def _compute_parameters(k, a_0, a_f, inc_0, inc_f):
"""Compute parameters of the model.
"""
delta_inc = abs(inc_f - inc_0)
V_0 = circular_velocity(k, a_0)
V_f = circular_velocity(k, a_f)
beta_0_ = beta_0(V_0, V_f, inc_0, inc_f)
return V_0, beta_0_, delta_inc
def _compute_parameters(k, a_0, a_f, inc_0, inc_f):
"""Compute parameters of the model.
"""
delta_inc = abs(inc_f - inc_0)
V_0 = circular_velocity(k, a_0)
V_f = circular_velocity(k, a_f)
beta_0_ = beta_0(V_0, V_f, inc_0, inc_f)
return V_0, beta_0_, delta_inc
def plot_problem(k=398600.0, a_0=7000.0, a_f=42166.0, inc_0=np.radians(28.5), i_f=0.0, f=3.5e-7, t_f=200):
"""Plot interesting quantities.
"""
t_domain = np.linspace(0, t_f, num=2000) * 86400 # s
V_0 = circular_velocity(k, a_0)
V_f = circular_velocity(k, a_f)
beta_0_ = beta_0(V_0, V_f, inc_0, i_f)
_, ax_l1 = plt.subplots()
ax_l1.set_xlabel("Time, days")
ax_l1.plot(t_domain / 86400, np.degrees(beta(
t_domain,
V_0=V_0,
f=f,
beta_0=beta_0_
)), color='k', linestyle='solid')
ax_l1.set_ylabel("Yaw, degrees")
ax_r1 = ax_l1.twinx()
ax_r1.plot(t_domain / 86400, 1e-3 * a(
t_domain,
k=k,
V_0=V_0,
f=f,
beta_0=beta_0_
), color='k', linestyle='dashed')
ax_r1.set_ylabel("Semimajor axis, km (thousands)")
_, ax_l2 = plt.subplots()
ax_l2.set_xlabel("Time, days")
ax_l2.plot(t_domain / 86400, V(
t_domain,
V_0=V_0,
f=f,
beta_0=beta_0_
), color='k', linestyle='solid')
ax_l2.set_ylabel("Velocity, km/s")
ax_r2 = ax_l2.twinx()
ax_r2.plot(t_domain / 86400, np.degrees(inc_0 - delta_inc(
t_domain,
V_0=V_0,
f=f,
beta_0=beta_0_
)), color='k', linestyle='solid')
ax_r2.set_ylabel("Inclination, degrees")
return ax_l1, ax_r1, ax_l2, ax_r2
def plot_problem(k=398600.0,
a_0=7000.0,
a_f=42166.0,
inc_0=np.radians(28.5),
i_f=0.0,
f=3.5e-7,
t_f=200):
"""Plot interesting quantities.
"""
t_domain = np.linspace(0, t_f, num=2000) * 86400 # s
V_0 = circular_velocity(k, a_0)
V_f = circular_velocity(k, a_f)
beta_0_ = beta_0(V_0, V_f, inc_0, i_f)
_, ax_l1 = plt.subplots()
ax_l1.set_xlabel("Time, days")
ax_l1.plot(t_domain / 86400,
np.degrees(beta(t_domain, V_0=V_0, f=f, beta_0=beta_0_)),
color='k',
linestyle='solid')
ax_l1.set_ylabel("Yaw, degrees")
ax_r1 = ax_l1.twinx()
ax_r1.plot(t_domain / 86400,
1e-3 * a(t_domain, k=k, V_0=V_0, f=f, beta_0=beta_0_),
color='k',
linestyle='dashed')
ax_r1.set_ylabel("Semimajor axis, km (thousands)")
_, ax_l2 = plt.subplots()
ax_l2.set_xlabel("Time, days")
ax_l2.plot(t_domain / 86400,
V(t_domain, V_0=V_0, f=f, beta_0=beta_0_),
color='k',
linestyle='solid')
ax_l2.set_ylabel("Velocity, km/s")
ax_r2 = ax_l2.twinx()
ax_r2.plot(t_domain / 86400,
np.degrees(inc_0 -
delta_inc(t_domain, V_0=V_0, f=f, beta_0=beta_0_)),
color='k',
linestyle='solid')
ax_r2.set_ylabel("Inclination, degrees")
return ax_l1, ax_r1, ax_l2, ax_r2
def test_simple_circular_velocity():
k = 398600 * u.km**3 / u.s**2
a = 7000 * u.km
expected_V = 7.5460491 * u.km / u.s
V = util.circular_velocity(k, a)
assert_quantity_allclose(V, expected_V)
def extra_quantities(k, a, ecc, argp_0, argp_f, f, A=0.0):
"""Extra quantities given by the model.
"""
V = circular_velocity(k, a)
delta_V_ = delta_V(V, ecc, argp_0, argp_f, f, A)
t_f_ = delta_V_ / f
return delta_V_, t_f_
def extra_quantities(k, a, ecc, argp_0, argp_f, f, A=0.0):
"""Extra quantities given by the model.
"""
V = circular_velocity(k, a)
delta_V_ = delta_V(V, ecc, argp_0, argp_f, f, A)
t_f_ = delta_V_ / f
return delta_V_, t_f_
def test_simple_circular_velocity():
k = 398600 * u.km ** 3 / u.s ** 2
a = 7000 * u.km
expected_V = 7.5460491 * u.km / u.s
V = util.circular_velocity(k, a)
assert_quantity_allclose(V, expected_V)
def extra_quantities(k, a, ecc_0, ecc_f, f):
"""Extra quantities given by the model.
"""
V_0 = circular_velocity(k, a)
delta_V_ = delta_V(V_0, ecc_0, ecc_f)
t_f_ = delta_V_ / f
return delta_V_, t_f_
def extra_quantities(k, a, ecc_0, ecc_f, inc_0, inc_f, argp, f):
"""Extra quantities given by the model.
"""
beta_ = beta(ecc_0, ecc_f, inc_0, inc_f, argp)
V_0 = circular_velocity(k, a)
delta_V_ = delta_V(V_0, ecc_0, ecc_f, beta_)
t_f_ = delta_V_ / f
return delta_V_, beta_, t_f_
def main():
# http://matplotlib.org/users/pgf.html#custom-preamble
# http://sbillaudelle.de/2015/02/23/seamlessly-embedding-matplotlib-output-into-latex.html
rc("pgf", rcfonts=False)
rc("text", usetex=True)
k = 398600
a = 42164
inc_domain = np.radians(np.linspace(0, 30))
fig1, ax = plt.subplots(figsize=(6, 6))
eccentricities = 0.1, 0.2, 0.4, 0.6, 0.8
beta_data = np.zeros((inc_domain.shape[0], len(eccentricities)))
for ii, ecc in enumerate(eccentricities):
beta_data[:, ii] = beta(ecc, 0.0, 0.0, inc_domain, 0.0)
ax.plot(np.degrees(inc_domain),
np.degrees(beta_data[:, ii]),
label="$e = %.1f$" % ecc)
ax.set_xlabel("Inclination change (deg)")
ax.set_ylabel(r"Yaw angle $|\beta| (deg)$")
ax.set_xlim(0, 30)
ax.set_ylim(0, 90)
ax.grid(True)
ax.legend()
fig1.savefig("combined_ei/chart_beta.pgf")
fig2, ax = plt.subplots(figsize=(6, 6))
eccentricities = 0.1, 0.2, 0.4, 0.6, 0.8
delta_V_data = np.zeros((inc_domain.shape[0], len(eccentricities)))
for ii, ecc in enumerate(eccentricities):
delta_V_data[:, ii] = delta_V(circular_velocity(k, a), ecc, 0.0,
beta_data[:, ii])
ax.plot(np.degrees(inc_domain),
delta_V_data[:, ii],
label="$e = %.1f$" % ecc)
ax.set_xlabel("Inclination change (deg)")
ax.set_ylabel(r"$\Delta V$ (km/s)")
ax.set_xlim(0, 30)
ax.set_ylim(0, 2.5)
ax.grid(True)
ax.legend()
fig2.savefig("combined_ei/chart_dV.pgf")
return fig1, fig2
def main():
# http://matplotlib.org/users/pgf.html#custom-preamble
# http://sbillaudelle.de/2015/02/23/seamlessly-embedding-matplotlib-output-into-latex.html
rc("pgf", rcfonts=False)
rc("text", usetex=True)
k = 398600
a = 42164
inc_domain = np.radians(np.linspace(0, 30))
fig1, ax = plt.subplots(figsize=(6, 6))
eccentricities = 0.1, 0.2, 0.4, 0.6, 0.8
beta_data = np.zeros((inc_domain.shape[0], len(eccentricities)))
for ii, ecc in enumerate(eccentricities):
beta_data[:, ii] = beta(ecc, 0.0, 0.0, inc_domain, 0.0)
ax.plot(np.degrees(inc_domain), np.degrees(beta_data[:, ii]), label="$e = %.1f$" % ecc)
ax.set_xlabel("Inclination change (deg)")
ax.set_ylabel(r"Yaw angle $|\beta| (deg)$")
ax.set_xlim(0, 30)
ax.set_ylim(0, 90)
ax.grid(True)
ax.legend()
fig1.savefig("combined_ei/chart_beta.pgf")
fig2, ax = plt.subplots(figsize=(6, 6))
eccentricities = 0.1, 0.2, 0.4, 0.6, 0.8
delta_V_data = np.zeros((inc_domain.shape[0], len(eccentricities)))
for ii, ecc in enumerate(eccentricities):
delta_V_data[:, ii] = delta_V(circular_velocity(k, a), ecc, 0.0, beta_data[:, ii])
ax.plot(np.degrees(inc_domain), delta_V_data[:, ii], label="$e = %.1f$" % ecc)
ax.set_xlabel("Inclination change (deg)")
ax.set_ylabel(r"$\Delta V$ (km/s)")
ax.set_xlim(0, 30)
ax.set_ylim(0, 2.5)
ax.grid(True)
ax.legend()
fig2.savefig("combined_ei/chart_dV.pgf")
return fig1, fig2