def run_example2():
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep import epoch, DAY2SEC, AU, MU_SUN, lambert_problem
from pykep.planet import jpl_lp
from pykep.orbit_plots import plot_planet, plot_lambert
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
t1 = epoch(0)
t2 = epoch(640)
dt = (t2.mjd2000 - t1.mjd2000) * DAY2SEC
axis.scatter([0], [0], [0], color='y')
pl = jpl_lp('earth')
plot_planet(pl, t0=t1, color=(0.8, 0.8, 1), legend=True, units=AU, ax=axis)
rE, vE = pl.eph(t1)
pl = jpl_lp('mars')
plot_planet(pl, t0=t2, color=(0.8, 0.8, 1), legend=True, units=AU, ax=axis)
rM, vM = pl.eph(t2)
l = lambert_problem(rE, rM, dt, MU_SUN)
plot_lambert(l, color='b', legend=True, units=AU, ax=axis)
plot_lambert(l, sol=1, color='g', legend=True, units=AU, ax=axis)
plot_lambert(l, sol=2, color='g', legend=True, units=AU, ax=axis)
plt.show()
def plot_orbits(self, pop, ax=None):
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
A1, A2 = self._ast1, self._ast2
if ax is None:
fig = plt.figure()
axis = fig.add_subplot(111, projection='3d')
else:
axis = ax
plot_planet(A1, ax=axis, s=10, t0=epoch(self.lb[0]))
plot_planet(A2, ax=axis, s=10, t0=epoch(self.ub[0]))
for ind in pop:
if ind.cur_f[0] == self._UNFEASIBLE:
continue
dep, arr = ind.cur_x
rdep, vdep = A1.eph(epoch(dep))
rarr, varr = A2.eph(epoch(arr))
l = lambert_problem(rdep, rarr, (arr - dep) *
DAY2SEC, A1.mu_central_body, False, 1)
axis = plot_lambert(l, ax=axis, alpha=0.8, color='k')
if ax is None:
plt.show()
return axis
def plot(self, x):
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep import epoch, AU, DAY2SEC
from pykep.sims_flanagan import sc_state
from pykep.orbit_plots import plot_planet, plot_sf_leg
start = epoch(x[0])
end = epoch(x[0] + x[1])
r, v = self.__earth.eph(start)
v = [a + b for a, b in zip(v, x[4:7])]
x0 = sc_state(r, v, self.__sc.mass)
r, v = self.__mars.eph(end)
xe = sc_state(r, v, x[3])
self.__leg.set(
start, x0, x[-3 * self.__nseg:], end, xe, x[2] * DAY2SEC)
fig = plt.figure()
axis = fig.gca(projection='3d')
# The Sun
axis.scatter([0], [0], [0], color='y')
# The leg
plot_sf_leg(self.__leg, units=AU, N=10, ax=axis)
# The planets
plot_planet(
self.__earth, start, units=AU, legend=True, color=(0.8, 0.8, 1), ax=axis)
plot_planet(
self.__mars, end, units=AU, legend=True, color=(0.8, 0.8, 1), ax=axis)
plt.show()
def plot(self, ax=None, clusters=None, orbits=False, only_core=False):
"""Plots the clusters."""
if self.n_clusters < 1:
return
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
if ax is None:
fig = plt.figure()
axis = fig.add_subplot(111, projection='3d')
else:
axis = ax
axis.view_init(elev=30.0, azim=135.0)
axis.set_aspect('equal')
if orbits:
from pykep.orbit_plots import plot_planet
members = self.core_members if only_core else self.members
for label in members if clusters is None else clusters:
for planet in members[label]:
plot_planet(
self._asteroids[planet], t0=self._epoch, s=0, ax=axis)
X, labels = list(zip(*[(x, label) for (x, label) in zip(self._X, self.labels)
if label > -.5 and (clusters is None or label in clusters)]))
data = [[x[0], x[1], x[2]] for x in X]
axis.scatter(*list(zip(*data)), c=labels, alpha=0.5)
self._axis_equal_3d(axis)
if ax is None:
plt.show()
return axis
def plot_innerKerbol(epoch=epoch(0)):
"""
Plots the Galilean Moons of Jupiter at epoch
USAGE: plot_moons(epoch = epoch(34654, epoch.epoch_type.MJD)):
* epoch: the epoch one wants the galilean moons to be plotted at
"""
from pykep.orbit_plots import plot_planet
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
print(epoch)
fig = plt.figure()
ax1 = fig.gca(projection='3d')
#plot_planet(ax,Moho,color = 'y', units = 1.0, t0 = epoch, legend=True)
#plot_planet(ax,Eve,color = 'm', units = 1.0, t0 = epoch, legend=True)
#lot_planet(ax=ax1,Kerbin,color = 'c', units = 1.0, t0, legend=True)
#plot_planet(ax = ax1,Duna,color = 'r', units = 1.0, t0 = epoch, legend=True)
plot_planet(Moho, t0=epoch, color='y', legend=True, units=KAU, ax=ax1)
plot_planet(Eve, t0=epoch, color='m', legend=True, units=KAU, ax=ax1)
plot_planet(Kerbin, t0=epoch, color='c', legend=True, units=KAU, ax=ax1)
plot_planet(Duna, t0=epoch, color='r', legend=True, units=KAU, ax=ax1)
plot_planet(Jool, t0=epoch, color='g', legend=True, units=KAU, ax=ax1)
ax1.set_xlim3d(-3, 3)
ax1.set_ylim3d(-3, 3)
ax1.set_zlim3d(-3, 3)
plt.show()
"""
def plot_orbits(self, pop, ax=None):
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
A1, A2 = self._ast1, self._ast2
if ax is None:
fig = plt.figure()
axis = fig.add_subplot(111, projection='3d')
else:
axis = ax
plot_planet(A1, axes=axis, s=10, t0=epoch(self.lb[0]))
plot_planet(A2, axes=axis, s=10, t0=epoch(self.ub[0]))
for ind in pop:
if ind.cur_f[0] == self._UNFEASIBLE:
continue
dep, arr = ind.cur_x
rdep, vdep = A1.eph(epoch(dep))
rarr, varr = A2.eph(epoch(arr))
l = lambert_problem(rdep, rarr, (arr - dep) *
DAY2SEC, A1.mu_central_body, False, 1)
axis = plot_lambert(l, axes=axis, alpha=0.8, color='k')
if ax is None:
plt.show()
return axis
def plot(self, x, axes=None, units=AU, N=60):
"""plot(self, x, axes=None, units=pk.AU, N=60)
Plots the spacecraft trajectory.
Args:
- x (``tuple``, ``list``, ``numpy.ndarray``): Decision chromosome.
- axes (``matplotlib.axes._subplots.Axes3DSubplot``): 3D axes to use for the plot
- units (``float``, ``int``): Length unit by which to normalise data.
- N (``float``): Number of points to plot per leg
"""
import matplotlib as mpl
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from pykep.orbit_plots import plot_planet, plot_lambert
# Creating the axes if necessary
if axes is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axes = fig.gca(projection='3d')
T = self._decode_tofs(x)
ep = np.insert(T, 0, x[0]) # [t0, T1, T2 ...]
ep = np.cumsum(ep) # [t0, t1, t2, ...]
_, _, _, l, _ = self._compute_dvs(x)
for pl, e in zip(self.seq, ep):
plot_planet(pl, epoch(e), units=units, legend=True,
color=(0.7, 0.7, 1), axes=axes)
for lamb in l:
plot_lambert(lamb, N=N, sol=0, units=units, color='k',
legend=False, axes=axes, alpha=0.8)
return axes
def plot(self, x):
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep import epoch, AU, DAY2SEC
from pykep.sims_flanagan import sc_state
from pykep.orbit_plots import plot_planet, plot_sf_leg
start = epoch(x[0])
end = epoch(x[0] + x[1])
r, v = self.__earth.eph(start)
v = [a + b for a, b in zip(v, x[4:7])]
x0 = sc_state(r, v, self.__sc.mass)
r, v = self.__mars.eph(end)
xe = sc_state(r, v, x[3])
self.__leg.set(
start, x0, x[-3 * self.__nseg:], end, xe, x[2] * DAY2SEC)
fig = plt.figure()
axis = fig.gca(projection='3d')
# The Sun
axis.scatter([0], [0], [0], color='y')
# The leg
plot_sf_leg(self.__leg, units=AU, N=10, axes=axis)
# The planets
plot_planet(
self.__earth, start, units=AU, legend=True, color=(0.8, 0.8, 1), axes=axis)
plot_planet(
self.__mars, end, units=AU, legend=True, color=(0.8, 0.8, 1), axes=axis)
plt.show()
def plot(self, x, ax=None):
"""
ax = prob.plot(x, ax=None)
- x: encoded trajectory
- ax: matplotlib axis where to plot. If None figure and axis will be created
- [out] ax: matplotlib axis where to plot
Plots the trajectory represented by a decision vector x on the 3d axis ax
Example::
ax = prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep import epoch, AU
from pykep.sims_flanagan import sc_state
from pykep.orbit_plots import plot_planet, plot_sf_leg
# Creating the axis if necessary
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
# Plotting the Sun ........
axis.scatter([0], [0], [0], color='y')
# Plotting the pykep.planet both at departure and arrival dates
for i in range(self.__num_legs):
idx = i * self.__dim_leg
plot_planet(self.__seq[i],
epoch(x[idx]),
units=AU,
legend=True,
color=(0.7, 0.7, 0.7),
s=30,
ax=axis)
plot_planet(self.__seq[i + 1],
epoch(x[idx] + x[idx + 1]),
units=AU,
legend=False,
color=(0.7, 0.7, 0.7),
s=30,
ax=axis)
# Computing the legs
self.fitness(x)
# Plotting the legs
for leg in self.__legs:
plot_sf_leg(leg, units=AU, N=10, ax=axis, legend=False)
return axis
def plot(self, x, ax=None):
"""
ax = prob.plot(x, ax=None)
- x: encoded trajectory
- ax: matplotlib axis where to plot. If None figure and axis will be created
- [out] ax: matplotlib axis where to plot
Plots the trajectory represented by a decision vector x on the 3d axis ax
Example::
ax = prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep import epoch, AU
from pykep.sims_flanagan import sc_state
from pykep.orbit_plots import plot_planet, plot_sf_leg
# Creating the axis if necessary
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
# Plotting the Sun ........
axis.scatter([0], [0], [0], color='y')
# Plotting the pykep.planet both at departure and arrival dates
for i in range(self.__num_legs):
idx = i * self.__dim_leg
plot_planet(self.__seq[i], epoch(x[idx]), units=AU, legend=True, color=(
0.7, 0.7, 0.7), s=30, ax=axis)
plot_planet(self.__seq[i + 1], epoch(x[idx] + x[idx + 1]),
units=AU, legend=False, color=(0.7, 0.7, 0.7), s=30, ax=axis)
# Computing the legs
self.fitness(x)
# Plotting the legs
for leg in self.__legs:
plot_sf_leg(leg, units=AU, N=10, ax=axis, legend=False)
return axis
def plot(self, x, axes=None, units=AU, N=60):
import matplotlib as mpl
import matplotlib.pyplot as plt
from pykep.orbit_plots import plot_planet
rvt_outs, rvt_ins, rvt_pls, _, _ = self._compute_dvs(x)
rvt_outs = [
rvt.rotate(self._rotation_axis, self._theta) for rvt in rvt_outs
]
rvt_ins[1:] = [
rvt.rotate(self._rotation_axis, self._theta) for rvt in rvt_ins[1:]
]
rvt_pls = [
rvt.rotate(self._rotation_axis, self._theta) for rvt in rvt_pls
]
ep = [epoch(rvt_pl._t * SEC2DAY) for rvt_pl in rvt_pls]
# Creating the axes if necessary
if axes is None:
mpl.rcParams["legend.fontsize"] = 10
fig = plt.figure()
axes = fig.gca(projection="3d")
plt.xlim([-1, 1])
# planets
for pl, e in zip(self._seq, ep):
plot_planet(pl,
e,
units=units,
legend=True,
color=(0.7, 0.7, 1),
axes=axes)
# lamberts and resonances
for i in range(0, len(self._seq) - 1):
pl = self._seq[i]
# stay at planet: it is a resonance colored black
is_reso = pl == self._seq[i + 1]
rvt_out = rvt_outs[i]
tof = rvt_ins[i + 1]._t - rvt_out._t
rvt_out.plot(tof,
units=units,
N=4 * N,
color="k" if is_reso else "r",
axes=axes)
return axes
def plot(self, x):
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep import epoch, AU
from pykep.sims_flanagan import sc_state
from pykep.orbit_plots import plot_planet, plot_sf_leg
t_E = epoch(x[0])
t_V = epoch(x[0] + x[1])
t_M = epoch(x[0] + x[1] + x[9])
rE, vE = self.__earth.eph(t_E)
rV, vV = self.__venus.eph(t_V)
rM, vM = self.__mercury.eph(t_M)
# First Leg
v = [a + b for a, b in zip(vE, x[3:6])]
x0 = sc_state(rE, v, self.__sc.mass)
v = [a + b for a, b in zip(vV, x[6:9])]
xe = sc_state(rV, v, x[2])
self.__leg1.set(
t_E, x0, x[-3 * (self.__nseg1 + self.__nseg2):-self.__nseg2 * 3],
t_V, xe)
# Second leg
v = [a + b for a, b in zip(vV, x[11:14])]
x0 = sc_state(rV, v, x[2])
v = [a + b for a, b in zip(vM, x[14:17])]
xe = sc_state(rM, v, x[10])
self.__leg2.set(t_E, x0, x[(-3 * self.__nseg2):], t_V, xe)
fig = plt.figure()
axis = fig.gca(projection='3d')
# The Sun
axis.scatter([0], [0], [0], color='y')
# The legs
plot_sf_leg(self.__leg1, units=AU, N=10, ax=axis)
plot_sf_leg(self.__leg2, units=AU, N=10, ax=axis)
# The planets
plot_planet(self.__earth,
t_E,
units=AU,
legend=True,
color=(0.7, 0.7, 1),
ax=axis)
plot_planet(self.__venus,
t_V,
units=AU,
legend=True,
color=(0.7, 0.7, 1),
ax=axis)
plot_planet(self.__mercury,
t_M,
units=AU,
legend=True,
color=(0.7, 0.7, 1),
ax=axis)
plt.show()
def plot_cluster_evolution(self,
cluster_id=None,
only_core=False,
epochs=range(7500, 8400, 100),
skip=100,
alpha=0.3):
"""
Plots a cluster evolution at 9 prefixed epochs.
"""
if self.n_clusters < 1:
print("No clusters have been found yet")
return
if cluster_id >= self.n_clusters or cluster_id < 0:
print(
"cluster_id should be larger then 0 and smaller than the number of clusters (-1)"
)
return
if len(epochs) != 9:
print(
"The epochs requested must be exactly 9 as to assemble 3x3 subplots"
)
return
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
from pykep.orbit_plots import plot_planet
from pykep import epoch
if only_core:
ids = self.core_members[cluster_id]
else:
ids = self.members[cluster_id]
fig = plt.figure()
for i, ep in enumerate(epochs):
axis = fig.add_subplot(3, 3, i + 1, projection='3d')
plt.axis('off')
plt.title(epoch(ep).__repr__()[:11])
for pl in self._asteroids[::skip]:
axis = plot_planet(pl, axes=axis, alpha=0.05, s=0)
for cluster_member in ids:
r, _ = self._asteroids[cluster_member].eph(epoch(ep))
axis.scatter([r[0]], [r[1]], [r[2]], marker='o', alpha=alpha)
plt.draw()
plt.show()
return fig
def plot(self, x):
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep import epoch, AU
from pykep.sims_flanagan import sc_state
from pykep.orbit_plots import plot_planet, plot_sf_leg
t_E = epoch(x[0])
t_V = epoch(x[0] + x[1])
t_M = epoch(x[0] + x[1] + x[9])
rE, vE = self.__earth.eph(t_E)
rV, vV = self.__venus.eph(t_V)
rM, vM = self.__mercury.eph(t_M)
# First Leg
v = [a + b for a, b in zip(vE, x[3:6])]
x0 = sc_state(rE, v, self.__sc.mass)
v = [a + b for a, b in zip(vV, x[6:9])]
xe = sc_state(rV, v, x[2])
self.__leg1.set(
t_E, x0, x[-3 * (self.__nseg1 + self.__nseg2):-self.__nseg2 * 3], t_V, xe)
# Second leg
v = [a + b for a, b in zip(vV, x[11:14])]
x0 = sc_state(rV, v, x[2])
v = [a + b for a, b in zip(vM, x[14:17])]
xe = sc_state(rM, v, x[10])
self.__leg2.set(t_E, x0, x[(-3 * self.__nseg2):], t_V, xe)
fig = plt.figure()
axis = fig.gca(projection='3d')
# The Sun
axis.scatter([0], [0], [0], color='y')
# The legs
plot_sf_leg(self.__leg1, units=AU, N=10, ax=axis)
plot_sf_leg(self.__leg2, units=AU, N=10, ax=axis)
# The planets
plot_planet(
self.__earth, t_E, units=AU, legend=True, color=(0.7, 0.7, 1), ax=axis)
plot_planet(
self.__venus, t_V, units=AU, legend=True, color=(0.7, 0.7, 1), ax=axis)
plot_planet(
self.__mercury, t_M, units=AU, legend=True, color=(0.7, 0.7, 1), ax=axis)
plt.show()
def plottransfer():
star = Star(1817514095, 1905216634)
origin = Planet(1817514095, 1905216634, -455609026)
target = Planet(1817514095, 1905216634, 272811578)
origin_orbit_radius = origin.planet.radius + 200000
target_orbit_radius = target.planet.radius + 200000
flight_time = int(flask_request.values['flight_time'])
t0 = epoch_from_string(str(datetime.now()))
t0_number = int(t0.mjd2000)
launch_time = int(flask_request.values['launch_time']) + t0_number
t1 = epoch(int(launch_time))
t2 = epoch(int(launch_time) + int(flight_time))
fig = plt.figure(figsize=(4, 4))
orbit_ax = fig.gca(projection='3d', proj_type='ortho')
orbit_ax.scatter([0], [0], [0], color='orange')
orbit_ax.set_aspect('equal')
x_fig = plt.figure(figsize=(4, 4))
x_ax = x_fig.gca()
x_ax.scatter([0], [0], color='orange')
y_fig = plt.figure(figsize=(4, 4))
y_ax = y_fig.gca()
y_ax.scatter([0], [0], color='orange')
z_fig = plt.figure(figsize=(4, 4))
z_ax = z_fig.gca()
z_ax.scatter([0], [0], color='orange')
plot_planet(origin.planet,
t0=t1,
color='green',
legend=True,
units=AU,
ax=orbit_ax)
plot_planet(target.planet,
t0=t2,
color='gray',
legend=True,
units=AU,
ax=orbit_ax)
o_x, o_y, o_z = plot_planet_2d(origin.planet, t0=t1)
t_x, t_y, t_z = plot_planet_2d(target.planet, t0=t2)
x_ax.plot(o_y, o_z, label=origin.planet.name, c='green')
x_ax.scatter(o_y[0], o_z[0], s=40, color='green')
x_ax.plot(t_y, t_z, label=target.planet.name, c='gray')
x_ax.scatter(t_y[0], t_z[0], s=40, color='gray')
y_ax.plot(o_x, o_z, label=origin.planet.name, c='green')
y_ax.scatter(o_x[0], o_z[0], s=40, color='green')
y_ax.plot(t_x, t_z, label=target.planet.name, c='gray')
y_ax.scatter(t_x[0], t_z[0], s=40, color='gray')
z_ax.plot(o_x, o_y, label=origin.planet.name, c='green')
z_ax.scatter(o_x[0], o_y[0], s=40, color='green')
z_ax.plot(t_x, t_y, label=target.planet.name, c='gray')
z_ax.scatter(t_x[0], t_y[0], s=40, color='gray')
max_value = max(max([abs(x) for x in orbit_ax.get_xlim()]),
max([abs(x) for x in orbit_ax.get_ylim()]))
max_z_value = max([abs(z) for z in orbit_ax.get_zlim()])
dt = (t2.mjd - t1.mjd) * DAY2SEC
r1, v1 = origin.planet.eph(t1)
r2, v2 = target.planet.eph(t2)
lambert = lambert_problem(list(r1), list(r2), dt, star.gm)
min_n = None
min_delta_v = None
for x in range(lambert.get_Nmax() + 1):
vp_vec = np.array(v1)
vs_vec = np.array(lambert.get_v1()[x])
vsp_vec = vs_vec - vp_vec
vsp = np.linalg.norm(vsp_vec)
vo = sqrt(vsp * vsp + 2 * origin.planet.mu_self / origin_orbit_radius)
inj_delta_v = vo - sqrt(origin.planet.mu_self / origin_orbit_radius)
vp_vec = np.array(v2)
vs_vec = np.array(lambert.get_v2()[x])
vsp_vec = vs_vec - vp_vec
vsp = np.linalg.norm(vsp_vec)
vo = sqrt(vsp * vsp + 2 * target.planet.mu_self / target_orbit_radius)
ins_delta_v = vo - sqrt(target.planet.mu_self / target_orbit_radius)
if min_delta_v is None or inj_delta_v + ins_delta_v < min_delta_v:
min_n = x
min_delta_v = inj_delta_v + ins_delta_v
plot_lambert(lambert,
color='purple',
sol=min_n,
legend=False,
units=AU,
ax=orbit_ax)
l_x, l_y, l_z = plot_lambert_2d(lambert, sol=min_n)
x_ax.plot(l_y, l_z, c='purple')
y_ax.plot(l_x, l_z, c='purple')
z_ax.plot(l_x, l_y, c='purple')
orbit_ax.set_xlim(-max_value * 1.2, max_value * 1.2)
orbit_ax.set_ylim(-max_value * 1.2, max_value * 1.2)
orbit_ax.set_zlim(-max_z_value * 1.2, max_z_value * 1.2)
x_ax.set_xlim(-1.0, 1.0)
x_ax.set_ylim(-0.05, 0.05)
y_ax.set_xlim(-1.0, 1.0)
y_ax.set_ylim(-0.05, 0.05)
z_ax.set_xlim(-1.0, 1.0)
z_ax.set_ylim(-1.0, 1.0)
fig.savefig('orbit')
x_fig.savefig('orbit-x')
y_fig.savefig('orbit-y')
z_fig.savefig('orbit-z')
plt.close('all')
return jsonify(success=True)
def plot(self, x, ax=None):
"""
ax = prob.plot(x, ax=None)
- x: encoded trajectory
- ax: matplotlib axis where to plot. If None figure and axis will be created
- [out] ax: matplotlib axis where to plot
Plots the trajectory represented by a decision vector x on the 3d axis ax
Example::
ax = prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep.orbit_plots import plot_planet, plot_lambert, plot_kepler
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
axis.scatter(0, 0, 0, color='y')
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T and the cartesian components of vinf
T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x)
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.n_legs + 1))
r_P = list([None] * (self.n_legs + 1))
v_P = list([None] * (self.n_legs + 1))
DV = list([None] * (self.n_legs + 1))
for i, planet in enumerate(self._seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=AU,
axes=axis,
N=150)
# 3 - We start with the first leg
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[4] * T[0] * DAY2SEC,
self.common_mu)
plot_kepler(r_P[0],
v0,
x[4] * T[0] * DAY2SEC,
self.common_mu,
N=100,
color='b',
legend=False,
units=AU,
axes=axis)
# Lambert arc to reach seq[1]
dt = (1 - x[4]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, self.common_mu, False, False)
plot_lambert(l, sol=0, color='r', legend=False, units=AU, axes=axis)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# First DSM occuring at time nu1*T1
DV[0] = norm([a - b for a, b in zip(v_beg_l, v)])
# 4 - And we proceed with each successive leg
for i in range(1, self.n_legs):
# Fly-by
v_out = fb_prop(v_end_l, v_P[i],
x[7 + (i - 1) * 4] * self._seq[i].radius,
x[6 + (i - 1) * 4], self._seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu)
plot_kepler(r_P[i],
v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu,
N=100,
color='b',
legend=False,
units=AU,
axes=axis)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[8 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, self.common_mu, False,
False)
plot_lambert(l,
sol=0,
color='r',
legend=False,
units=AU,
N=1000,
axes=axis)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
plt.show()
return axis
def plot(self, x, axes=None):
"""
ax = prob.plot_trajectory(x, axes=None)
- x: encoded trajectory
- axes: matplotlib axis where to plot. If None figure and axis will be created
- [out] ax: matplotlib axis where to plot
Plots the trajectory represented by a decision vector x on the 3d axis ax
Example::
ax = prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep.orbit_plots import plot_planet, plot_lambert, plot_kepler
if axes is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axes = fig.gca(projection='3d')
axes.scatter(0, 0, 0, color='y')
# 1 - we 'decode' the chromosome recording the various deep space
# manouvres timing (days) in the list T
T = list([0] * (self.N_max - 1))
for i in range(len(T)):
T[i] = log(x[2 + 4 * i])
total = sum(T)
T = [x[1] * time / total for time in T]
# 2 - We compute the starting and ending position
r_start, v_start = self.start.eph(epoch(x[0]))
if self.phase_free:
r_target, v_target = self.target.eph(epoch(x[-1]))
else:
r_target, v_target = self.target.eph(epoch(x[0] + x[1]))
plot_planet(self.start, t0=epoch(x[0]), color=(
0.8, 0.6, 0.8), legend=True, units=AU, ax=axes, s=0)
plot_planet(self.target, t0=epoch(
x[0] + x[1]), color=(0.8, 0.6, 0.8), legend=True, units=AU, ax=axes, s=0)
DV_list = x[5::4]
maxDV = max(DV_list)
DV_list = [s / maxDV * 30 for s in DV_list]
colors = ['b', 'r'] * (len(DV_list) + 1)
# 3 - We loop across inner impulses
rsc = r_start
vsc = v_start
for i, time in enumerate(T[:-1]):
theta = 2 * pi * x[3 + 4 * i]
phi = acos(2 * x[4 + 4 * i] - 1) - pi / 2
Vinfx = x[5 + 4 * i] * cos(phi) * cos(theta)
Vinfy = x[5 + 4 * i] * cos(phi) * sin(theta)
Vinfz = x[5 + 4 * i] * sin(phi)
# We apply the (i+1)-th impulse
vsc = [a + b for a, b in zip(vsc, [Vinfx, Vinfy, Vinfz])]
axes.scatter(rsc[0] / AU, rsc[1] / AU, rsc[2] /
AU, color='k', s=DV_list[i])
plot_kepler(rsc, vsc, T[i] * DAY2SEC, self.__common_mu,
N=200, color=colors[i], legend=False, units=AU, ax=axes)
rsc, vsc = propagate_lagrangian(
rsc, vsc, T[i] * DAY2SEC, self.__common_mu)
cw = (ic2par(rsc, vsc, self.start.mu_central_body)[2] > pi / 2)
# We now compute the remaining two final impulses
# Lambert arc to reach seq[1]
dt = T[-1] * DAY2SEC
l = lambert_problem(rsc, r_target, dt, self.__common_mu, cw, False)
plot_lambert(l, sol=0, color=colors[
i + 1], legend=False, units=AU, ax=axes, N=200)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
DV1 = norm([a - b for a, b in zip(v_beg_l, vsc)])
DV2 = norm([a - b for a, b in zip(v_end_l, v_target)])
axes.scatter(rsc[0] / AU, rsc[1] / AU, rsc[2] / AU,
color='k', s=min(DV1 / maxDV * 30, 40))
axes.scatter(r_target[0] / AU, r_target[1] / AU,
r_target[2] / AU, color='k', s=min(DV2 / maxDV * 30, 40))
return axes
ast_orbel = (2.77 * AU, 0.075, 9.65 * DEG2RAD, 80.33 * DEG2RAD,
72.52 * DEG2RAD, 95.99 * DEG2RAD) # a,e,i,W,w,M (SI and RAD)
ast_mu = 6e10
ast_radius = 1e5
ast_name = 'asteroid'
asteroid = keplerian(ast_time, ast_orbel, MU_SUN, ast_mu, ast_radius,
ast_radius * 1.1, ast_name)
rA, vA = asteroid.eph(ast_time)
#earth
pl = jpl_lp('earth')
rE, vE = pl.eph(ast_time)
# plot
fig = plt.figure()
axis = fig.gca(projection='3d')
axis.scatter([0], [0], [0], color='y') #sun
plot_planet(asteroid,
t0=ast_time,
color=(1, 0.4, 0),
legend=True,
units=AU,
ax=axis) #asteroid
plot_planet(pl,
t0=ast_time,
color=(0.8, 0.8, 1),
legend=True,
units=AU,
ax=axis) #earth
plt.show()
def plot(self, x, ax=None):
"""
ax = prob.plot(x, ax=None)
- x: encoded trajectory
- ax: matplotlib axis where to plot. If None figure and axis will be created
- [out] ax: matplotlib axis where to plot
Plots the trajectory represented by a decision vector x on the 3d axis ax
Example::
ax = prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep.orbit_plots import plot_planet, plot_lambert, plot_kepler
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
axis.scatter(0, 0, 0, color='y')
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T and the cartesian components of vinf
T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x)
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs + 1))
r_P = list([None] * (self.__n_legs + 1))
v_P = list([None] * (self.__n_legs + 1))
DV = list([None] * (self.__n_legs + 1))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(planet, t0=t_P[i], color=(
0.8, 0.6, 0.8), legend=True, units=AU, ax=axis)
# 3 - We start with the first leg
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(
r_P[0], v0, x[5] * T[0] * DAY2SEC, self.common_mu)
plot_kepler(r_P[0], v0, x[5] * T[0] * DAY2SEC, self.common_mu,
N=100, color='b', legend=False, units=AU, ax=axis)
# Lambert arc to reach seq[1]
dt = (1 - x[5]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, self.common_mu, False, False)
plot_lambert(l, sol=0, color='r', legend=False, units=AU, ax=axis)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# First DSM occuring at time nu1*T1
DV[0] = norm([a - b for a, b in zip(v_beg_l, v)])
# 4 - And we proceed with each successive leg
for i in range(1, self.__n_legs):
# Fly-by
v_out = fb_prop(v_end_l, v_P[i], x[
8 + (i - 1) * 4] * self.seq[i].radius, x[7 + (i - 1) * 4], self.seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(
r_P[i], v_out, x[9 + (i - 1) * 4] * T[i] * DAY2SEC, self.common_mu)
plot_kepler(r_P[i], v_out, x[9 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu, N=100, color='b', legend=False, units=AU, ax=axis)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[9 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt,
self.common_mu, False, False)
plot_lambert(l, sol=0, color='r', legend=False,
units=AU, N=1000, ax=axis)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
plt.show()
return axis
def plot(self, x, axes=None):
"""
ax = prob.plot(x, ax=None)
- x: encoded trajectory
- ax: matplotlib axis where to plot. If None figure and axis will be created
- [out] ax: matplotlib axis where to plot
Plots the trajectory represented by a decision vector x on the 3d axis ax
Example::
ax = prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep.orbit_plots import plot_sf_leg, plot_planet
# Creating the axis if necessary
if axes is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
else:
ax = axes
# Plotting the Sun ........
ax.scatter([0], [0], [0], color=['y'])
# We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self._n_legs + 1))
r_P = list([None] * (self._n_legs + 1))
v_P = list([None] * (self._n_legs + 1))
for i in range(len(self._seq)):
t_P[i] = epoch(x[0] + sum(x[1:i * 8:8]))
r_P[i], v_P[i] = self._seq[i].eph(t_P[i])
plot_planet(self._seq[i],
t0=t_P[i],
units=AU,
legend=False,
color=(0.7, 0.7, 0.7),
s=30,
axes=ax)
# We assemble the constraints.
# 1 - Mismatch Constraints
for i in range(self._n_legs):
# Departure velocity of the spacecraft in the heliocentric frame
v0 = [a + b for a, b in zip(v_P[i], x[3 + 8 * i:6 + 8 * i])]
if i == 0:
m0 = self._mass[1]
else:
m0 = x[2 + 8 * (i - 1)]
x0 = sc_state(r_P[i], v0, m0)
vf = [a + b for a, b in zip(v_P[i + 1], x[6 + 8 * i:9 + 8 * i])]
xf = sc_state(r_P[i + 1], vf, x[2 + 8 * i])
idx_start = 1 + 8 * self._n_legs + sum(self._n_seg[:i]) * 3
idx_end = 1 + 8 * self._n_legs + sum(self._n_seg[:i + 1]) * 3
self._leg.set(t_P[i], x0, x[idx_start:idx_end], t_P[i + 1], xf)
plot_sf_leg(self._leg, units=AU, N=10, axes=ax, legend=False)
return axes
def plot(self, x, ax=None):
"""
ax = prob.plot(x, ax=None)
- x: encoded trajectory
- ax: matplotlib axis where to plot. If None figure and axis will be created
- [out] ax: matplotlib axis where to plot
Plots the trajectory represented by a decision vector x on the 3d axis ax
Example::
ax = prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep import epoch, AU
from pykep.sims_flanagan import sc_state
from pykep.orbit_plots import plot_planet, plot_sf_leg
# Creating the axis if necessary
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
# Plotting the Sun ........
axis.scatter([0], [0], [0], color='y')
# Plotting the legs .......
# 1 - We decode the chromosome extracting the time of flights
T = list([0] * (self.__n_legs))
for i in range(self.__n_legs):
T[i] = x[1 + i * 8]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs + 1))
r_P = list([None] * (self.__n_legs + 1))
v_P = list([None] * (self.__n_legs + 1))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
# 3 - We iterate through legs to compute mismatches and throttles
# constraints
ceq = list()
cineq = list()
m0 = self.__sc.mass
for i in range(self.__n_legs):
# First Leg
v = [a + b for a, b in zip(v_P[i], x[(3 + i * 8):(6 + i * 8)])]
x0 = sc_state(r_P[i], v, m0)
v = [a + b for a,
b in zip(v_P[i + 1], x[(6 + i * 8):(11 + i * 8)])]
xe = sc_state(r_P[i + 1], v, x[2 + i * 8])
throttles = x[(1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i])):(
1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i]) + 3 * self.__n_seg[i])]
self.__leg.set(t_P[i], x0, throttles, t_P[i + 1], xe)
# update mass!
m0 = x[2 + 8 * i]
plot_sf_leg(self.__leg, units=AU, N=10, ax=axis)
# Plotting planets
for i, planet in enumerate(self.seq):
plot_planet(planet, t_P[i], units=AU,
legend=True, color=(0.7, 0.7, 1), ax=axis)
plt.show()
return axis
def _fitness_impl(self, decoded_x, logging=False, plotting=False, ax=None):
""" Computation of the objective function. """
saturn_distance_violated = 0
# decode x
t0, u, v, dep_vinf, etas, T, betas, rps = decoded_x
# convert incoming velocity vector
theta, phi = 2.0 * pi * u, acos(2.0 * v - 1.0) - pi / 2.0
Vinfx = dep_vinf * cos(phi) * cos(theta)
Vinfy = dep_vinf * cos(phi) * sin(theta)
Vinfz = dep_vinf * sin(phi)
# epochs and ephemerides of the planetary encounters
t_P = list([None] * (self._n_legs + 1))
r_P = list([None] * (self._n_legs + 1))
v_P = list([None] * (self._n_legs + 1))
lamberts = list([None] * (self._n_legs))
v_outs = list([None] * (self._n_legs))
DV = list([0.0] * (self._n_legs + 1))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(t0 + sum(T[0:i]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
# first leg
v_outs[0] = [Vinfx, Vinfy, Vinfz] # bug fixed
# check first leg up to DSM
saturn_distance_violated += self.check_distance(
r_P[0], v_outs[0], t0, etas[0] * T[0])
r, v = propagate_lagrangian(r_P[0], v_outs[0],
etas[0] * T[0] * DAY2SEC, self.common_mu)
# Lambert arc to reach seq[1]
dt = (1.0 - etas[0]) * T[0] * DAY2SEC
lamberts[0] = lambert_problem(r, r_P[1], dt, self.common_mu, self.cw,
0)
v_end_l = lamberts[0].get_v2()[0]
v_beg_l = lamberts[0].get_v1()[0]
# First DSM occuring at time eta0*T0
DV[0] = norm([a - b for a, b in zip(v_beg_l, v)])
# checking first leg after DSM
saturn_distance_violated += self.check_distance(
r, v_beg_l, etas[0] * T[0], T[0])
# successive legs
for i in range(1, self._n_legs):
# Fly-by
v_outs[i] = fb_prop(v_end_l, v_P[i],
rps[i - 1] * self.seq[i].radius, betas[i - 1],
self.seq[i].mu_self)
# checking next leg up to DSM
saturn_distance_violated += self.check_distance(
r_P[i], v_outs[i], T[i - 1], etas[i] * T[i])
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_outs[i],
etas[i] * T[i] * DAY2SEC,
self.common_mu)
# Lambert arc to reach next body
dt = (1 - etas[i]) * T[i] * DAY2SEC
lamberts[i] = lambert_problem(r, r_P[i + 1], dt, self.common_mu,
self.cw, 0)
v_end_l = lamberts[i].get_v2()[0]
v_beg_l = lamberts[i].get_v1()[0]
# DSM occuring at time eta_i*T_i
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
# checking next leg after DSM
saturn_distance_violated += self.check_distance(
r, v_beg_l, etas[i] * T[i], T[i])
# single dv penalty for now
if saturn_distance_violated > 0:
DV[-1] += DV_PENALTY
arr_vinf = norm([a - b for a, b in zip(v_end_l, v_P[-1])])
# last Delta-v
if self._add_vinf_arr:
DV[-1] = arr_vinf
if self._add_vinf_dep:
DV[0] += dep_vinf
# pretty printing
if logging:
print("First leg: {} to {}".format(self.seq[0].name,
self.seq[1].name))
print("Departure: {0} ({1:0.6f} mjd2000)".format(
t_P[0], t_P[0].mjd2000))
print("Duration: {0:0.6f}d".format(T[0]))
print("VINF: {0:0.3f}m/s".format(dep_vinf))
print("DSM after {0:0.6f}d".format(etas[0] * T[0]))
print("DSM magnitude: {0:0.6f}m/s".format(DV[0]))
for i in range(1, self._n_legs):
print("\nleg {}: {} to {}".format(i + 1, self.seq[i].name,
self.seq[i + 1].name))
print("Duration: {0:0.6f}d".format(T[i]))
print("Fly-by epoch: {0} ({1:0.6f} mjd2000)".format(
t_P[i], t_P[i].mjd2000))
print("Fly-by radius: {0:0.6f} planetary radii".format(rps[i -
1]))
print("DSM after {0:0.6f}d".format(etas[i] * T[i]))
print("DSM magnitude: {0:0.6f}m/s".format(DV[i]))
print("\nArrival at {}".format(self.seq[-1].name))
print("Arrival epoch: {0} ({1:0.6f} mjd2000)".format(
t_P[-1], t_P[-1].mjd2000))
print("Arrival Vinf: {0:0.3f}m/s".format(arr_vinf))
print("Total mission time: {0:0.6f}d ({1:0.3f} years)".format(
sum(T),
sum(T) / 365.25))
# plotting
if plotting:
ax.scatter(0, 0, 0, color='chocolate')
for i, planet in enumerate(self.seq):
plot_planet(planet,
t0=t_P[i],
color=pl2c[planet.name],
legend=True,
units=AU,
ax=ax)
for i in range(0, self._n_legs):
plot_kepler(r_P[i],
v_outs[i],
etas[i] * T[i] * DAY2SEC,
self.common_mu,
N=100,
color='b',
legend=False,
units=AU,
ax=ax)
for l in lamberts:
plot_lambert(l,
sol=0,
color='r',
legend=False,
units=AU,
N=1000,
ax=ax)
# returning building blocks for objectives
return (DV, T, arr_vinf, lamberts)
def plot(self, x, axes=None):
"""
ax = prob.plot_trajectory(x, axes=None)
- x: encoded trajectory
- axes: matplotlib axis where to plot. If None figure and axis will be created
- [out] ax: matplotlib axis where to plot
Plots the trajectory represented by a decision vector x on the 3d axis ax
Example::
ax = prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep.orbit_plots import plot_planet, plot_lambert, plot_kepler
if axes is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axes = fig.gca(projection='3d')
axes.scatter(0, 0, 0, color='y')
# 1 - we 'decode' the chromosome recording the various deep space
# manouvres timing (days) in the list T
T = list([0] * (self.N_max - 1))
for i in range(len(T)):
T[i] = log(x[2 + 4 * i])
total = sum(T)
T = [x[1] * time / total for time in T]
# 2 - We compute the starting and ending position
r_start, v_start = self.start.eph(epoch(x[0]))
if self.phase_free:
r_target, v_target = self.target.eph(epoch(x[-1]))
else:
r_target, v_target = self.target.eph(epoch(x[0] + x[1]))
plot_planet(self.start,
t0=epoch(x[0]),
color=(0.8, 0.6, 0.8),
legend=True,
units=AU,
ax=axes,
s=0)
plot_planet(self.target,
t0=epoch(x[0] + x[1]),
color=(0.8, 0.6, 0.8),
legend=True,
units=AU,
ax=axes,
s=0)
DV_list = x[5::4]
maxDV = max(DV_list)
DV_list = [s / maxDV * 30 for s in DV_list]
colors = ['b', 'r'] * (len(DV_list) + 1)
# 3 - We loop across inner impulses
rsc = r_start
vsc = v_start
for i, time in enumerate(T[:-1]):
theta = 2 * pi * x[3 + 4 * i]
phi = acos(2 * x[4 + 4 * i] - 1) - pi / 2
Vinfx = x[5 + 4 * i] * cos(phi) * cos(theta)
Vinfy = x[5 + 4 * i] * cos(phi) * sin(theta)
Vinfz = x[5 + 4 * i] * sin(phi)
# We apply the (i+1)-th impulse
vsc = [a + b for a, b in zip(vsc, [Vinfx, Vinfy, Vinfz])]
axes.scatter(rsc[0] / AU,
rsc[1] / AU,
rsc[2] / AU,
color='k',
s=DV_list[i])
plot_kepler(rsc,
vsc,
T[i] * DAY2SEC,
self.__common_mu,
N=200,
color=colors[i],
legend=False,
units=AU,
ax=axes)
rsc, vsc = propagate_lagrangian(rsc, vsc, T[i] * DAY2SEC,
self.__common_mu)
cw = (ic2par(rsc, vsc, self.start.mu_central_body)[2] > pi / 2)
# We now compute the remaining two final impulses
# Lambert arc to reach seq[1]
dt = T[-1] * DAY2SEC
l = lambert_problem(rsc, r_target, dt, self.__common_mu, cw, False)
plot_lambert(l,
sol=0,
color=colors[i + 1],
legend=False,
units=AU,
ax=axes,
N=200)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
DV1 = norm([a - b for a, b in zip(v_beg_l, vsc)])
DV2 = norm([a - b for a, b in zip(v_end_l, v_target)])
axes.scatter(rsc[0] / AU,
rsc[1] / AU,
rsc[2] / AU,
color='k',
s=min(DV1 / maxDV * 30, 40))
axes.scatter(r_target[0] / AU,
r_target[1] / AU,
r_target[2] / AU,
color='k',
s=min(DV2 / maxDV * 30, 40))
return axes
def plot(self, x, ax=None):
"""
ax = prob.plot(x, ax=None)
- x: encoded trajectory
- ax: matplotlib axis where to plot. If None figure and axis will be created
- [out] ax: matplotlib axis where to plot
Plots the trajectory represented by a decision vector x on the 3d axis ax
Example::
ax = prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pykep import epoch, AU
from pykep.sims_flanagan import sc_state
from pykep.orbit_plots import plot_planet, plot_sf_leg
# Creating the axis if necessary
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
# Plotting the Sun ........
axis.scatter([0], [0], [0], color='y')
# Plotting the legs .......
# 1 - We decode the chromosome extracting the time of flights
T = list([0] * (self.__n_legs))
for i in range(self.__n_legs):
T[i] = x[1 + i * 8]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs + 1))
r_P = list([None] * (self.__n_legs + 1))
v_P = list([None] * (self.__n_legs + 1))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
# 3 - We iterate through legs to compute mismatches and throttles
# constraints
ceq = list()
cineq = list()
m0 = self.__sc.mass
for i in range(self.__n_legs):
# First Leg
v = [a + b for a, b in zip(v_P[i], x[(3 + i * 8):(6 + i * 8)])]
x0 = sc_state(r_P[i], v, m0)
v = [
a + b for a, b in zip(v_P[i + 1], x[(6 + i * 8):(11 + i * 8)])
]
xe = sc_state(r_P[i + 1], v, x[2 + i * 8])
throttles = x[(1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i])):(
1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i]) +
3 * self.__n_seg[i])]
self.__leg.set(t_P[i], x0, throttles, t_P[i + 1], xe)
# update mass!
m0 = x[2 + 8 * i]
plot_sf_leg(self.__leg, units=AU, N=10, ax=axis)
# Plotting planets
for i, planet in enumerate(self.seq):
plot_planet(planet,
t_P[i],
units=AU,
legend=True,
color=(0.7, 0.7, 1),
ax=axis)
plt.show()
return axis
