def _mga_incipit_cstrs_ctor(self,
seq=[gtoc6('io'),
gtoc6('io'),
gtoc6('europa')],
t0=[epoch(7305.0), epoch(11323.0)],
tof=[[100, 200], [3, 200], [4, 100]],
Tmax=300.00,
Dmin=2.0):
"""
USAGE: mga_incipit_cstrs(seq = [gtoc6('io'),gtoc6('io'),gtoc6('europa')], t0 = [epoch(6905.0),epoch(11323.0)], tof = [[100,200],[3,200],[4,100]], Tmax = 365.25, Dmin = 0.2)
* seq: list of jupiter moons defining the trajectory incipit
* t0: list of two epochs defining the launch window
* tof: list of n lists containing the lower and upper bounds for the legs flight times (days)
"""
# We construct the arg list for the original constructor exposed by
# boost_python
arg_list = []
arg_list.append(seq)
arg_list.append(t0[0])
arg_list.append(t0[1])
arg_list.append(tof)
arg_list.append(Tmax)
arg_list.append(Dmin)
self._orig_init(*arg_list)
def _mga_1dsm_tof_ctor(
self, seq=[
jpl_lp('earth'), jpl_lp('venus'), jpl_lp('earth')], t0=[
epoch(0), epoch(1000)], tof=[
[
50, 900], [
50, 900]], vinf=[
0.5, 2.5], multi_objective=False, add_vinf_dep=False, add_vinf_arr=True):
"""
Constructs an mga_1dsm problem (tof-encoding)
USAGE: problem.mga_1dsm(seq = [jpl_lp('earth'),jpl_lp('venus'),jpl_lp('earth')], t0 = [epoch(0),epoch(1000)], tof = [ [50, 900], [50, 900] ], vinf = [0.5, 2.5], multi_objective = False, add_vinf_dep = False, add_vinf_arr = True)
* seq: list of PyKEP planets defining the encounter sequence (including the starting planet)
* t0: list of two epochs defining the launch window
* tof: list of intervals defining the times of flight (days)
* vinf: list of two floats defining the minimum and maximum allowed initial hyperbolic velocity at launch (km/sec)
* multi_objective: when True constructs a multiobjective problem (dv, T)
* add_vinf_dep: when True the computed Dv includes the initial hyperbolic velocity (at launch)
* add_vinf_arr: when True the computed Dv includes the final hyperbolic velocity (at arrival)
"""
# We construct the arg list for the original constructor exposed by
# boost_python
arg_list = []
arg_list.append(seq)
arg_list.append(t0[0])
arg_list.append(t0[1])
arg_list.append(tof)
arg_list.append(vinf[0])
arg_list.append(vinf[1])
arg_list.append(multi_objective)
arg_list.append(add_vinf_dep)
arg_list.append(add_vinf_arr)
self._orig_init(*arg_list)
def _mga_incipit_cstrs_ctor(
self, seq=[
gtoc6('io'), gtoc6('io'), gtoc6('europa')], t0=[
epoch(7305.0), epoch(11323.0)], tof=[
[
100, 200], [
3, 200], [
4, 100]], Tmax=300.00, Dmin=2.0):
"""
USAGE: mga_incipit_cstrs(seq = [gtoc6('io'),gtoc6('io'),gtoc6('europa')], t0 = [epoch(6905.0),epoch(11323.0)], tof = [[100,200],[3,200],[4,100]], Tmax = 365.25, Dmin = 0.2)
* seq: list of jupiter moons defining the trajectory incipit
* t0: list of two epochs defining the launch window
* tof: list of n lists containing the lower and upper bounds for the legs flight times (days)
"""
# We construct the arg list for the original constructor exposed by
# boost_python
arg_list = []
arg_list.append(seq)
arg_list.append(t0[0])
arg_list.append(t0[1])
arg_list.append(tof)
arg_list.append(Tmax)
arg_list.append(Dmin)
self._orig_init(*arg_list)
def _mga_1dsm_tof_plot(self, x):
"""
Plots the trajectory represented by the decision vector 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
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
axis.scatter(0, 0, 0, color='y')
seq = self.get_sequence()
# 2 - We plot the first leg
r_P0, v_P0 = seq[0].eph(epoch(x[0]))
plot_planet(seq[0],
t0=epoch(x[0]),
color=(0.8, 0.6, 0.8),
legend=True,
units=AU,
ax=axis)
r_P1, v_P1 = seq[1].eph(epoch(x[0] + x[5]))
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
v0 = [a + b for a, b in zip(v_P0, [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P0, v0, x[4] * x[5] * DAY2SEC,
seq[0].mu_central_body)
plot_kepler(r_P0,
v0,
x[4] * x[5] * DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU,
ax=axis)
# Lambert arc to reach seq[1]
dt = (1 - x[4]) * x[5] * DAY2SEC
l = lambert_problem(r, r_P1, dt, seq[0].mu_central_body)
plot_lambert(l, sol=0, color='r', legend=False, units=AU, ax=axis)
v_end_l = l.get_v2()[0]
vinf_in = [a - b for a, b in zip(v_end_l, v_P1)]
_part_plot(x[6:], AU, axis, seq[1:], x[0] + x[5], vinf_in)
return axis
def _mga_1dsm_tof_plot(self, x):
"""
Plots the trajectory represented by the decision vector 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
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
axis.scatter(0, 0, 0, color='y')
seq = self.get_sequence()
# 2 - We plot the first leg
r_P0, v_P0 = seq[0].eph(epoch(x[0]))
plot_planet(seq[0], t0=epoch(x[0]), color=(
0.8, 0.6, 0.8), legend=True, units = AU, ax=axis)
r_P1, v_P1 = seq[1].eph(epoch(x[0] + x[5]))
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
v0 = [a + b for a, b in zip(v_P0, [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(
r_P0, v0, x[4] * x[5] * DAY2SEC, seq[0].mu_central_body)
plot_kepler(
r_P0,
v0,
x[4] *
x[5] *
DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU,
ax=axis)
# Lambert arc to reach seq[1]
dt = (1 - x[4]) * x[5] * DAY2SEC
l = lambert_problem(r, r_P1, dt, seq[0].mu_central_body)
plot_lambert(l, sol=0, color='r', legend=False, units=AU, ax=axis)
v_end_l = l.get_v2()[0]
vinf_in = [a - b for a, b in zip(v_end_l, v_P1)]
_part_plot(x[6:], AU, axis, seq[1:], x[0] + x[5], vinf_in)
return axis
def _pl2pl_fixed_time_ctor(self, ast0=gtoc7(7422), ast1=gtoc7(14254), t0=epoch(9818),
t1=epoch(10118), sc=spacecraft(2000, 0.3, 3000), n_seg=5, obj="fin_m"):
"""
Constructs a Planet 2 Planet problem with fixed time.
Chromosome is defined as:
x = [m_f, Th_0_x, Th_0_y, Th_0_z, .., Th_n_x, Th_n_y, Th_n_z]
, where 'm_f' is the final mass, while 'Th_i_j' is the throttle component in direction 'j' (x,y,z) for the 'i'-th segment.
USAGE: problem.pl2pl_fixed_time(ast0=gtoc7(7422), ast1=gtoc7(14254), t0=epoch(9818),
t1=epoch(10118), sc=spacecraft(2000, 0.3, 3000), n_seg = 5)
* ast0: first planet
* ast0: second planet
* t0: departure epoch (from planet ast0)
* t1: arrival epoch (to planet ast1)
* sc: spacecraft object
* n_seg: number of segments
"""
# We construct the arg list for the original constructor exposed by
# boost_python
from PyGMO.problem._problem import _pl2pl2_fixed_time_objective
def objective(x):
return {
"fin_m": _pl2pl2_fixed_time_objective.FIN_M,
"crit_m": _pl2pl2_fixed_time_objective.FIN_INI_M
}[x]
arg_list = []
arg_list.append(ast0)
arg_list.append(ast1)
arg_list.append(t0)
arg_list.append(t1)
arg_list.append(sc)
arg_list.append(n_seg)
arg_list.append(objective(obj))
self._orig_init(*arg_list)
def _part_plot(x, units, axis, seq, start_mjd2000, vinf_in):
"""
Plots the trajectory represented by a decision vector x = [beta,rp,eta,T] * N
associated to a sequence seq, a start_mjd2000 and an incoming vinf_in
"""
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
legs = len(x) // 4
common_mu = seq[0].mu_central_body
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T
T = x[3::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (legs + 1))
r_P = list([None] * (legs + 1))
v_P = list([None] * (legs + 1))
for i, planet in enumerate(seq):
t_P[i] = epoch(start_mjd2000 + sum(T[: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 = units, ax=axis)
v_end_l = [a + b for a, b in zip(v_P[0], vinf_in)]
# 4 - And we iterate on the legs
for i in range(0, legs):
# Fly-by
v_out = fb_prop(v_end_l,
v_P[i],
x[1 + 4 * i] * seq[i].radius,
x[4 * i],
seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(
r_P[i], v_out, x[4 * i + 2] * T[i] * DAY2SEC, common_mu)
plot_kepler(r_P[i], v_out, x[4 * i + 2] * T[i] * DAY2SEC,
common_mu, N=500, color='b', legend=False, units=units, ax=axis)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, common_mu, False, False)
plot_lambert(
l, sol=0, color='r', legend=False, units=units, N=500, ax=axis)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
def _mga_incipit_plot(self, x, plot_leg_0=False):
"""
Plots the trajectory represented by the decision vector x
Example::
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
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d', aspect='equal')
ax.scatter(0, 0, 0, color='y')
JR = 71492000.0
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
r_P, v_P = seq[0].eph(epoch(x[0] + x[3]))
# 3 - We start with the first leg: a lambert arc
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
# phi close to zero is in the moon orbit plane injection
r = [cos(phi) * sin(theta), cos(phi) * cos(theta), sin(phi)]
r = [JR * 1000 * d for d in r]
l = lambert_problem(r, r_P, x[3] * DAY2SEC, common_mu, False, False)
if (plot_leg_0):
plot_lambert(ax, l, sol=0, color='k', legend=False, units=JR, N=500)
# Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
vinf_in = [a - b for a, b in zip(v_end_l, v_P)]
_part_plot(x[4:], JR, ax, seq, x[0] + x[3], vinf_in)
return ax
def _mga_incipit_plot(self, x, plot_leg_0=False):
"""
Plots the trajectory represented by the decision vector x
Example::
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
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d', aspect='equal')
ax.scatter(0, 0, 0, color='y')
JR = 71492000.0
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
r_P, v_P = seq[0].eph(epoch(x[0] + x[3]))
# 3 - We start with the first leg: a lambert arc
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
# phi close to zero is in the moon orbit plane injection
r = [cos(phi) * sin(theta), cos(phi) * cos(theta), sin(phi)]
r = [JR * 1000 * d for d in r]
l = lambert_problem(r, r_P, x[3] * DAY2SEC, common_mu, False, False)
if (plot_leg_0):
plot_lambert(ax, l, sol=0, color='k', legend=False, units=JR, N=500)
# Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
vinf_in = [a - b for a, b in zip(v_end_l, v_P)]
_part_plot(x[4:], JR, ax, seq, x[0] + x[3], vinf_in)
return ax
def _mga_part_ctor(self,
seq=[gtoc6('europa'),
gtoc6('europa'),
gtoc6('europa')],
tof=[[5, 50], [5, 50]],
t0=epoch(11000),
v_inf_in=[1500.0, 350.0, 145.0]):
"""
USAGE: mga_part(seq = [gtoc6('europa'),gtoc6('europa'),gtoc6('europa')], tof = [[5,50],[5,50]], t0 = epoch(11000), v_inf_in[1500.0,350.0,145.0])
* seq: list of jupiter moons defining the trajectory incipit
* tof: list of n lists containing the lower and upper bounds for the legs flight times (days)
* t0: starting epoch
* v_inf_in: Incoming spacecraft relative velocity
"""
# We construct the arg list for the original constructor exposed by
# boost_python
arg_list = []
arg_list.append(seq)
arg_list.append(tof)
arg_list.append(t0)
arg_list.append(v_inf_in)
self._orig_init(*arg_list)
def _mga_part_ctor(
self, seq=[
gtoc6('europa'), gtoc6('europa'), gtoc6('europa')], tof=[
[
5, 50], [
5, 50]], t0=epoch(11000), v_inf_in=[
1500.0, 350.0, 145.0]):
"""
USAGE: mga_part(seq = [gtoc6('europa'),gtoc6('europa'),gtoc6('europa')], tof = [[5,50],[5,50]], t0 = epoch(11000), v_inf_in[1500.0,350.0,145.0])
* seq: list of jupiter moons defining the trajectory incipit
* tof: list of n lists containing the lower and upper bounds for the legs flight times (days)
* t0: starting epoch
* v_inf_in: Incoming spacecraft relative velocity
"""
# We construct the arg list for the original constructor exposed by
# boost_python
arg_list = []
arg_list.append(seq)
arg_list.append(tof)
arg_list.append(t0)
arg_list.append(v_inf_in)
self._orig_init(*arg_list)
def _mga_part_plot_old(self, x):
"""
Plots the trajectory represented by the decision vector x
Example::
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
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d', aspect='equal')
ax.scatter(0, 0, 0, color='y')
JR = 71492000.0
legs = len(x) / 4
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
start_mjd2000 = self.t0.mjd2000
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T
T = x[3::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (legs + 1))
r_P = list([None] * (legs + 1))
v_P = list([None] * (legs + 1))
for i, planet in enumerate(seq):
t_P[i] = epoch(start_mjd2000 + sum(T[:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax,
planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=JR)
v_end_l = [a + b for a, b in zip(v_P[0], self.vinf_in)]
# 4 - And we iterate on the legs
for i in range(0, legs):
# Fly-by
v_out = fb_prop(v_end_l, v_P[i], x[1 + 4 * i] * seq[i - 1].radius,
x[4 * i], seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[4 * i + 2] * T[i] * DAY2SEC, common_mu)
plot_kepler(ax,
r_P[i],
v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
common_mu,
N=500,
color='b',
legend=False,
units=JR)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, common_mu, False, False)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=JR, N=500)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
plt.show()
return ax
def _mga_incipit_plot_old(self, x, plot_leg_0=False):
"""
Plots the trajectory represented by the decision vector x
Example::
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
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d', aspect='equal')
ax.scatter(0, 0, 0, color='y')
JR = 71492000.0
legs = len(x) / 4
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T
T = x[3::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * legs)
r_P = list([None] * legs)
v_P = list([None] * legs)
DV = list([None] * legs)
for i, planet in enumerate(seq):
t_P[i] = epoch(x[0] + sum(T[:i + 1]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax,
planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=JR)
# 3 - We start with the first leg: a lambert arc
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
# phi close to zero is in the moon orbit plane injection
r = [cos(phi) * sin(theta), cos(phi) * cos(theta), sin(phi)]
r = [JR * 1000 * d for d in r]
l = lambert_problem(r, r_P[0], T[0] * DAY2SEC, common_mu, False, False)
if (plot_leg_0):
plot_lambert(ax, l, sol=0, color='k', legend=False, units=JR, N=500)
# Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# 4 - And we proceed with each successive leg
for i in range(1, legs):
# Fly-by
v_out = fb_prop(v_end_l, v_P[i - 1], x[1 + 4 * i] * seq[i - 1].radius,
x[4 * i], seq[i - 1].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i - 1], v_out,
x[4 * i + 2] * T[i] * DAY2SEC, common_mu)
plot_kepler(ax,
r_P[i - 1],
v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
common_mu,
N=500,
color='b',
legend=False,
units=JR)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i], dt, common_mu, False, False)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=JR, N=500)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
plt.show()
return ax
def _mga_1dsm_tof_plot_old(self, x):
"""
Plots the trajectory represented by the decision vector 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
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.scatter(0, 0, 0, color='y')
seq = self.get_sequence()
n = (len(seq) - 1)
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T
T = x[5::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (n + 1))
r_P = list([None] * (n + 1))
v_P = list([None] * (n + 1))
DV = list([None] * (n + 1))
for i, planet in enumerate(seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax,
planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=AU)
# 3 - We start with the first leg
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
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,
seq[0].mu_central_body)
plot_kepler(ax,
r_P[0],
v0,
x[4] * T[0] * DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU)
# Lambert arc to reach seq[1]
dt = (1 - x[4]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, seq[0].mu_central_body)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=AU)
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, n):
# Fly-by
v_out = fb_prop(v_end_l, v_P[i], x[7 + (i - 1) * 4] * seq[i].radius,
x[6 + (i - 1) * 4], 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,
seq[0].mu_central_body)
plot_kepler(ax,
r_P[i],
v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU)
# 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, seq[0].mu_central_body)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=AU)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# DSM occurring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
return ax
def _mga_1dsm_tof_plot_old(self, x):
"""
Plots the trajectory represented by the decision vector 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
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.scatter(0, 0, 0, color='y')
seq = self.get_sequence()
n = (len(seq) - 1)
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T
T = x[5::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (n + 1))
r_P = list([None] * (n + 1))
v_P = list([None] * (n + 1))
DV = list([None] * (n + 1))
for i, planet in enumerate(seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax, planet, t0=t_P[i], color=(
0.8, 0.6, 0.8), legend=True, units = AU)
# 3 - We start with the first leg
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
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, seq[0].mu_central_body)
plot_kepler(
ax,
r_P[0],
v0,
x[4] *
T[0] *
DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU)
# Lambert arc to reach seq[1]
dt = (1 - x[4]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, seq[0].mu_central_body)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=AU)
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, n):
# Fly-by
v_out = fb_prop(v_end_l,
v_P[i],
x[7 + (i - 1) * 4] * seq[i].radius,
x[6 + (i - 1) * 4],
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, seq[0].
mu_central_body)
plot_kepler(ax,
r_P[i],
v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU)
# 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, seq[0].mu_central_body)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=AU)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# DSM occurring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
return ax
def _mga_incipit_plot_old(self, x, plot_leg_0=False):
"""
Plots the trajectory represented by the decision vector x
Example::
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
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d', aspect='equal')
ax.scatter(0, 0, 0, color='y')
JR = 71492000.0
legs = len(x) // 4
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T
T = x[3::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * legs)
r_P = list([None] * legs)
v_P = list([None] * legs)
DV = list([None] * legs)
for i, planet in enumerate(seq):
t_P[i] = epoch(x[0] + sum(T[:i + 1]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax, planet, t0=t_P[i], color=(
0.8, 0.6, 0.8), legend=True, units = JR)
# 3 - We start with the first leg: a lambert arc
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
# phi close to zero is in the moon orbit plane injection
r = [cos(phi) * sin(theta), cos(phi) * cos(theta), sin(phi)]
r = [JR * 1000 * d for d in r]
l = lambert_problem(r, r_P[0], T[0] * DAY2SEC, common_mu, False, False)
if (plot_leg_0):
plot_lambert(ax, l, sol=0, color='k', legend=False, units=JR, N=500)
# Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# 4 - And we proceed with each successive leg
for i in range(1, legs):
# Fly-by
v_out = fb_prop(v_end_l,
v_P[i - 1],
x[1 + 4 * i] * seq[i - 1].radius,
x[4 * i],
seq[i - 1].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(
r_P[i - 1], v_out, x[4 * i + 2] * T[i] * DAY2SEC, common_mu)
plot_kepler(ax,
r_P[i - 1],
v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
common_mu,
N=500,
color='b',
legend=False,
units=JR)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i], dt, common_mu, False, False)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=JR, N=500)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
plt.show()
return ax
def _mga_part_plot_old(self, x):
"""
Plots the trajectory represented by the decision vector x
Example::
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
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d', aspect='equal')
ax.scatter(0, 0, 0, color='y')
JR = 71492000.0
legs = len(x) // 4
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
start_mjd2000 = self.t0.mjd2000
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T
T = x[3::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (legs + 1))
r_P = list([None] * (legs + 1))
v_P = list([None] * (legs + 1))
for i, planet in enumerate(seq):
t_P[i] = epoch(start_mjd2000 + sum(T[:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax, planet, t0=t_P[i], color=(
0.8, 0.6, 0.8), legend=True, units = JR)
v_end_l = [a + b for a, b in zip(v_P[0], self.vinf_in)]
# 4 - And we iterate on the legs
for i in range(0, legs):
# Fly-by
v_out = fb_prop(v_end_l,
v_P[i],
x[1 + 4 * i] * seq[i - 1].radius,
x[4 * i],
seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(
r_P[i], v_out, x[4 * i + 2] * T[i] * DAY2SEC, common_mu)
plot_kepler(ax, r_P[i], v_out, x[4 * i + 2] * T[i] * DAY2SEC,
common_mu, N=500, color='b', legend=False, units=JR)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, common_mu, False, False)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=JR, N=500)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
plt.show()
return ax
