Lambert method. More...

Classes
struct	lambert
	Lambert orbital element starting and ending set. More...

Functions
bool	Target (double t0, double tTrans, const lambert d, ml_matrix &vTrans, ml_matrix &deltaV)
	Perform targeting between two orbits. More...

ml_matrix	Lambert (const ml_matrix &r1, const ml_matrix &r2, double dT, int tM, double mu, double &a, double &p, int maxIter=10, double tol=1e-10)

double	Zeta (double x)

double	CubicRoot (double h1, double h2)

Detailed Description

Lambert method.

Function Documentation

◆ Target()

bool Target	(	double	t0,
		double	tTrans,
		const lambert	d,
		ml_matrix &	vTrans,
		ml_matrix &	deltaV
	)

Perform targeting between two orbits.

Uses rv_orb_gen to propagate the first orbit to t0 and the second orbit to t0+tTrans. Chooses the long or short was based on angular momentum and computes the Lambert solution. Finally, checks for a hit Earth condition.

Parameters

t0	Start time
tTrans	Transfer time
d	Lambert structure with two sets of orbital elements
vTrans	The resulting transfer velocities (3x2)
deltaV	The resulting delta-V's (3x2)

Returns: A flag indicating a feasible transfer was found that doesn't hit the Earth

References lambert::el1, lambert::el2, Lambert(), MU_EARTH, rv_orb_gen(), and sct_sign().

◆ Lambert()

ml_matrix Lambert	(	const ml_matrix &	r1,
		const ml_matrix &	r2,
		double	dT,
		int	tM,
		double	mu,
		double &	a,
		double &	p,
		int	maxIter,
		double	tol
	)

Solves the Lambert time of flight problem using Battin's method.

MATLAB Form:

[vT, a, p, tol] = Lambert( r1, r2, dT, tM, tol, maxIter )

Parameters

r1	(3,1) Initial position vector
r2	(3,1) Final position vector
dT	Time between position 2 and 1
tM	direct (1) or retrograde (-1)
mu	Gravitational parameter
a	Resulting semi-major axis of the trajectory
p	Resulting parameter for the orbit

Returns: Matrix (3,2) Transfer velocity

References: Battin, R. H. "An Introduction to the Mathematics and Methods of Astrodynamics", AIAA Education Series.

Vallado, D. A. Fundamentals of Astrodynamics and Applications.

References PI.

Referenced by lambert_tof(), and Target().

Classes