def plot_initial_geometry(ni=0.0, mu=0.5): """ Visualizes the initial spaceraft conditions for the gtoc6 problem. Given a point on the initial spheres, \ it assumes a velocity (almost) pointing toward Jupiter. THIS IS ONLY A VISUALIZATION, the initial velocityshould not be taken as realistic. """ from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt from math import sin,cos,acos,pi from PyKEP.orbit_plots import plot_kepler, plot_planet from PyKEP import DAY2SEC, propagate_lagrangian, epoch from scipy.linalg import norm ep=epoch(0.0) days=300.0 r = [JR*1000*cos(ni)*cos(mu), JR*1000*cos(ni)*sin(mu),JR*1000*sin(ni)] VINF = 3400.0 v = [-d/norm(r)*3400 for d in r] v = [d+200 for d in v] fig = plt.figure() ax = fig.gca(projection='3d', aspect='equal') plot_planet(ax,io,color = 'r', units = JR, t0 = ep, legend=True) plot_planet(ax,europa,color = 'b', units = JR, t0 = ep, legend=True) plot_planet(ax,ganymede,color = 'k', units = JR, t0 = ep, legend=True) plot_planet(ax,callisto,color = 'y', units = JR, t0 = ep, legend=True) plot_kepler(ax,r,v,days*DAY2SEC,MU_JUPITER, N=200, units = JR, color = 'b') plt.plot([r[0]/JR],[r[1]/JR],[r[2]/JR],'o') plt.show()
def _mga_part_plot(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 xrange(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_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()
ax = fig.gca(projection='3d')
ax.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(ax,
seq[0],
t0=epoch(x[0]),
color=(0.8, 0.6, 0.8),
legend=True,
units=AU)
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(ax,
r_P0,
v0,
x[4] * x[5] * DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU)
# 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(ax, l, sol=0, color='r', legend=False, units=AU)
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, ax, seq[1:], x[0] + x[5], vinf_in)
return ax
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()
ax = fig.gca(projection='3d')
ax.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(ax, seq[0], t0=epoch(x[0]), color=(
0.8, 0.6, 0.8), legend=True, units = AU)
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(
ax,
r_P0,
v0,
x[4] *
x[5] *
DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU)
# 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(ax, l, sol=0, color='r', legend=False, units=AU)
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, ax, seq[1:], x[0] + x[5], vinf_in)
return ax
def _part_plot(x, units, ax, 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(ax,
planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=units)
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(ax,
r_P[i],
v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
common_mu,
N=500,
color='b',
legend=False,
units=units)
# 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=units, N=500)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
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 plot_initial_geometry(ni=0.0, mu=0.5):
"""
Visualizes the initial spaceraft conditions for the gtoc6 problem. Given a point on the initial spheres, \
it assumes a velocity (almost) pointing toward Jupiter.
THIS IS ONLY A VISUALIZATION, the initial velocityshould not be taken as realistic.
"""
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from math import sin, cos, acos, pi
from PyKEP.orbit_plots import plot_kepler, plot_planet
from PyKEP import DAY2SEC, propagate_lagrangian, epoch
from scipy.linalg import norm
ep = epoch(0.0)
days = 300.0
r = [
JR * 1000 * cos(ni) * cos(mu), JR * 1000 * cos(ni) * sin(mu),
JR * 1000 * sin(ni)
]
VINF = 3400.0
v = [-d / norm(r) * 3400 for d in r]
v = [d + 200 for d in v]
fig = plt.figure()
ax = fig.gca(projection='3d', aspect='equal')
plot_planet(ax, io, color='r', units=JR, t0=ep, legend=True)
plot_planet(ax, europa, color='b', units=JR, t0=ep, legend=True)
plot_planet(ax, ganymede, color='k', units=JR, t0=ep, legend=True)
plot_planet(ax, callisto, color='y', units=JR, t0=ep, legend=True)
plot_kepler(ax,
r,
v,
days * DAY2SEC,
MU_JUPITER,
N=200,
units=JR,
color='b')
plt.plot([r[0] / JR], [r[1] / JR], [r[2] / JR], 'o')
plt.show()
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_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 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, 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 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=axis)
plot_planet(self.target, t0=epoch(x[0] + x[1]), color=(0.8, 0.6, 0.8), legend=True, units = AU, ax=axis)
# 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])]
plot_kepler(rsc, vsc, T[
i] * DAY2SEC, self.__common_mu, N=200, color='b', legend=False, units=AU, ax=axis)
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='r', legend=False, units=AU, ax=axis, N=200)
plt.show()
return axis
def plot(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 mpl.rcParams['legend.fontsize'] = 10 fig = plt.figure() ax = fig.gca(projection='3d') ax.scatter(0,0,0, color='y') #1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience T = list([0]*(self.__n_legs)) for i in xrange(self.__n_legs): T[i] = (x[4+4*i]/sum(x[4::4]))*x[3] #2 - We compute the epochs and ephemerides of the planetary encounters t_P = list([None] * (self.__n_legs)) r_P = list([None] * (self.__n_legs)) v_P = list([None] * (self.__n_legs)) DV = list([None] * (self.__n_legs)) for i,planet in enumerate(self.seq): t_P[i] = epoch(x[0]+sum(T[:i+1])) r_P[i],v_P[i] = self.seq[i].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 r = [cos(phi)*sin(theta), cos(phi)*cos(theta), sin(phi)] #phi close to zero is in the moon orbit plane injection r = [JR*1000*d for d in r] l = lambert_problem(r,r_P[0],T[0]*DAY2SEC,self.common_mu, False, False) 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] #First DSM occuring at the very beginning (will be cancelled by the optimizer) DV[0] = abs(norm(v_beg_l) - 3400) #4 - And we proceed with each successive leg for i in xrange(1,self.__n_legs): #Fly-by v_out = fb_prop(v_end_l,v_P[i-1],x[6+(i-1)*4]*self.seq[i-1].radius,x[5+(i-1)*4],self.seq[i-1].mu_self) #s/c propagation before the DSM r,v = propagate_lagrangian(r_P[i-1],v_out,x[4*i+3]*T[i]*DAY2SEC,self.common_mu) plot_kepler(ax,r_P[i-1],v_out,x[7+(i-1)*4]*T[i]*DAY2SEC,self.common_mu,N = 500, color='b', legend=False, units = JR) #Lambert arc to reach Earth during (1-nu2)*T2 (second segment) dt = (1-x[7+(i-1)*4])*T[i]*DAY2SEC l = lambert_problem(r,r_P[i],dt,self.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] #DSM occuring at time nu2*T2 DV[i] = norm([a-b for a,b in zip(v_beg_l,v)]) plt.show()
def plot(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
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.scatter(0, 0, 0, color='y')
#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] * (self.__n_legs))
r_P = list([None] * (self.__n_legs))
v_P = list([None] * (self.__n_legs))
DV = list([None] * (self.__n_legs))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[:i + 1]))
r_P[i], v_P[i] = self.seq[i].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
r = [cos(phi) * sin(theta),
cos(phi) * cos(theta),
sin(phi)] #phi close to zero is in the moon orbit plane injection
r = [JR * 1000 * d for d in r]
l = lambert_problem(r, r_P[0], T[0] * DAY2SEC, self.common_mu, False,
False)
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]
#First DSM occuring at the very beginning (will be cancelled by the optimizer)
DV[0] = abs(norm(v_beg_l) - 3400)
#4 - And we proceed with each successive leg
for i in xrange(1, self.__n_legs):
#Fly-by
v_out = fb_prop(v_end_l, v_P[i - 1],
x[1 + 4 * i] * self.seq[i - 1].radius, x[4 * i],
self.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,
self.common_mu)
plot_kepler(ax,
r_P[i - 1],
v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
self.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, self.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]
#DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
plt.show()
return ax
def plot(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
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.scatter(0, 0, 0, color='y')
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = list([0] * (self.__n_legs))
#a[-i] = x[-1-(i-1)*4]
for i in xrange(self.__n_legs - 1):
j = i + 1
T[-j] = (x[5] - sum(T[-(j - 1):])) * x[-1 - (j - 1) * 4]
T[0] = x[5] - sum(T)
#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(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,
self.common_mu)
plot_kepler(ax,
r_P[0],
v0,
x[4] * T[0] * DAY2SEC,
self.common_mu,
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, self.common_mu, False, False)
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, 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(ax,
r_P[i],
v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu,
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, self.common_mu, False,
False)
plot_lambert(ax,
l,
sol=0,
color='r',
legend=False,
units=AU,
N=1000)
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()
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): """ 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 mpl.rcParams['legend.fontsize'] = 10 fig = plt.figure() axis = fig.gca(projection='3d') axis.scatter(0,0,0, color='y') #1 - we 'decode' the chromosome recording the various times of flight (days) in the list T T = list([0]*(self.__n_legs)) for i in range(0, self.__n_legs): T[i] = x[4+3*(self.__n_legs - 1) + i+1] #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 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,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, ax=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, ax=axis) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] #First DSM occurring 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[6+(i-1)*3]*self.seq[i].radius,x[5+(i-1)*3],self.seq[i].mu_self) #s/c propagation before the DSM r,v = propagate_lagrangian(r_P[i],v_out,x[7+(i-1)*3]*T[i]*DAY2SEC,self.common_mu) plot_kepler(r_P[i],v_out,x[7+(i-1)*3]*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[7+(i-1)*3])*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 occurring at time nu2*T2 DV[i] = norm([a-b for a,b in zip(v_beg_l,v)]) plt.show() return axis
v3 = np.array([-7557.86574,0,0])
r1a = math.sqrt(r1[0]**2+r1[1]**2+r1[2]**2)
MU_EARTH = 3.986004418e14
dt = 3.1415926535* math.sqrt((r1a+100000)**3/MU_EARTH) # seconds
l = lambert_problem(r1, r2, dt*.5, MU_EARTH)
fig2 = plt.figure(2)
axis2 = fig2.gca(projection='3d')
axis2.scatter([0], [0], [0], color='y')
plot_lambert(l, sol=0, ax=axis2, color='r')
# plot_lambert(l, sol=1, ax=axis2, color='r')
x0 = l.get_x()[0]
plot_kepler(r1, v0, dt*2, MU_EARTH, N=600, units=1, color='b',legend=False, ax=axis2)
plot_kepler(r2, v3, dt*2.2, MU_EARTH, N=600, units=1, color='b',legend=False, ax=axis2)
axis2.set_ylim3d(-1.2*6378000,1.2*6378000)
axis2.set_xlim3d(-1.2*6378000,1.2*6378000)
plt.xlabel('X coordinate [m]')
plt.ylabel('Y coordinate [m]')
# plt.zlabel('Z coordinate [m]')
# plt.ylabel('DV [m/s]')
plt.title('Lambert transfers for 200km altitude increase with different time of flight')
plt.show()
# dt = 3*3.1415926535* math.sqrt((r1a+100000)**3/MU_EARTH) # seconds
l = lambert_problem(r1, r2, dt*2.4, MU_EARTH)
fig2 = plt.figure(2)
axis2 = fig2.gca(projection='3d')
axis2.scatter([0], [0], [0], color='y')
def AIO(self,x, doplot = True, doprint = True, rtrn_desc = True, dists_class = None):
P = doprint
plots_datas = list([None] * (self.__n))
PLDists = list([None] * (self.__n-1))
FBDates = list([None] * (self.__n-1))
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = list([0]*(self.__n))
#a[-i] = x[-1-(i-1)*4]
for i in xrange(self.__n-1):
j = i+1;
T[-j] = (x[5] - sum(T[-(j-1):])) * x[-1-(j-1)*4]
T[0] = x[5] - sum(T)
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n+1))
r_P = list([None] * (self.__n+1))
v_P = list([None] * (self.__n+1))
DV = list([None] * (self.__n+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 start with the first leg
if P: print "First Leg: " + self.seq[0].name + " to " + self.seq[1].name
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)
if P:
print("Departure: " + str(t_P[0]) + " (" + str(t_P[0].mjd2000) + " mjd2000) \n"
"Duration: " + str(T[0]) + " days\n"
"VINF: " + str(x[3] / 1000) + " km/sec\n"
"C3: " + str((x[3] / 1000)**2) + " km^2/s^2")
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, MU_SUN)
if P: print "DSM after " + str(x[4]*T[0]) + " days"
#Lambert arc to reach seq[1]
dt = (1-x[4])*T[0]*DAY2SEC
l = lambert_problem(r, r_P[1], dt, MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# Append data needed for potential plot generation
plots_datas[0] = [v0, x[4]*T[0]*DAY2SEC, l]
#First DSM occuring at time nu1*T1
DV[0] = norm([a-b for a,b in zip(v_beg_l,v)])
if P: print "DSM magnitude: " + str(DV[0]) + "m/s"
#4 - And we proceed with each successive leg
for i in range(1,self.__n):
if P:
print("\nleg no. " + str(i+1) + ": " + self.seq[i].name + " to " + self.seq[i+1].name + "\n"
"Duration: " + str(T[i]) + "days")
#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)
PLDists[i-1] = (x[7+(i-1)*4] -1)*self.seq[i].radius/1000.
FBDates[i-1] = t_P[i]
if P:
print("Fly-by epoch: " + str(t_P[i]) + " (" + str(t_P[i].mjd2000) + " mjd2000) \n"
"Fly-by radius: " + str(x[7+(i-1)*4]) + " planetary radii\n"
"Fly-by distance: " + str( (x[7+(i-1)*4] -1)*self.seq[i].radius/1000.) + " km")
#s/c propagation before the DSM
r,v = propagate_lagrangian(r_P[i], v_out, x[8+(i-1)*4]*T[i]*DAY2SEC, MU_SUN)
if P: print "DSM after " + str(x[8+(i-1)*4]*T[i]) + " days"
#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, MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# Append data needed for potential plot generation
plots_datas[i] = [v_out, x[8+(i-1)*4]*T[i]*DAY2SEC, l]
#DSM occuring at time nu2*T2
DV[i] = norm([a-b for a,b in zip(v_beg_l,v)])
if P: print "DSM magnitude: " + str(DV[i]) + "m/s"
#Last Delta-v
if P: print "\nArrival at " + self.seq[-1].name
DV[-1] = norm([a-b for a,b in zip(v_end_l,v_P[-1])])
if P:
print("Arrival Vinf: " + str(DV[-1]) + "m/s \n"
"Total mission time: " + str(sum(T)/365.25) + " years (" + str(sum(T)) + " days) \n"
"DSMs mag: " + str(sum(DV[:-1])) + "m/s \n"
"Entry Vel: " + str(sqrt(2*(0.5*(DV[-1])**2 + 61933310.95))) + "m/s \n"
"Entry epoch: " + str(epoch(t_P[0].mjd2000 + sum(T))) )
if doplot:
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
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure(figsize=(8, 8), dpi=80)
ax = fig.gca(projection='3d')
ax.scatter(0,0,0, color='y')
for i,planet in enumerate(self.seq):
plot_planet(ax, planet, t0=t_P[i], color=(0.8,0.6,0.8), legend=True, units = AU)
for i, tpl in enumerate(plots_datas):
plot_kepler(ax, r_P[i], tpl[0], tpl[1], MU_SUN ,N = 100, color='b', legend=False, units = AU)
plot_lambert(ax, tpl[2], sol = 0, color='r', legend=False, units = AU)
fig.tight_layout()
plt.show()
if dists_class is not None:
for i, tpl in enumerate(plots_datas):
dists_class.positions_kepler(r_P[i], tpl[0], tpl[1], MU_SUN ,index = 2*i)
dists_class.positions_lambert(tpl[2], sol = 0, index = 2*(i+.5))
dists_class.set_launch_epoch(t_P[0].mjd2000)
return dists_class
if rtrn_desc:
import numpy as np
from math import atan2
desc = dict()
for i in range(len(x)):
desc[i] = x[i]
theta = 2*pi*x[1]
phi = acos(2*x[2]-1)-pi/2
axtl = 23.43929*DEG2RAD # Earth axial tlit
mactran = np.matrix([ [1, 0, 0],
[0, cos(axtl), -sin(axtl)],
[0, sin(axtl), cos(axtl)] ]) # Macierz przejscia z helio do ECI
macdegs = np.matrix([ [cos(phi)*cos(theta)],
[cos(phi)*sin(theta)],
[sin(phi)] ])
aaa = mactran.dot(macdegs)
theta_earth = atan2(aaa[1,0], aaa[0,0]) # Rektascensja asym
phi_earth = asin(aaa[2,0]) # Deklinacja asym
desc['RA'] = 360+RAD2DEG*theta_earth
desc['DEC'] = phi_earth*RAD2DEG
desc['Ldate'] = str(t_P[0])
desc['C3'] = (x[3] / 1000)**2
desc['dVmag'] = sum(DV[:-1])
desc['VinfRE'] = DV[-1]
desc['VRE'] = (DV[-1]**2 + 2*61933310.95)**.5
desc['REDate'] = str(epoch(t_P[0].mjd2000 + sum(T)))
for i in range(1,self.__n):
desc[self.seq[i].name[0].capitalize()+'Dist'] = PLDists[i-1]
desc[self.seq[i].name[0].capitalize()+'FBDate'] = str(FBDates[i-1])
return desc
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 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=axis)
plot_planet(self.target,
t0=epoch(x[0] + x[1]),
color=(0.8, 0.6, 0.8),
legend=True,
units=AU,
ax=axis)
# 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])]
plot_kepler(rsc,
vsc,
T[i] * DAY2SEC,
self.__common_mu,
N=200,
color='b',
legend=False,
units=AU,
ax=axis)
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='r',
legend=False,
units=AU,
ax=axis,
N=200)
plt.show()
return axis