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use crate::dimensions::Vector3;
use crate::errors::NyxError;
use std::f64::consts::PI;
const TAU: f64 = 2.0 * PI;
const LAMBERT_EPSILON: f64 = 1e-4;
const LAMBERT_EPSILON_TIME: f64 = 1e-4;
const LAMBERT_EPSILON_RAD: f64 = (5e-5 / 180.0) * PI;
pub enum TransferKind {
Auto,
ShortWay,
LongWay,
NRevs(u8),
}
#[derive(Debug)]
pub struct LambertSolution {
pub v_init: Vector3<f64>,
pub v_final: Vector3<f64>,
pub phi: f64,
}
pub fn standard(
r_init: Vector3<f64>,
r_final: Vector3<f64>,
tof: f64,
gm: f64,
kind: TransferKind,
) -> Result<LambertSolution, NyxError> {
let r_init_norm = r_init.norm();
let r_final_norm = r_final.norm();
let cos_dnu = r_init.dot(&r_final) / (r_init_norm * r_final_norm);
let dm = match kind {
TransferKind::Auto => {
let mut dnu = r_final[1].atan2(r_final[0]) - r_init[1].atan2(r_final[1]);
if dnu > TAU {
dnu -= TAU;
} else if dnu < 0.0 {
dnu += TAU;
}
if dnu > std::f64::consts::PI {
-1.0
} else {
1.0
}
}
TransferKind::ShortWay => 1.0,
TransferKind::LongWay => -1.0,
_ => return Err(NyxError::LambertMultiRevNotSupported),
};
let nu_init = r_init[1].atan2(r_init[0]);
let nu_final = r_final[1].atan2(r_final[0]);
let a = dm * (r_init_norm * r_final_norm * (1.0 + cos_dnu)).sqrt();
if nu_final - nu_init < LAMBERT_EPSILON_RAD && a.abs() < LAMBERT_EPSILON {
return Err(NyxError::TargetsTooClose);
}
let mut phi_upper = 4.0 * PI.powi(2);
let mut phi_lower = -4.0 * PI.powi(2);
let mut phi = 0.0;
let mut c2: f64 = 1.0 / 2.0;
let mut c3: f64 = 1.0 / 6.0;
let mut iter: usize = 0;
let mut cur_tof: f64 = 0.0;
let mut y = 0.0;
while (cur_tof - tof).abs() > LAMBERT_EPSILON_TIME {
if iter > 1000 {
return Err(NyxError::MaxIterReached(format!(
"Lambert solver failed after {} iterations",
1000
)));
}
iter += 1;
y = r_init_norm + r_final_norm + a * (phi * c3 - 1.0) / c2.sqrt();
if a > 0.0 && y < 0.0 {
for _ in 0..500 {
phi += 0.1;
y = r_init_norm + r_final_norm + a * (phi * c3 - 1.0) / c2.sqrt();
if y >= 0.0 {
break;
}
}
if y < 0.0 {
return Err(NyxError::LambertNotReasonablePhi);
}
}
let chi = (y / c2).sqrt();
cur_tof = (chi.powi(3) * c3 + a * y.sqrt()) / gm.sqrt();
if cur_tof < tof {
phi_lower = phi;
} else {
phi_upper = phi;
}
phi = (phi_upper + phi_lower) / 2.0;
if phi > LAMBERT_EPSILON {
let sqrt_phi = phi.sqrt();
let (s_sphi, c_sphi) = sqrt_phi.sin_cos();
c2 = (1.0 - c_sphi) / phi;
c3 = (sqrt_phi - s_sphi) / phi.powi(3).sqrt();
} else if phi < -LAMBERT_EPSILON {
let sqrt_phi = (-phi).sqrt();
c2 = (1.0 - sqrt_phi.cosh()) / phi;
c3 = (sqrt_phi.sinh() - sqrt_phi) / (-phi).powi(3).sqrt();
} else {
c2 = 0.5;
c3 = 1.0 / 6.0;
}
}
let f = 1.0 - y / r_init_norm;
let g_dot = 1.0 - y / r_final_norm;
let g = a * (y / gm).sqrt();
Ok(LambertSolution {
v_init: (r_final - f * r_init) / g,
v_final: (1.0 / g) * (g_dot * r_final - r_init),
phi,
})
}
#[test]
fn test_lambert_vallado_shortway() {
let ri = Vector3::new(15945.34, 0.0, 0.0);
let rf = Vector3::new(12214.83899, 10249.46731, 0.0);
let tof_s = 76.0 * 60.0;
let gm = 3.98600433e5;
let exp_vi = Vector3::new(2.058913, 2.915965, 0.0);
let exp_vf = Vector3::new(-3.451565, 0.910315, 0.0);
let sol = standard(ri, rf, tof_s, gm, TransferKind::ShortWay).unwrap();
assert!((sol.v_init - exp_vi).norm() < 1e-6);
assert!((sol.v_final - exp_vf).norm() < 1e-6);
}
#[test]
fn test_lambert_vallado_lonway() {
let ri = Vector3::new(15945.34, 0.0, 0.0);
let rf = Vector3::new(12214.83899, 10249.46731, 0.0);
let tof_s = 76.0 * 60.0;
let gm = 3.98600433e5;
let exp_vi = Vector3::new(-3.811158, -2.003854, 0.0);
let exp_vf = Vector3::new(4.207569, 0.914724, 0.0);
let sol = standard(ri, rf, tof_s, gm, TransferKind::LongWay).unwrap();
assert!((sol.v_init - exp_vi).norm() < 1e-6);
assert!((sol.v_final - exp_vf).norm() < 1e-6);
}