def hermite(dt, tfinal):
particles, marr = fn.init_2body(0)
etot0 = fn.e_tot(particles, marr)
time = 0
iterations = 2
while time < tfinal:
acc, jerk = fn.forces_hermite(particles, marr)
old_x = np.copy(particles[:, 0, :])
old_v = np.copy(particles[:, 1, :])
old_a = np.copy(acc)
old_j = np.copy(jerk)
particles[:,
0, :] += particles[:,
1, :] * dt + acc * dt**2 / 2 + jerk * dt**3 / 6
particles[:, 1, :] += acc * dt + jerk * dt**2 / 2
for i in range(iterations):
acc, jerk = fn.forces_hermite(particles, marr)
particles[:, 1, :] = old_v + (old_a + acc) * dt / 2 + (
(old_j - jerk) * dt**2) / 12
particles[:,
0, :] = old_x + (old_v + particles[:, 1, :]) * dt / 2 + (
(old_a - acc) * dt**2) / 12
x_and_v.append(particles.tolist())
time += dt
etot1 = fn.e_tot(particles, marr)
e_error = (etot1 - etot0) / etot0
return x_and_v, e_error
def midpoint(dt, tfinal):
particles, marr = fn.init_2body(0)
etot0 = fn.e_tot(particles, marr)
time = 0
x_and_v = []
while time < tfinal:
acc = fn.forces(particles, marr)
particles_mid = np.zeros((pars.Np, 2, 3))
particles_mid[:,
0, :] = particles[:, 0, :] + particles[:, 1, :] * dt / 2
particles_mid[:, 1, :] = particles[:, 1, :] + acc * dt / 2
amid = fn.forces(particles_mid, marr)
particles[:, 0, :] += particles_mid[:, 1, :] * dt
particles[:, 1, :] += amid * dt
x_and_v.append(particles.tolist())
time += dt
etot1 = fn.e_tot(particles, marr)
e_error = (etot1 - etot0) / etot0
return x_and_v, e_error
def leapfrog(dt, tfinal, tau, drag=False, init_e=0.0):
save_file = open(
"object_time_x,v,m_dt=" + str(dt) + "_tfinal=" + str(tfinal) +
"_tau=" + str(tau) + ".csv", "w")
particles, marr = fn.init_2body(init_e)
etot0 = fn.e_tot(particles, marr)
eccentricity = []
semi_major_axis = []
x_and_v = []
vkep_list = []
time_list = []
time = 0
while time < tfinal:
if drag:
acc, v_kep, v_r = fn.forces_total(particles, marr, tau)
else:
acc = fn.forces(particles, marr)
v_kep = []
particles[:, 1, :] += acc * dt / 2
particles[:, 0, :] += particles[:, 1, :] * dt
if drag:
acc, v_kep, v_r = fn.forces_total(particles, marr, tau, v_r=v_r)
else:
acc = fn.forces(particles, marr)
particles[:, 1, :] += acc * dt / 2
x_and_v.append(particles.tolist())
# print 'next'
ecc, a = fn.get_orbital_elements(particles, marr)
for i in [0, 1]:
np.savetxt(save_file,np.c_[i, time, particles[i,0,0], particles[i,0,1], particles[i,0,2], \
particles[i,1,0], particles[i,1,1], particles[i,1,2], marr[i], v_kep], delimiter=',', fmt='%.10e')
# eccentricity.append(np.sqrt(sum(ecc)**2))
# semi_major_axis.append(a)
# vkep_list.append(v_kep)
# time_list.append(time)
time += dt
if a < 0.15:
break
def euler(dt, tfinal):
particles, marr = fn.init_2body(0)
etot0 = fn.e_tot(particles, marr)
time = 0
x_and_v = []
while time < tfinal:
acc = fn.forces(particles, marr)
particles[:, 0, :] += particles[:, 1, :] * dt
particles[:, 1, :] += acc * dt
x_and_v.append(particles.tolist())
time += dt
etot1 = fn.e_tot(particles, marr)
e_error = (etot1 - etot0) / etot0
return x_and_v, e_error
def hermite(dt, tfinal):
particles, marr = fn.init_2body(0)
etot0 = fn.e_tot(particles, marr)
time = 0
iterations = 2
x_and_v = []
ecc = []
a_list = []
while time < tfinal:
acc, jerk = fn.forces_hermite(particles, marr)
old_x = np.copy(particles[:, 0, :])
old_v = np.copy(particles[:, 1, :])
old_a = np.copy(acc)
old_j = np.copy(jerk)
particles[:,
0, :] += particles[:,
1, :] * dt + acc * dt**2 / 2 + jerk * dt**3 / 6
particles[:, 1, :] += acc * dt + jerk * dt**2 / 2
for i in range(iterations):
acc, jerk = fn.forces_hermite(particles, marr)
particles[:, 1, :] = old_v + (old_a + acc) * dt / 2 + (
(old_j - jerk) * dt**2) / 12
particles[:,
0, :] = old_x + (old_v + particles[:, 1, :]) * dt / 2 + (
(old_a - acc) * dt**2) / 12
x_and_v.append(particles.tolist())
e, a = fn.get_orbital_elements(particles, marr)
ecc.append(np.sqrt(sum(e**2)))
a_list.append(a)
time += dt
etot1 = fn.e_tot(particles, marr)
e_error = (etot1 - etot0) / etot0
return x_and_v, e_error, ecc, a_list
def leapfrog_drag(dt, tfinal):
particles, marr = fn.init_2body(0)
etot0 = fn.e_tot(particles, marr)
time = 0
while time < tfinal:
acc = fn.forces(particles, marr)[0]
particles[0, 1, :] += acc * dt / 2
particles[0, 0, :] += particles[0, 1, :] * dt
acc = fn.forces(particles, marr)[0]
particles[0, 1, :] += acc * dt / 2
grav = fn.forces(particles, marr)[1]
drag = fn.forces_migration(particles, marr)
acc = grav + drag
particles[1, 1, :] += acc * dt / 2
particles[1, 0, :] += particles[1, 1, :] * dt
grav = fn.forces(particles, marr)[1]
drag = fn.forces_migration(particles, marr)
acc = grav + drag * 1e1
particles[1, 1, :] += acc * dt / 2
eccentricity, semi_major_axis = fn.get_orbital_elements(
particles, marr)
eccentricity_save.append(eccentricity.tolist())
semi_major_axis_save.append(semi_major_axis.tolist())
x_and_v.append(particles.tolist())
time += dt
etot1 = fn.e_tot(particles, marr)
e_error = (etot1 - etot0) / etot0
return x_and_v, e_error, eccentricity_save, semi_major_axis_save