vulcan::gravity::spherical_harmonics Namespace Reference

Classes
struct	GravityCoefficients
	Gravity model coefficients container. More...

Functions
const GravityCoefficients &	default_coefficients ()
	Default Earth model with zonal harmonics only.
template<typename Scalar>
Scalar	legendre_Pnm (int n, int m, const Scalar &x)
	Compute associated Legendre polynomial P_nm(x).
template<typename Scalar>
Vec3< Scalar >	acceleration (const Vec3< Scalar > &r_ecef, const GravityCoefficients &coeffs=default_coefficients())
	Spherical harmonic gravitational acceleration.
template<typename Scalar>
Scalar	potential (const Vec3< Scalar > &r_ecef, const GravityCoefficients &coeffs=default_coefficients())
	Spherical harmonic gravitational potential.

Function Documentation

acceleration()

template<typename Scalar>

Vec3< Scalar > vulcan::gravity::spherical_harmonics::acceleration	(	const Vec3< Scalar > &	r_ecef,
		const GravityCoefficients &	coeffs = default_coefficients() )

Spherical harmonic gravitational acceleration.

General expansion using partial derivatives in spherical coordinates, then transformed to ECEF.

Template Parameters

Scalar

double or casadi::MX

Parameters

r_ecef	Position in ECEF [m]
coeffs	Gravity coefficients (C, S, n_max)

Returns

Acceleration in ECEF [m/s²]

Note

For symbolic mode, n_max must be fixed at trace time (structural loop).

default_coefficients()

const GravityCoefficients & vulcan::gravity::spherical_harmonics::default_coefficients ( )

inline

Default Earth model with zonal harmonics only.

legendre_Pnm()

template<typename Scalar>

Scalar vulcan::gravity::spherical_harmonics::legendre_Pnm	(	int	n,
		int	m,
		const Scalar &	x )

Compute associated Legendre polynomial P_nm(x).

Uses recurrence relations, fully symbolic-compatible. Loop bounds are structural (integers), so this works in symbolic mode.

Template Parameters

Scalar

double or casadi::MX

Parameters

n	Degree
m	Order
x	Argument (typically sin(latitude))

Returns

P_nm(x)

potential()

template<typename Scalar>

Scalar vulcan::gravity::spherical_harmonics::potential	(	const Vec3< Scalar > &	r_ecef,
		const GravityCoefficients &	coeffs = default_coefficients() )

Spherical harmonic gravitational potential.

U = μ/r Σ Σ (R_eq/r)^n [C_nm cos(mλ) + S_nm sin(mλ)] P_nm(sin φ)

Template Parameters

Scalar

double or casadi::MX

Parameters

r_ecef	Position in ECEF [m]
coeffs	Gravity coefficients (C, S, n_max)

Returns

Gravitational potential [m²/s²]