def propagateLambert():
### Using ephemeris
# Lambert trajectory obtain terminal velocity vectors
date0 = np.array([27,1,2016,0])
t_0 = AL_Eph.DateConv(date0,'calendar') #To JD
transfertime = 250
# Create bodies
sun = AL_2BP.Body('sun', 'yellow', mu = Cts.mu_S_m)
earth = AL_2BP.Body('earth', 'blue', mu = Cts.mu_E_m)
mars = AL_2BP.Body('mars', 'red', mu = Cts.mu_M_m)
# Calculate trajectory of the bodies based on ephem
earthephem = pk.planet.jpl_lp('earth')
marsephem = pk.planet.jpl_lp('mars')
r_E, v_E = earthephem.eph(t_0.JD_0)
r_M, v_M = marsephem.eph(t_0.JD_0 + transfertime)
orbit_E = AL_2BP.BodyOrbit(np.append(r_E, v_E), 'Cartesian', sun)
earth.addOrbit(orbit_E)
orbit_M = AL_2BP.BodyOrbit(np.append(r_M, v_M), 'Cartesian', sun)
mars.addOrbit(orbit_M)
# Create transfer in the first moment
lambert = AL_TR.Lambert(np.array(r_E), np.array(r_M), AL_BF.days2sec(transfertime), sun.mu)
v_0, v_f = lambert.TerminalVelVect()
print(v_0)
# Propagate
orbit_sp = AL_2BP.BodyOrbit(np.append(r_E, v_0), 'Cartesian', sun)
x = orbit_sp.Propagation(AL_BF.days2sec(transfertime), 'Cartesian') # Coordinates after propagation
r0 = np.array(r_E)
rf = np.array(r_M)
print('Mars', r_M, 'Propagation', x, 'Error', abs(rf - x[0:3])) # Almost zero
fig = plt.figure()
ax = fig.gca(projection = '3d')
ax.scatter(0,0,0, color = 'yellow', s = 100)
ax.scatter(r0[0],r0[1],r0[2], color = 'blue')
ax.scatter(rf[0],rf[1],rf[2], color = 'red')
ax.scatter(x[0], x[1], x[2], color = 'green')
AL_Plot.set_axes_equal(ax)
plt.show() # Validated
def test_Exposin():
# Verify with example
print("VERIFICATION")
r1 = 1
r2 = 5
psi = np.pi/2
k2 = 1/4
# eSin = AL_Sh.shapingMethod(sun.mu / Cts.AU_m**3)
# gammaOptim_v = eSin.start(r1, r2, psi, 365*1.5, k2) # verified
# Ni = 1
# print(gammaOptim_v)
# eSin.plot_sphere(r1, r2, psi, gammaOptim_v[Ni], Ni) # verified
# Real life case
sun = AL_2BP.Body('sun', 'yellow', mu = Cts.mu_S_m)
earth = AL_2BP.Body('earth', 'blue', mu = Cts.mu_E_m)
mars = AL_2BP.Body('mars', 'red', mu = Cts.mu_M_m)
# Calculate trajectory of the bodies based on ephem
earthephem = pk.planet.jpl_lp('earth')
marsephem = pk.planet.jpl_lp('mars')
date0 = np.array([27,1,2018,0])
t0 = AL_Eph.DateConv(date0,'calendar') #To JD
t_t = 350
r_E, v_E = earthephem.eph( t0.JD_0 )
r_M, v_M = marsephem.eph(t0.JD_0+ t_t )
r_1 = r_E
r_2 = r_M
r_1_norm = np.linalg.norm( r_1 )
r_2_norm = np.linalg.norm( r_2 )
dot = np.dot(r_1[0:2], r_2[0:2]) # dot product between [x1, y1] and [x2, y2]
det = r_1[0]*r_2[1] - r_2[0]*r_1[1] # determinant
psi = np.arctan2(det, dot)
psi = AL_BF.convertRange(psi, 'rad', 0 ,2*np.pi)
k2 = 1/12
eSin = AL_Sh.shapingMethod(sun.mu / AL_BF.AU**3)
gammaOptim_v = eSin.calculategamma1(r_1_norm / AL_BF.AU, r_2_norm / AL_BF.AU, psi, \
t_t, k2, plot = False)
Ni = 1
eSin.calculateExposin(Ni, gammaOptim_v[Ni],r_1_norm / AL_BF.AU, r_2_norm / AL_BF.AU, psi )
eSin.plot_sphere(r_1_norm / AL_BF.AU, r_2_norm / AL_BF.AU, psi)
v1, v2 = eSin.terminalVel(r_1_norm / AL_BF.AU, r_2_norm / AL_BF.AU, psi)
t, a_T = eSin.calculateThrustProfile(r_1_norm / AL_BF.AU, r_2_norm / AL_BF.AU, psi)
# print('a', a_T*AL_BF.AU)
print("body coord", v1, v2)
# print(v1[0]*Cts.AU_m, v1[1], v2[0]*Cts.AU_m, v2[1])
# To heliocentric coordinates (2d approximation)
def to_helioc(r, vx, vy):
v_body = np.array([vx, vy, 0])
# Convert to heliocentric
angle = np.arctan2(r[1], r[0])
v_h = AL_BF.rot_matrix(v_body, angle, 'z')
return v_h
v_1 = to_helioc(r_1, v1[0]*AL_BF.AU, v1[1]*AL_BF.AU)
v_2 = to_helioc(r_2, v2[0]*AL_BF.AU, v2[1]*AL_BF.AU)
# def to_helioc(r, v, gamma):
# v_body = np.array([v*np.sin(gamma), \
# v*np.cos(gamma),\
# 0])
# # Convert to heliocentric
# angle = np.arctan2(r[1], r[0])
# v_h = AL_BF.rot_matrix(v_body, angle, 'z')
# return v_h
# v_1 = to_helioc(r_1, v1[0]*Cts.AU_m, v1[1])
# v_2 = to_helioc(r_2, v2[0]*Cts.AU_m, v2[1])
print("Helioc vel", v_1, v_2)
print("with respect to body ", v_1-v_E, v_2-v_M)
v_1_E = np.linalg.norm(v_1-v_E)
v_2_M = np.linalg.norm(v_2-v_M)
print("Final vel", v_1_E, v_2_M)
################################################3
# Propagate with terminal velocity vectors
SF = CONFIG.SimsFlan_config()
Fit = Fitness(Nimp = SF.Nimp)
decv = np.zeros(len(SF.bnds))
decv[6] = t0.JD_0
decv[7] = AL_BF.days2sec(t_t)
decv[0:3] = AL_BF.convert3dvector(v_1-v_E,'cartesian')
decv[3:6] = AL_BF.convert3dvector(v_2- v_M,'cartesian')
print('decv', decv[0:9])
for i in range(SF.Nimp):
# Acceleration on segment is average of extreme accelerations
t_i = AL_BF.days2sec(t_t) / (SF.Nimp+1) *i
t_i1 = AL_BF.days2sec(t_t) / (SF.Nimp+1) *(i+1)
#find acceleration at a certain time
a_i = eSin.accelerationAtTime(t_i)
a_i1 = eSin.accelerationAtTime(t_i1)
a = (a_i+a_i1)/2 # find the acceleration at a certain time
print("a", a_i, a_i1, a)
deltav_i = AL_BF.days2sec(t_t) / (SF.Nimp+1) * a*AL_BF.AU
print(deltav_i)
decv[8+3*i] = deltav_i /100
decv[8+3*i+1] = 0
decv[8+3*i+2] = 0
Fit.calculateFeasibility(decv, plot = True, thrust = 'tangential')
Fit.printResult()