Case 9: Sphere launched ballistically eastward along Equator

Verifies	Translational EOM
Gravitation	J2
Geodesy	WGS-84 rotating
Atmosphere	US 1976 STD
Winds	still air
Vehicle	Sphere with constant \(C_D\)
Notes	Initial velocity is \(\sqrt{2000}\) ft/s aligned 45 degrees from vertical, heading east; zero angular rate relative to launch platform.

from simupy.block_diagram import BlockDiagram
import simupy_flight
import numpy as np

from nesc_testcase_helper import plot_nesc_comparisons, int_opts, benchmark
from nesc_testcase_helper import ft_per_m, kg_per_slug

Ixx = 3.6 * kg_per_slug / (ft_per_m**2)  # slug-ft2
Iyy = 3.6 * kg_per_slug / (ft_per_m**2)  # slug-ft2
Izz = 3.6 * kg_per_slug / (ft_per_m**2)  # slug-ft2
Ixy = 0.0 * kg_per_slug / (ft_per_m**2)  # slug-ft2
Iyz = 0.0 * kg_per_slug / (ft_per_m**2)  # slug-ft2
Izx = 0.0 * kg_per_slug / (ft_per_m**2)  # slug-ft2
m = 1.0 * kg_per_slug  # slug

x = 0.0
y = 0.0
z = 0.0

S_A = 0.1963495 / (ft_per_m**2)
b_l = 1.0
c_l = 1.0
a_l = b_l

lat_ic = 0.0 * np.pi / 180
long_ic = 0.0 * np.pi / 180
h_ic = 0.0 / ft_per_m
V_N_ic = 000.0 / ft_per_m
V_E_ic = 1000.0 / ft_per_m
V_D_ic = -1000.0 / ft_per_m
psi_ic = 90.0 * np.pi / 180
theta_ic = 0.0 * np.pi / 180
phi_ic = 0.0 * np.pi / 180
omega_X_ic = 0.0 * np.pi / 180
omega_Y_ic = -0.004178073 * np.pi / 180
omega_Z_ic = 0.0 * np.pi / 180


planet = simupy_flight.Planet(
    gravity=simupy_flight.earth_J2_gravity,
    winds=simupy_flight.get_constant_winds(),
    atmosphere=simupy_flight.atmosphere_1976,
    planetodetics=simupy_flight.Planetodetic(
        a=simupy_flight.earth_equitorial_radius,
        omega_p=simupy_flight.earth_rotation_rate,
        f=simupy_flight.earth_f,
    ),
)

vehicle = simupy_flight.Vehicle(
    base_aero_coeffs=simupy_flight.get_constant_aero(CD_b=0.1),
    m=m,
    I_xx=Ixx,
    I_yy=Iyy,
    I_zz=Izz,
    I_xy=Ixy,
    I_yz=Iyz,
    I_xz=Izx,
    x_com=x,
    y_com=y,
    z_com=z,
    x_mrc=x,
    y_mrc=y,
    z_mrc=z,
    S_A=S_A,
    a_l=a_l,
    b_l=b_l,
    c_l=c_l,
    d_l=0.0,
)

BD = BlockDiagram(planet, vehicle)
BD.connect(planet, vehicle, inputs=np.arange(planet.dim_output))
BD.connect(vehicle, planet, inputs=np.arange(vehicle.dim_output))

planet.initial_condition = planet.ic_from_planetodetic(
    long_ic, lat_ic, h_ic, V_N_ic, V_E_ic, V_D_ic, psi_ic, theta_ic, phi_ic
)
planet.initial_condition[-3:] = omega_X_ic, omega_Y_ic, omega_Z_ic

with benchmark() as b:
    res = BD.simulate(30, integrator_options=int_opts)