vulcan::orbital::anomaly Namespace Reference

Functions
template<typename Scalar>
Scalar	mean_to_eccentric (const Scalar &M, const Scalar &e, double tol=1e-12, int max_iter=50)
	Solve Kepler's equation: M = E - e*sin(E).
template<typename Scalar>
Scalar	eccentric_to_true (const Scalar &E, const Scalar &e)
	Convert eccentric anomaly to true anomaly.
template<typename Scalar>
Scalar	true_to_eccentric (const Scalar &nu, const Scalar &e)
	Convert true anomaly to eccentric anomaly.
template<typename Scalar>
Scalar	eccentric_to_mean (const Scalar &E, const Scalar &e)
	Convert eccentric anomaly to mean anomaly.
template<typename Scalar>
Scalar	true_to_mean (const Scalar &nu, const Scalar &e)
	Convert true anomaly to mean anomaly.
template<typename Scalar>
Scalar	mean_to_true (const Scalar &M, const Scalar &e)
	Convert mean anomaly to true anomaly.

Function Documentation

eccentric_to_mean()

template<typename Scalar>

Scalar vulcan::orbital::anomaly::eccentric_to_mean	(	const Scalar &	E,
		const Scalar &	e )

Convert eccentric anomaly to mean anomaly.

Direct application of Kepler's equation: M = E - e*sin(E)

Template Parameters

Scalar

double or casadi::MX

Parameters

E	Eccentric anomaly [rad]
e	Eccentricity [-]

Returns

Mean anomaly [rad]

eccentric_to_true()

template<typename Scalar>

Scalar vulcan::orbital::anomaly::eccentric_to_true	(	const Scalar &	E,
		const Scalar &	e )

Convert eccentric anomaly to true anomaly.

Template Parameters

Scalar

double or casadi::MX

Parameters

E	Eccentric anomaly [rad]
e	Eccentricity [-]

Returns

True anomaly [rad]

mean_to_eccentric()

template<typename Scalar>

Scalar vulcan::orbital::anomaly::mean_to_eccentric	(	const Scalar &	M,
		const Scalar &	e,
		double	tol = 1e-12,
		int	max_iter = 50 )

Solve Kepler's equation: M = E - e*sin(E).

Uses Newton-Raphson iteration. For symbolic types, uses fixed iterations to enable automatic differentiation.

Template Parameters

Scalar

double or casadi::MX

Parameters

M	Mean anomaly [rad]
e	Eccentricity [-]
tol	Convergence tolerance (numeric only)
max_iter	Maximum iterations (numeric only)

Returns

Eccentric anomaly [rad]

mean_to_true()

template<typename Scalar>

Scalar vulcan::orbital::anomaly::mean_to_true	(	const Scalar &	M,
		const Scalar &	e )

Convert mean anomaly to true anomaly.

Template Parameters

Scalar

double or casadi::MX

Parameters

M	Mean anomaly [rad]
e	Eccentricity [-]

Returns

True anomaly [rad]

true_to_eccentric()

template<typename Scalar>

Scalar vulcan::orbital::anomaly::true_to_eccentric	(	const Scalar &	nu,
		const Scalar &	e )

Convert true anomaly to eccentric anomaly.

Template Parameters

Scalar

double or casadi::MX

Parameters

nu	True anomaly [rad]
e	Eccentricity [-]

Returns

Eccentric anomaly [rad]

true_to_mean()

template<typename Scalar>

Scalar vulcan::orbital::anomaly::true_to_mean	(	const Scalar &	nu,
		const Scalar &	e )

Convert true anomaly to mean anomaly.

Template Parameters

Scalar

double or casadi::MX

Parameters

nu	True anomaly [rad]
e	Eccentricity [-]

Returns

Mean anomaly [rad]