max(), df_u['y'].max()) +
min(df_s['y'].min(), df_u['y'].min()))
Zb = 0.5 * max_range * np.mgrid[-1:2:2, -1:2:2, -1:2:2][2].flatten(
) + 0.5 * (max(df_s['z'].max(), df_u['z'].max()) +
min(df_s['z'].min(), df_u['z'].min()))
# Comment or uncomment following both lines to test the fake bounding box:
for xb, yb, zb in zip(Xb, Yb, Zb):
ax0.plot([xb], [yb], [zb], 'w')
ax0.set_xlabel('x [-]')
ax0.set_ylabel('y [-]')
ax0.set_zlabel('z [-]')
ax1.set_xlabel('x [-]')
ax1.set_ylabel('y [-]')
ax2.set_xlabel('x [-]')
ax2.set_ylabel('z [-]')
ax3.set_xlabel('y [-]')
ax3.set_ylabel('z [-]')
ax0.grid(True, which='both', ls=':')
ax1.grid(True, which='both', ls=':')
ax2.grid(True, which='both', ls=':')
ax3.grid(True, which='both', ls=':')
fig.tight_layout()
fig.subplots_adjust(top=0.9)
plt.suptitle(
'Near-heteroclinic connection for $min(\Delta r) \enskip \\forall \Delta V < 0.5$ (at $\mathcal{W}^{U+} \cup \mathcal{W}^{S-}$, C = 3.1, $\\theta$ = '
+ str(theta) + '$^\circ$)',
size=self.suptitleSize)
# plt.show()
plt.savefig('../../data/figures/poincare_sections/' +
str(self.numberOfOrbitsPerManifold) + '/' +
self.orbitType + '_3.1_heteroclinic_connection_' +
str(theta) + '.pdf')
plt.close()
pass
def plot_result(self):
color_palette_green = sns.dark_palette(
'green', n_colors=self.numberOfOrbitsPerManifold)
color_palette_red = sns.dark_palette(
'red', n_colors=self.numberOfOrbitsPerManifold)
plt.figure(figsize=(5 * (1 + np.sqrt(5)) / 2, 5))
gs = gridspec.GridSpec(2, 2)
ax1 = plt.subplot(gs[0, :])
ax2 = plt.subplot(gs[1, 0])
ax3 = plt.subplot(gs[1, 1])
# Subplot 1: manifolds
for i in range(self.numberOfOrbitsPerManifold):
ax1.plot(self.WS.xs(i)['x'],
self.WS.xs(i)['y'],
color=color_palette_green[i],
alpha=0.5)
ax1.plot(self.WU.xs(i)['x'],
self.WU.xs(i)['y'],
color=color_palette_red[i],
alpha=0.5)
x_range = np.arange(ax1.get_xlim()[0], ax1.get_xlim()[1], 0.001)
y_range = np.arange(ax1.get_ylim()[0] * 1.2,
ax1.get_ylim()[1] * 1.2, 0.001)
X, Y = np.meshgrid(x_range, y_range)
Z = cr3bp_velocity(X, Y, self.C[0])
if Z.min() < 0:
ax1.contourf(X, Y, Z, [Z.min(), 0], colors='black', alpha=0.2)
if self.U_section == 2:
# ax1.axvline(1 - self.massParameter, color='black')
ax1.plot([1 - self.massParameter, 1 - self.massParameter],
[-0.11, 0.01],
color='black',
linewidth=3)
ax1.text(s='$\sum_2$', x=(1 - 0.5 * self.massParameter), y=0.01)
bodies_df = load_bodies_location()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = bodies_df['Moon']['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df['Moon']['x']
y = bodies_df['Moon']['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df['Moon']['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
# ax1.scatter(x, y, color='black', s=1)
ax1.contourf(x, y, z, [z.min(), 0], colors='black')
ax1.grid(True, which='both', ls=':')
ax1.set_title('$C_1 = ' + str(self.C[0]) + ', C_2 = ' +
str(self.C[1]) + '$')
ax1.set_aspect('equal', adjustable='box')
# Subplot 2: poincare
v_max = 2
if self.U_section in set([2, 3]):
variable_axis = 'y'
elif self.U_section in set([3, 4]):
variable_axis = 'x'
ax2.plot(
self.poincareWS[abs(self.poincareWS[variable_axis + 'dot']) <
v_max][variable_axis].values,
self.poincareWS[abs(self.poincareWS[variable_axis +
'dot']) < v_max][variable_axis
+
'dot'].values,
color='g')
ax2.plot(
self.poincareWU[abs(self.poincareWU[variable_axis + 'dot']) <
v_max][variable_axis].values,
self.poincareWU[abs(self.poincareWU[variable_axis +
'dot']) < v_max][variable_axis
+
'dot'].values,
color='r')
# Find entry of lowest difference in derivative of variable_axis (which is the variable with maximum spread in phase plane)
s = set(
np.round(self.poincareWS[variable_axis + 'dot'],
self.roundOrderConnection))
intersections = list(
s.intersection(
np.round(self.poincareWU[variable_axis + 'dot'],
self.roundOrderConnection)))
poincare_w_s_in_v = self.poincareWS[np.round(
self.poincareWS[variable_axis + 'dot'],
self.roundOrderConnection).isin(intersections)]
poincare_w_u_in_v = self.poincareWU[np.round(
self.poincareWU[variable_axis + 'dot'],
self.roundOrderConnection).isin(intersections)]
# Use tuples to bind pairs of position and velocity
subset = poincare_w_s_in_v[[variable_axis, variable_axis + 'dot']]
tuples_w_s_in_v = [
tuple(np.round(x, self.roundOrderConnection))
for x in subset.values
]
subset = poincare_w_u_in_v[[variable_axis, variable_axis + 'dot']]
tuples_w_u_in_v = [
tuple(np.round(x, self.roundOrderConnection))
for x in subset.values
]
s = set(tuples_w_s_in_v)
intersections = list(s.intersection(tuples_w_u_in_v))
for intersection in intersections:
poincare_temp = poincare_w_s_in_v[np.round(
poincare_w_s_in_v[variable_axis], self.roundOrderConnection) ==
intersection[0]]
poincare_temp = poincare_temp[np.round(
poincare_temp[variable_axis + 'dot'],
self.roundOrderConnection) == intersection[1]]
idx_s = int(poincare_temp.index.values)
poincare_temp = poincare_w_u_in_v[np.round(
poincare_w_u_in_v[variable_axis], self.roundOrderConnection) ==
intersection[0]]
poincare_temp = poincare_temp[np.round(
poincare_temp[variable_axis + 'dot'],
self.roundOrderConnection) == intersection[1]]
idx_u = int(poincare_temp.index.values)
ax2.scatter(self.poincareWS[variable_axis][idx_s],
self.poincareWS[variable_axis + 'dot'][idx_s],
color='black')
ax2.scatter(self.poincareWU[variable_axis][idx_u],
self.poincareWU[variable_axis + 'dot'][idx_u],
color='black')
ax1.plot(self.WS.xs(idx_s)['x'],
self.WS.xs(idx_s)['y'],
color='black')
ax1.plot(self.WU.xs(idx_u)['x'],
self.WU.xs(idx_u)['y'],
color='black')
ax2.set_xlabel('$' + variable_axis + '$')
ax2.set_ylabel('$\dot{' + variable_axis + '}$')
ax2.set_ylim([-1.5, 1.5])
ax2.grid(True, which='both', ls=':')
title = '$\sum_' + str(self.U_section) + '$'
ax2.set_title(title)
# Subplot 3: x error
# ax3.axhline(abs(self.poincareWS['y'][46] - self.poincareWU['y'][65]))
# ax3.axhline(abs(self.poincareWS['y'][37] - self.poincareWU['y'][77]))
# ax3.axhline(abs(self.poincareWS['ydot'][46] - self.poincareWU['ydot'][65]))
# ax3.axhline(abs(self.poincareWS['ydot'][37] - self.poincareWU['ydot'][77]))
if self.U_section == (2 or 3):
ax3.semilogy(abs((1 - self.massParameter) -
self.poincareWS['x'].values),
color='g')
ax3.semilogy(abs((1 - self.massParameter) -
self.poincareWU['x'].values),
color='r')
ax3.set_ylabel('$\| x - (1-\mu) \|$')
elif self.U_section == (1 or 4):
ax3.semilogy(abs(self.poincareWS['y'].values), color='g')
ax3.semilogy(abs(self.poincareWU['y'].values), color='r')
ax3.set_ylabel('$\| y \|$')
ax3.set_xlabel('orbitId [-]')
ax3.grid(True, which='both', ls=':')
plt.tight_layout()
# plt.savefig('../../data/figures/heteroclinic_connection.pdf')
# plt.savefig('../../data/figures/homoclinic_connection.pdf')
pass
def animate(self):
self.W_S_plus = [
load_manifold_refactored(
'../../../data/raw/manifolds/refined_for_c/L' + str(1) + '_' +
self.orbitType + '_' + str(self.orbitIds[0]) +
'_W_S_plus.txt'),
load_manifold_refactored(
'../../../data/raw/manifolds/refined_for_c/L' + str(2) + '_' +
self.orbitType + '_' + str(self.orbitIds[1]) + '_W_S_plus.txt')
]
self.W_S_min = [
load_manifold_refactored(
'../../../data/raw/manifolds/refined_for_c/L' + str(1) + '_' +
self.orbitType + '_' + str(self.orbitIds[0]) + '_W_S_min.txt'),
load_manifold_refactored(
'../../../data/raw/manifolds/refined_for_c/L' + str(2) + '_' +
self.orbitType + '_' + str(self.orbitIds[1]) + '_W_S_min.txt')
]
self.W_U_plus = [
load_manifold_refactored(
'../../../data/raw/manifolds/refined_for_c/L' + str(1) + '_' +
self.orbitType + '_' + str(self.orbitIds[0]) +
'_W_U_plus.txt'),
load_manifold_refactored(
'../../../data/raw/manifolds/refined_for_c/L' + str(2) + '_' +
self.orbitType + '_' + str(self.orbitIds[1]) + '_W_U_plus.txt')
]
self.W_U_min = [
load_manifold_refactored(
'../../../data/raw/manifolds/refined_for_c/L' + str(1) + '_' +
self.orbitType + '_' + str(self.orbitIds[0]) + '_W_U_min.txt'),
load_manifold_refactored(
'../../../data/raw/manifolds/refined_for_c/L' + str(2) + '_' +
self.orbitType + '_' + str(self.orbitIds[1]) + '_W_U_min.txt')
]
self.numberOfOrbitsPerManifold = len(
set(self.W_S_plus[0].index.get_level_values(0)))
color_palette_green = sns.dark_palette(
'green', n_colors=self.numberOfOrbitsPerManifold)
color_palette_red = sns.dark_palette(
'red', n_colors=self.numberOfOrbitsPerManifold)
self.lines = [
self.ax.plot([], [],
color=color_palette_red[idx],
alpha=self.orbitAlpha)[0]
for idx in range(self.numberOfOrbitsPerManifold)
]
self.lines.extend([
self.ax.plot([], [],
color=color_palette_green[idx],
alpha=self.orbitAlpha)[0]
for idx in range(self.numberOfOrbitsPerManifold)
])
self.lines.extend([
self.ax.plot([], [],
color=color_palette_red[idx],
alpha=self.orbitAlpha)[0]
for idx in range(self.numberOfOrbitsPerManifold)
])
self.lines.extend([
self.ax.plot([], [],
color=color_palette_green[idx],
alpha=self.orbitAlpha)[0]
for idx in range(self.numberOfOrbitsPerManifold)
])
self.lines.extend([
self.ax.plot([], [],
color=color_palette_red[idx],
alpha=self.orbitAlpha)[0]
for idx in range(self.numberOfOrbitsPerManifold)
])
self.lines.extend([
self.ax.plot([], [],
color=color_palette_green[idx],
alpha=self.orbitAlpha)[0]
for idx in range(self.numberOfOrbitsPerManifold)
])
self.lines.extend([
self.ax.plot([], [],
color=color_palette_green[idx],
alpha=self.orbitAlpha)[0]
for idx in range(self.numberOfOrbitsPerManifold)
])
self.lines.extend([
self.ax.plot([], [],
color=color_palette_red[idx],
alpha=self.orbitAlpha)[0]
for idx in range(self.numberOfOrbitsPerManifold)
])
# Text object to display absolute normalized time of trajectories within the manifolds
self.timeText = self.ax.text2D(0.05,
0.05,
s='$\|t\| \\approx 0$',
transform=self.ax.transAxes,
size=self.timeTextSize)
# Plot zero velocity surface
x_range = np.arange(self.xLim[0], self.xLim[1], 0.001)
y_range = np.arange(self.yLim[0], self.yLim[1], 0.001)
x_mesh, y_mesh = np.meshgrid(x_range, y_range)
z_mesh = cr3bp_velocity(x_mesh, y_mesh, self.cLevel)
if z_mesh.min() < 0:
self.ax.contour(x_mesh,
y_mesh,
z_mesh, [z_mesh.min(), 0],
colors='black',
alpha=0.3)
# Plot both orbits
for k in range(2):
orbit_df = load_orbit('../../../data/raw/orbits/refined_for_c/L' +
str(k + 1) + '_' + self.orbitType + '_' +
str(self.orbitIds[k]) + '.txt')
self.ax.plot(orbit_df['x'],
orbit_df['y'],
orbit_df['z'],
color=self.orbitColor,
alpha=self.orbitAlpha,
linewidth=self.orbitLinewidth)
# Plot both primaries
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
bodies_df = load_bodies_location()
for body in bodies_df:
x = bodies_df[body]['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
self.ax.plot_surface(x, y, z, color='black')
# Plot Lagrange points 1 and 2
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
for lagrange_point_nr in lagrange_point_nrs:
self.ax.scatter3D(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x',
s=self.lagrangePointMarkerSize)
title = self.orbitTypeForTitle + ' $\{ \mathcal{W}^{S \pm}, \mathcal{W}^{U \pm} \}$ - Orthographic projection (C = ' + str(
c_level) + ')'
# self.ax.set_xlim3d(self.xLim)
# self.ax.set_ylim3d(self.yLim)
# self.ax.set_zlim3d(self.zLim)
self.ax.set_xlim(self.xLim)
self.ax.set_ylim(self.yLim)
self.ax.set_zlim(self.zLim)
self.ax.axis('off')
# fig.tight_layout()
self.fig.subplots_adjust(top=0.9)
self.fig.suptitle(title, size=self.suptitleSize)
self.initialElevation = self.ax.elev
self.initialAzimuth = self.ax.azim
# Determine the maximum value of t
t_max = 0
for lagrange_point_idx in [0, 1]:
for index in range(self.numberOfOrbitsPerManifold):
t_max = max(
t_max,
abs(self.W_S_plus[lagrange_point_idx].xs(index).head(
1).index.values[0]))
t_max = max(
t_max,
abs(self.W_S_min[lagrange_point_idx].xs(index).head(
1).index.values[0]))
t_max = max(
t_max,
abs(self.W_U_plus[lagrange_point_idx].xs(index).tail(
1).index.values[0]))
t_max = max(
t_max,
abs(self.W_U_min[lagrange_point_idx].xs(index).tail(
1).index.values[0]))
print('Maximum value for t = ' + str(t_max) + ', animation t: = ')
# Introduce a new time-vector for linearly spaced time throughout the animation
self.t = np.linspace(0, t_max, np.round(t_max / 0.01) + 1)
self.animation_function = animation.FuncAnimation(
self.fig,
self.update_lines,
init_func=self.initiate_lines,
frames=len(self.t),
interval=1,
blit=True)
self.empty_writer_object = animation.writers['ffmpeg']
self.animation_writer = self.empty_writer_object(
fps=30, metadata=dict(artist='Koen Langemeijer'))
self.file_name = '../../../data/animations/manifolds/spatial_manifolds_rotating_no_axes_' + self.orbitType + '_' + str(
self.cLevel) + '.mp4'
self.animation_function.save(self.file_name,
writer=self.animation_writer)
def animate(self):
color_palette_green = sns.dark_palette(
'green', n_colors=self.numberOfOrbitsPerManifold)
color_palette_red = sns.dark_palette(
'red', n_colors=self.numberOfOrbitsPerManifold)
self.lines = [
self.ax.plot([], [],
color='red',
linewidth=self.orbitLinewidth,
alpha=self.orbitAlpha)[0],
self.ax.plot([], [],
color='green',
linewidth=self.orbitLinewidth,
alpha=self.orbitAlpha)[0]
]
# Text object to display absolute normalized time of trajectories within the manifolds
self.timeText = self.ax.text2D(0.05,
0.05,
s='$\|t\| \\approx 0$',
transform=self.ax.transAxes,
size=self.timeTextSize)
# Plot zero velocity surface
x_range = np.arange(self.xLim[0], self.xLim[1], 0.001)
y_range = np.arange(self.yLim[0], self.yLim[1], 0.001)
x_mesh, y_mesh = np.meshgrid(x_range, y_range)
z_mesh = cr3bp_velocity(x_mesh, y_mesh, self.cLevel)
if z_mesh.min() < 0:
# plt.contour(x_mesh, y_mesh, z_mesh, [z_mesh.min(), 0], colors='black', alpha=0.3)
self.ax.contour(x_mesh,
y_mesh,
z_mesh,
list(np.linspace(z_mesh.min(), 0, 10)),
cmap='gist_gray_r',
alpha=0.5)
# Plot both orbits
for k in range(2):
orbit_df = load_orbit(
'../../../data/raw/orbits/refined_for_c/L' + str(k + 1) + '_' +
self.orbitType + '_' +
str(self.orbitIds[self.orbitType][k + 1][self.cLevel]) +
'.txt')
self.ax.plot(orbit_df['x'],
orbit_df['y'],
orbit_df['z'],
color=self.orbitColor,
alpha=self.orbitAlpha,
linewidth=2,
linestyle=':')
# Plot both primaries
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
bodies_df = load_bodies_location()
for body in bodies_df:
x = bodies_df[body]['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
self.ax.plot_surface(x, y, z, color='black')
# Plot Lagrange points 1 and 2
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
for lagrange_point_nr in lagrange_point_nrs:
self.ax.scatter3D(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x',
s=self.lagrangePointMarkerSize)
title = self.orbitTypeForTitle + ' $\{ \mathcal{W}^{S \pm}, \mathcal{W}^{U \pm} \}$ - Orthographic projection (C = ' + str(
self.cLevel) + ')'
self.ax.set_xlim(self.xLim)
self.ax.set_ylim(self.yLim)
self.ax.set_zlim(self.zLim)
self.ax.set_xlabel('x [-]')
self.ax.set_ylabel('y [-]')
self.ax.set_zlabel('z [-]')
self.ax.grid(True, which='both', ls=':')
# self.fig.tight_layout()
self.fig.subplots_adjust(top=0.9)
self.fig.suptitle(title, size=self.suptitleSize)
# Fix overlap between labels and ticks
self.ax.xaxis._axinfo['label']['space_factor'] = 6.0
self.ax.yaxis._axinfo['label']['space_factor'] = 6.0
self.ax.zaxis._axinfo['label']['space_factor'] = 6.0
# Determine the maximum value of t
t_max = max(abs(self.W_U_plus.index)) + max(abs(self.W_S_min.index))
print('Maximum value for unstable = ' +
str(max(abs(self.W_U_plus.index))))
print('Maximum value for stable = ' +
str(max(abs(self.W_S_min.index))))
print('Maximum value for t = ' + str(t_max) + ', animation t: = ')
# Introduce a new time-vector for linearly spaced time throughout the animation
self.t = np.linspace(0, t_max, 150)
self.animation_function = animation.FuncAnimation(
self.fig,
self.update_lines,
init_func=self.initiate_lines,
frames=len(self.t),
interval=1,
blit=True)
self.empty_writer_object = animation.writers['ffmpeg']
self.animation_writer = self.empty_writer_object(
fps=30, metadata=dict(artist='Koen Langemeijer'))
self.file_name = '../../../data/animations/natural_connections/spatial_heteroclinic_' + self.orbitType + '_' + str(
int(self.theta)) + '.mp4'
self.animation_function.save(self.file_name,
writer=self.animation_writer)
def animate(self):
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
self.W_S_plus = [load_manifold('../../../data/raw/manifolds/L' + str(1) + '_' + self.orbitType + '_' + str(self.orbitIds[0]) + '_W_S_plus.txt'),
load_manifold('../../../data/raw/manifolds/L' + str(2) + '_' + self.orbitType + '_' + str(self.orbitIds[1]) + '_W_S_plus.txt')]
self.W_S_min = [load_manifold('../../../data/raw/manifolds/L' + str(1) + '_' + self.orbitType + '_' + str(self.orbitIds[0]) + '_W_S_min.txt'),
load_manifold('../../../data/raw/manifolds/L' + str(2) + '_' + self.orbitType + '_' + str(self.orbitIds[1]) + '_W_S_min.txt')]
self.W_U_plus = [load_manifold('../../../data/raw/manifolds/L' + str(1) + '_' + self.orbitType + '_' + str(self.orbitIds[0]) + '_W_U_plus.txt'),
load_manifold('../../../data/raw/manifolds/L' + str(2) + '_' + self.orbitType + '_' + str(self.orbitIds[1]) + '_W_U_plus.txt')]
self.W_U_min = [load_manifold('../../../data/raw/manifolds/L' + str(1) + '_' + self.orbitType + '_' + str(self.orbitIds[0]) + '_W_U_min.txt'),
load_manifold('../../../data/raw/manifolds/L' + str(2) + '_' + self.orbitType + '_' + str(self.orbitIds[1]) + '_W_U_min.txt')]
self.numberOfOrbitsPerManifold = len(set(self.W_S_plus[0].index.get_level_values(0)))
color_palette_green = sns.dark_palette('green', n_colors=self.numberOfOrbitsPerManifold)
color_palette_red = sns.dark_palette('red', n_colors=self.numberOfOrbitsPerManifold)
self.lines = [plt.plot([], [], color=color_palette_red[idx], alpha=self.orbitAlpha)[0] for idx in range(self.numberOfOrbitsPerManifold)]
self.lines.extend([plt.plot([], [], color=color_palette_green[idx], alpha=self.orbitAlpha)[0] for idx in range(self.numberOfOrbitsPerManifold)])
self.lines.extend([plt.plot([], [], color=color_palette_red[idx], alpha=self.orbitAlpha)[0] for idx in range(self.numberOfOrbitsPerManifold)])
self.lines.extend([plt.plot([], [], color=color_palette_green[idx], alpha=self.orbitAlpha)[0] for idx in range(self.numberOfOrbitsPerManifold)])
self.lines.extend([plt.plot([], [], color=color_palette_red[idx], alpha=self.orbitAlpha)[0] for idx in range(self.numberOfOrbitsPerManifold)])
self.lines.extend([plt.plot([], [], color=color_palette_green[idx], alpha=self.orbitAlpha)[0] for idx in range(self.numberOfOrbitsPerManifold)])
self.lines.extend([plt.plot([], [], color=color_palette_green[idx], alpha=self.orbitAlpha)[0] for idx in range(self.numberOfOrbitsPerManifold)])
self.lines.extend([plt.plot([], [], color=color_palette_red[idx], alpha=self.orbitAlpha)[0] for idx in range(self.numberOfOrbitsPerManifold)])
# Text object to display absolute normalized time of trajectories within the manifolds
self.timeText = ax.text2D(0.05, 0.05, s='$\|t\| \\approx 0$', transform=ax.transAxes, size=self.timeTextSize)
# Plot zero velocity surface
x_range = np.arange(self.xLim[0], self.xLim[1], 0.001)
y_range = np.arange(self.yLim[0], self.yLim[1], 0.001)
x_mesh, y_mesh = np.meshgrid(x_range, y_range)
z_mesh = cr3bp_velocity(x_mesh, y_mesh, c_level)
if z_mesh.min() < 0:
plt.contour(x_mesh, y_mesh, z_mesh, [z_mesh.min(), 0], colors='black', alpha=0.3)
# Plot both orbits
for k in range(2):
orbit_df = load_orbit('../../../data/raw/orbits/L' + str(k+1) + '_' + self.orbitType + '_' + str(self.orbitIds[k]) + '.txt')
plt.plot(orbit_df['x'], orbit_df['y'], orbit_df['z'], color=self.orbitColor, alpha=self.orbitAlpha, linewidth=self.orbitLinewidth)
# Plot both primaries
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
bodies_df = load_bodies_location()
for body in bodies_df:
x = bodies_df[body]['r'] * np.outer(np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
ax.plot_surface(x, y, z, color='black')
# Plot Lagrange points 1 and 2
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
for lagrange_point_nr in lagrange_point_nrs:
ax.scatter3D(lagrange_points_df[lagrange_point_nr]['x'], lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'], color='black', marker='x', s=self.lagrangePointMarkerSize)
title = self.orbitTypeForTitle + ' $\{ \mathcal{W}^{S \pm}, \mathcal{W}^{U \pm} \}$ - Spatial overview at C = ' + str(c_level)
ax.set_xlim3d(self.xLim)
ax.set_ylim3d(self.yLim)
ax.set_zlim3d(self.zLim)
ax.set_xlabel('x [-]')
ax.set_ylabel('y [-]')
ax.set_zlabel('z [-]')
ax.grid(True, which='both', ls=':')
fig.tight_layout()
fig.subplots_adjust(top=0.9)
plt.suptitle(title, size=self.suptitleSize)
# Fix overlap between labels and ticks
ax.xaxis._axinfo['label']['space_factor'] = 6.0
ax.yaxis._axinfo['label']['space_factor'] = 6.0
ax.zaxis._axinfo['label']['space_factor'] = 6.0
# Determine the maximum value of t
t_max = 0
for lagrange_point_idx in [0, 1]:
for index in range(self.numberOfOrbitsPerManifold):
t_max = max(t_max, abs(self.W_S_plus[lagrange_point_idx].xs(index).tail(1).index.values[0]))
t_max = max(t_max, abs(self.W_S_min[lagrange_point_idx].xs(index).tail(1).index.values[0]))
t_max = max(t_max, abs(self.W_U_plus[lagrange_point_idx].xs(index).tail(1).index.values[0]))
t_max = max(t_max, abs(self.W_U_min[lagrange_point_idx].xs(index).tail(1).index.values[0]))
print('Maximum value for t = ' + str(t_max) + ', animation t: = ')
# Introduce a new time-vector for linearly spaced time throughout the animation
self.t = np.linspace(0, t_max, np.round(t_max / 0.04) + 1)
animation_function = animation.FuncAnimation(fig, self.update_lines, init_func=self.initiate_lines,
frames=len(self.t), interval=1, blit=True)
#
# # Determine the maximum number of frames
# number_of_frames = 0
# for lagrange_point_idx in [0, 1]:
# for index in range(self.numberOfOrbitsPerManifold):
# number_of_frames = max(number_of_frames, len(self.W_S_plus[lagrange_point_idx].xs(index)['x']))
# number_of_frames = max(number_of_frames, len(self.W_S_min[lagrange_point_idx].xs(index)['x']))
# number_of_frames = max(number_of_frames, len(self.W_U_plus[lagrange_point_idx].xs(index)['x']))
# number_of_frames = max(number_of_frames, len(self.W_U_min[lagrange_point_idx].xs(index)['x']))
#
# animation_function = animation.FuncAnimation(fig, self.update_lines, init_func=self.initiate_lines,
# frames=int(number_of_frames), interval=1, blit=True)
empty_writer_object = animation.writers['ffmpeg']
animation_writer = empty_writer_object(fps=30, metadata=dict(artist='Koen Langemeijer'))
file_name = '../../../data/animations/manifolds/spatial_manifolds_' + orbit_type + '_' + str(c_level) + '.mp4'
animation_function.save(file_name, writer=animation_writer)
def plot_horizontal_to_halo(self):
fig = plt.figure(figsize=self.figSize)
ax1 = fig.add_subplot(2, 2, 1, projection='3d')
ax2 = fig.add_subplot(2, 2, 2)
ax3 = fig.add_subplot(2, 2, 3)
ax4 = fig.add_subplot(2, 2, 4)
horizontal_color = self.plottingColors['tripleLine'][2]
halo_color = self.plottingColors['tripleLine'][0]
# Plot bifurcations
line_width = 2
plot_alpha = 1
df = load_orbit('../../data/raw/orbits/L1_horizontal_' +
str(self.horizontalBifurcations[0]) + '.txt')
l1, = ax1.plot(df['x'],
df['y'],
df['z'],
color=horizontal_color,
alpha=plot_alpha,
linewidth=1,
label='Horizontal Lyapunov')
ax1.plot(df['x'],
df['y'],
df['z'],
color=horizontal_color,
alpha=plot_alpha,
linewidth=line_width)
ax2.plot(df['x'],
df['y'],
color=horizontal_color,
alpha=plot_alpha,
linewidth=line_width)
ax3.plot(df['y'],
df['z'],
color=horizontal_color,
alpha=plot_alpha,
linewidth=line_width)
ax4.plot(df['x'],
df['z'],
color=horizontal_color,
alpha=plot_alpha,
linewidth=line_width)
number_of_orbits = 10
line_width = 1
plot_alpha = 0.5
for i in [
int(i)
for i in (np.linspace(1, self.haloMaxId, number_of_orbits))
]:
df = load_orbit('../../data/raw/orbits/L1_halo_' + str(i) + '.txt')
l2, = ax1.plot(df['x'],
df['y'],
df['z'],
color=halo_color,
alpha=plot_alpha,
linewidth=line_width,
label='Halo')
ax2.plot(df['x'],
df['y'],
color=halo_color,
alpha=plot_alpha,
linewidth=line_width)
ax3.plot(df['y'],
df['z'],
color=halo_color,
alpha=plot_alpha,
linewidth=line_width)
ax4.plot(df['x'],
df['z'],
color=halo_color,
alpha=plot_alpha,
linewidth=line_width)
# Lagrange points and bodies
lagrange_points_df = load_lagrange_points_location()
lagrange_point_nrs = ['L1', 'L2']
for lagrange_point_nr in lagrange_point_nrs:
ax1.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax2.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['y'],
color='black',
marker='x')
ax3.scatter(lagrange_points_df[lagrange_point_nr]['y'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
ax4.scatter(lagrange_points_df[lagrange_point_nr]['x'],
lagrange_points_df[lagrange_point_nr]['z'],
color='black',
marker='x')
bodies_df = load_bodies_location()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
for body in ['Moon']:
x = bodies_df[body]['r'] * np.outer(
np.cos(u), np.sin(v)) + bodies_df[body]['x']
y = bodies_df[body]['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df[body]['r'] * np.outer(np.ones(np.size(u)),
np.cos(v))
ax1.plot_surface(x, y, z, color='black')
ax2.contourf(x, y, z, colors='black')
ax3.contourf(y, z, x, colors='black')
ax4.contourf(x, z, y, colors='black')
ax1.set_xlabel('x [-]')
ax1.set_ylabel('y [-]')
ax1.set_zlabel('z [-]')
ax1.grid(True, which='both', ls=':')
ax2.set_xlabel('x [-]')
ax2.set_ylabel('y [-]')
ax2.grid(True, which='both', ls=':')
ax3.set_xlabel('y [-]')
ax3.set_ylabel('z [-]')
ax3.grid(True, which='both', ls=':')
ax4.set_xlabel('x [-]')
ax4.set_ylabel('z [-]')
ax4.grid(True, which='both', ls=':')
plt.tight_layout()
plt.subplots_adjust(top=0.9)
ax1.legend(frameon=True, handles=[l1, l2])
plt.suptitle(
'$L_1$ Bifurcation - Halo family connecting to horizontal Lyapunov orbits',
size=self.suptitleSize)
plt.savefig('../../data/figures/orbits/L1_bifurcation_halo.pdf',
transparent=True)
plt.close()
pass
C = float(config[orbit_type][orbit_name]['C'])
x_range = np.arange(0.5, 1.5, 0.001)
y_range = np.arange(-0.5, 0.5, 0.001)
X, Y = np.meshgrid(x_range, y_range)
Z = cr3bp_velocity(X, Y, C)
if Z.min() < 0:
plt.contourf(X, Y, Z, [Z.min(), 0], colors='black', alpha=0.05)
title = 'C = ' + str(round(C, 3)) + \
', T = ' + str(round(float(config[orbit_type][orbit_name]['T']), 3))
plt.title(title, size=30)
phi = np.linspace(0, 2 * np.pi, 100)
theta = np.linspace(0, np.pi, 100)
bodies = load_bodies_location()
for body in bodies:
x_body = bodies[body]['r'] * np.outer(
np.cos(phi), np.sin(theta)) + bodies[body]['x']
y_body = bodies[body]['r'] * np.outer(
np.sin(phi), np.sin(theta)) + bodies[body]['y']
plt.plot(x_body, y_body, color='black')
lagrange_points = load_lagrange_points_location()
for lagrange_point in ['L1', 'L2']:
ax.scatter(lagrange_points[lagrange_point]['x'],
lagrange_points[lagrange_point]['y'],
color='grey',
marker='d',
alpha=0.75)
ax.text(lagrange_points[lagrange_point]['x'],
def plot_result(self):
color_palette_green = sns.dark_palette('green', n_colors=self.numberOfOrbitsPerManifold)
color_palette_red = sns.dark_palette('red', n_colors=self.numberOfOrbitsPerManifold)
C = 3.15
x_range = np.arange(0.8, 1.2, 0.001)
y_range = np.arange(-0.15, 0.15, 0.001)
X, Y = np.meshgrid(x_range, y_range)
Z = cr3bp_velocity(X, Y, C)
plt.figure(figsize=(5*(1+np.sqrt(5))/2, 5))
gs = gridspec.GridSpec(2, 2)
ax1 = plt.subplot(gs[0, :])
ax2 = plt.subplot(gs[1, 0])
ax3 = plt.subplot(gs[1, 1])
# Subplot 1: manifolds
for i in range(self.numberOfOrbitsPerManifold):
ax1.plot(self.WS.xs(i)['x'], self.WS.xs(i)['y'], color=color_palette_green[i], alpha=0.5)
ax1.plot(self.WU.xs(i)['x'], self.WU.xs(i)['y'], color=color_palette_red[i], alpha=0.5)
ax1.plot(self.WS.xs(46)['x'], self.WS.xs(46)['y'], color='black')
ax1.plot(self.WS.xs(37)['x'], self.WS.xs(37)['y'], color='black')
ax1.plot(self.WU.xs(65)['x'], self.WU.xs(65)['y'], color='black')
ax1.plot(self.WU.xs(77)['x'], self.WU.xs(77)['y'], color='black')
if Z.min() < 0:
ax1.contourf(X, Y, Z, [Z.min(), 0], colors='black', alpha=0.2)
if self.U_section == 2:
# ax1.axvline(1 - self.massParameter, color='black')
ax1.plot([1 - self.massParameter, 1 - self.massParameter], [-0.11, 0.01], color='black', linewidth=3)
ax1.text(s='$\sum_2$', x=(1-0.5*self.massParameter), y=0.01)
bodies_df = load_bodies_location()
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = bodies_df['Moon']['r'] * np.outer(np.cos(u), np.sin(v)) + bodies_df['Moon']['x']
y = bodies_df['Moon']['r'] * np.outer(np.sin(u), np.sin(v))
z = bodies_df['Moon']['r'] * np.outer(np.ones(np.size(u)), np.cos(v))
# ax1.scatter(x, y, color='black', s=1)
ax1.contourf(x, y, z, [z.min(), 0], colors='black')
ax1.grid(True, which='both', ls=':')
# Subplot 2: poincare
v_max = 2
ax2.plot(self.poincareWS[abs(self.poincareWS['ydot']) < v_max]['y'].values, self.poincareWS[abs(self.poincareWS['ydot']) < v_max]['ydot'].values, color='g')
ax2.plot(self.poincareWU[abs(self.poincareWU['ydot']) < v_max]['y'].values, self.poincareWU[abs(self.poincareWU['ydot']) < v_max]['ydot'].values, color='r')
ax2.scatter(self.poincareWS['y'][46], self.poincareWS['ydot'][46], color='black')
ax2.scatter(self.poincareWU['y'][65], self.poincareWU['ydot'][65], color='black')
ax2.scatter(self.poincareWS['y'][37], self.poincareWS['ydot'][37], color='black')
ax2.scatter(self.poincareWU['y'][77], self.poincareWU['ydot'][77], color='black')
# y_1 y_2
# WS 46 41
# WU 65 83
# x_intersection = -0.0491777
# print(self.poincareWS[self.poincareWS['y'] == x_intersection + abs(self.poincareWS['y'] - x_intersection).min()])
# print(self.poincareWS[self.poincareWS['y'] == x_intersection - abs(self.poincareWS['y'] - x_intersection).min()])
# print(self.poincareWU[self.poincareWU['y'] == x_intersection + abs(self.poincareWU['y'] - x_intersection).min()])
# print(self.poincareWU[self.poincareWU['y'] == x_intersection - abs(self.poincareWU['y'] - x_intersection).min()])
ax2.set_xlabel('$y$')
ax2.set_ylabel('$\dot{y}$')
ax2.set_ylim([-1.5, 1.5])
ax2.grid(True, which='both', ls=':')
title = '$\sum_' + str(self.U_section) + '$'
ax2.set_title(title)
# Subplot 3: x error
ax3.axhline(abs(self.poincareWS['y'][46] - self.poincareWU['y'][65]))
ax3.axhline(abs(self.poincareWS['y'][37] - self.poincareWU['y'][77]))
ax3.axhline(abs(self.poincareWS['ydot'][46] - self.poincareWU['ydot'][65]))
ax3.axhline(abs(self.poincareWS['ydot'][37] - self.poincareWU['ydot'][77]))
ax3.semilogy((1 - self.massParameter) - self.poincareWS['x'].values)
ax3.set_ylabel('$\| x - (1-\mu) \|$')
ax3.set_xlabel('orbitId [-]')
ax3.grid(True, which='both', ls=':')
plt.tight_layout()
# plt.savefig('../../data/figures/heteroclinic_connection.pdf')
pass