def plot_taylor_disturbance(r0, v0, m0, thrust, disturbance, tof, mu, veff, N=60, units=1, color='b', legend=False, axes=None):
"""
ax = plot_taylor_disturbance(r, v, m, thrust, disturbance, t, mu, veff, N=60, units=1, color='b', legend=False, axes=None):
- axes: 3D axis object created using fig.gca(projection='3d')
- r0: initial position (cartesian coordinates)
- v0: initial velocity (cartesian coordinates)
- m0: initial mass
- thrust: cartesian components for the constant thrust
- disturbance: cartesian components for a constant disturbance (will not affect mass)
- tof: propagation time
- mu: gravitational parameter
- veff: the product Isp * g0
- N: number of points to be plotted along one arc
- units: the length unit to be used in the plot
- color: matplotlib color to use to plot the line
- legend: when True it plots also the legend
Plots the result of a taylor propagation of constant thrust
"""
from pykep import propagate_taylor_disturbance
import matplotlib.pyplot as plt
if axes is None:
fig = plt.figure()
ax = fig.gca(projection='3d')
else:
ax = axes
# We define the integration time ...
dt = tof / (N - 1)
# ... and calcuate the cartesian components for r
x = [0.0] * N
y = [0.0] * N
z = [0.0] * N
# Replace r0, v0 and m0
r = r0
v = v0
m = m0
# We calculate the spacecraft position at each dt
for i in range(N):
x[i] = r[0] / units
y[i] = r[1] / units
z[i] = r[2] / units
r, v, m = propagate_taylor_disturbance(
r, v, m, thrust, disturbance, dt, mu, veff, -10, -10)
# And we plot
if legend:
label = 'constant thrust arc'
else:
label = None
ax.plot(x, y, z, c=color, label=label)
return ax
def _propagate(self, x):
# 1 - We decode the chromosome
t0 = x[0]
T = x[1]
m_f = x[2]
# We extract the number of segments for forward and backward
# propagation
n_seg = self.__n_seg
fwd_seg = self.__fwd_seg
bwd_seg = self.__bwd_seg
# We extract information on the spacecraft
m_i = self.__sc.mass
max_thrust = self.__sc.thrust
isp = self.__sc.isp
veff = isp * pk.G0
# And on the leg
throttles = [x[3 + 3 * i: 6 + 3 * i] for i in range(n_seg)]
# Return lists
n_points_fwd = fwd_seg + 1
n_points_bwd = bwd_seg + 1
rfwd = [[0.0] * 3] * (n_points_fwd)
vfwd = [[0.0] * 3] * (n_points_fwd)
mfwd = [0.0] * (n_points_fwd)
ufwd = [[0.0] * 3] * (fwd_seg)
dfwd = [[0.0] * 3] * (fwd_seg) # distances E/S
rbwd = [[0.0] * 3] * (n_points_bwd)
vbwd = [[0.0] * 3] * (n_points_bwd)
mbwd = [0.0] * (n_points_bwd)
ubwd = [[0.0] * 3] * (bwd_seg)
dbwd = [[0.0] * 3] * (bwd_seg)
# 2 - We compute the initial and final epochs and ephemerides
t_i = pk.epoch(t0)
r_i, v_i = self.__earth.eph(t_i)
if self.__start == 'l1':
r_i = [r * 0.99 for r in r_i]
v_i = [v * 0.99 for v in v_i]
elif self.__start == 'l2':
r_i = [r * 1.01 for r in r_i]
v_i = [v * 1.01 for v in v_i]
t_f = pk.epoch(t0 + T)
r_f, v_f = self.target.eph(t_f)
# 3 - Forward propagation
fwd_grid = t0 + T * self.__fwd_grid # days
fwd_dt = T * self.__fwd_dt # seconds
# Initial conditions
rfwd[0] = r_i
vfwd[0] = v_i
mfwd[0] = m_i
# Propagate
for i, t in enumerate(throttles[:fwd_seg]):
if self.__sep:
r = math.sqrt(rfwd[i][0]**2 + rfwd[i][1]
** 2 + rfwd[i][2]**2) / pk.AU
max_thrust, isp = self._sep_model(r)
veff = isp * pk.G0
ufwd[i] = [max_thrust * thr for thr in t]
if self.__earth_gravity:
r_E, v_E = self.__earth.eph(pk.epoch(fwd_grid[i]))
dfwd[i] = [a - b for a, b in zip(r_E, rfwd[i])]
r3 = sum([r**2 for r in dfwd[i]])**(3 / 2)
disturbance = [mfwd[i] * pk.MU_EARTH /
r3 * ri for ri in dfwd[i]]
rfwd[i + 1], vfwd[i + 1], mfwd[i + 1] = pk.propagate_taylor_disturbance(
rfwd[i], vfwd[i], mfwd[i], ufwd[i], disturbance, fwd_dt[i], pk.MU_SUN, veff, -10, -10)
else:
rfwd[i + 1], vfwd[i + 1], mfwd[i + 1] = pk.propagate_taylor(
rfwd[i], vfwd[i], mfwd[i], ufwd[i], fwd_dt[i], pk.MU_SUN, veff, -10, -10)
# 4 - Backward propagation
bwd_grid = t0 + T * self.__bwd_grid # days
bwd_dt = T * self.__bwd_dt # seconds
# Final conditions
rbwd[-1] = r_f
vbwd[-1] = v_f
mbwd[-1] = m_f
# Propagate
for i, t in enumerate(throttles[-1:-bwd_seg - 1:-1]):
if self.__sep:
r = math.sqrt(rbwd[-i - 1][0]**2 + rbwd[-i - 1]
[1]**2 + rbwd[-i - 1][2]**2) / pk.AU
max_thrust, isp = self._sep_model(r)
veff = isp * pk.G0
ubwd[-i - 1] = [max_thrust * thr for thr in t]
if self.__earth_gravity:
r_E, v_E = self.__earth.eph(pk.epoch(bwd_grid[-i - 1]))
dbwd[-i - 1] = [a - b for a, b in zip(r_E, rbwd[-i - 1])]
r3 = sum([r**2 for r in dbwd[-i - 1]])**(3 / 2)
disturbance = [mfwd[i] * pk.MU_EARTH /
r3 * ri for ri in dbwd[-i - 1]]
rbwd[-i - 2], vbwd[-i - 2], mbwd[-i - 2] = pk.propagate_taylor_disturbance(
rbwd[-i - 1], vbwd[-i - 1], mbwd[-i - 1], ubwd[-i - 1], disturbance, -bwd_dt[-i - 1], pk.MU_SUN, veff, -10, -10)
else:
rbwd[-i - 2], vbwd[-i - 2], mbwd[-i - 2] = pk.propagate_taylor(
rbwd[-i - 1], vbwd[-i - 1], mbwd[-i - 1], ubwd[-i - 1], -bwd_dt[-i - 1], pk.MU_SUN, veff, -10, -10)
return rfwd, rbwd, vfwd, vbwd, mfwd, mbwd, ufwd, ubwd, fwd_dt, bwd_dt, dfwd, dbwd
def _propagate(self, x):
# 1 - We decode the chromosome
t0 = x[0]
T = x[1]
m_f = x[2]
# We extract the number of segments for forward and backward
# propagation
n_seg = self.__n_seg
fwd_seg = self.__fwd_seg
bwd_seg = self.__bwd_seg
# We extract information on the spacecraft
m_i = self.__sc.mass
max_thrust = self.__sc.thrust
isp = self.__sc.isp
veff = isp * pk.G0
# And on the leg
throttles = [x[3 + 3 * i:6 + 3 * i] for i in range(n_seg)]
# Return lists
n_points_fwd = fwd_seg + 1
n_points_bwd = bwd_seg + 1
rfwd = [[0.0] * 3] * (n_points_fwd)
vfwd = [[0.0] * 3] * (n_points_fwd)
mfwd = [0.0] * (n_points_fwd)
ufwd = [[0.0] * 3] * (fwd_seg)
dfwd = [[0.0] * 3] * (fwd_seg) # distances E/S
rbwd = [[0.0] * 3] * (n_points_bwd)
vbwd = [[0.0] * 3] * (n_points_bwd)
mbwd = [0.0] * (n_points_bwd)
ubwd = [[0.0] * 3] * (bwd_seg)
dbwd = [[0.0] * 3] * (bwd_seg)
# 2 - We compute the initial and final epochs and ephemerides
t_i = pk.epoch(t0)
r_i, v_i = self.__earth.eph(t_i)
if self.__start == 'l1':
r_i = [r * 0.99 for r in r_i]
v_i = [v * 0.99 for v in v_i]
elif self.__start == 'l2':
r_i = [r * 1.01 for r in r_i]
v_i = [v * 1.01 for v in v_i]
t_f = pk.epoch(t0 + T)
r_f, v_f = self.target.eph(t_f)
# 3 - Forward propagation
fwd_grid = t0 + T * self.__fwd_grid # days
fwd_dt = T * self.__fwd_dt # seconds
# Initial conditions
rfwd[0] = r_i
vfwd[0] = v_i
mfwd[0] = m_i
# Propagate
for i, t in enumerate(throttles[:fwd_seg]):
if self.__sep:
r = math.sqrt(rfwd[i][0]**2 + rfwd[i][1]**2 +
rfwd[i][2]**2) / pk.AU
max_thrust, isp = self._sep_model(r)
veff = isp * pk.G0
ufwd[i] = [max_thrust * thr for thr in t]
if self.__earth_gravity:
r_E, v_E = self.__earth.eph(pk.epoch(fwd_grid[i]))
dfwd[i] = [a - b for a, b in zip(r_E, rfwd[i])]
r3 = sum([r**2 for r in dfwd[i]])**(3 / 2)
disturbance = [
mfwd[i] * pk.MU_EARTH / r3 * ri for ri in dfwd[i]
]
rfwd[i +
1], vfwd[i +
1], mfwd[i +
1] = pk.propagate_taylor_disturbance(
rfwd[i], vfwd[i], mfwd[i], ufwd[i],
disturbance, fwd_dt[i], pk.MU_SUN,
veff, -10, -10)
else:
rfwd[i + 1], vfwd[i + 1], mfwd[i + 1] = pk.propagate_taylor(
rfwd[i], vfwd[i], mfwd[i], ufwd[i], fwd_dt[i], pk.MU_SUN,
veff, -10, -10)
# 4 - Backward propagation
bwd_grid = t0 + T * self.__bwd_grid # days
bwd_dt = T * self.__bwd_dt # seconds
# Final conditions
rbwd[-1] = r_f
vbwd[-1] = v_f
mbwd[-1] = m_f
# Propagate
for i, t in enumerate(throttles[-1:-bwd_seg - 1:-1]):
if self.__sep:
r = math.sqrt(rbwd[-i - 1][0]**2 + rbwd[-i - 1][1]**2 +
rbwd[-i - 1][2]**2) / pk.AU
max_thrust, isp = self._sep_model(r)
veff = isp * pk.G0
ubwd[-i - 1] = [max_thrust * thr for thr in t]
if self.__earth_gravity:
r_E, v_E = self.__earth.eph(pk.epoch(bwd_grid[-i - 1]))
dbwd[-i - 1] = [a - b for a, b in zip(r_E, rbwd[-i - 1])]
r3 = sum([r**2 for r in dbwd[-i - 1]])**(3 / 2)
disturbance = [
mfwd[i] * pk.MU_EARTH / r3 * ri for ri in dbwd[-i - 1]
]
rbwd[-i -
2], vbwd[-i -
2], mbwd[-i -
2] = pk.propagate_taylor_disturbance(
rbwd[-i - 1], vbwd[-i - 1],
mbwd[-i - 1], ubwd[-i - 1],
disturbance, -bwd_dt[-i - 1],
pk.MU_SUN, veff, -10, -10)
else:
rbwd[-i - 2], vbwd[-i - 2], mbwd[-i - 2] = pk.propagate_taylor(
rbwd[-i - 1], vbwd[-i - 1], mbwd[-i - 1], ubwd[-i - 1],
-bwd_dt[-i - 1], pk.MU_SUN, veff, -10, -10)
return rfwd, rbwd, vfwd, vbwd, mfwd, mbwd, ufwd, ubwd, fwd_dt, bwd_dt, dfwd, dbwd