cqsp::common::systems::lambert::Izzo Class Reference

#include <izzo.h>

Public Member Functions
	Izzo (const glm::dvec3 &r1, const glm::dvec3 &r2, const double &tof=3.1415926535/2, const double &mu=1., const bool cw=false, const int &multi_revs=5)
const std::vector< glm::dvec3 > &	get_v1 () const
const std::vector< glm::dvec3 > &	get_v2 () const
const glm::dvec3 &	get_r1 () const
const glm::dvec3 &	get_r2 () const
const double &	get_tof () const
const double &	get_mu () const
const std::vector< double > &	get_x () const
const std::vector< int > &	get_iters () const
int	get_Nmax () const
void	solve ()

Private Member Functions
int	householder (const double T, double &x0, const int N, const double eps, const int iter_max)
void	dTdx (double &DT, double &DDT, double &DDDT, const double x0, const double tof)
void	x2tof (double &tof, const double x0, const int N)
void	x2tof2 (double &tof, const double x0, const int N)
double	hypergeometricF (double z, double tol)

Private Attributes
const glm::dvec3	r1
const glm::dvec3	r2
const double	tof
const double	mu
std::vector< glm::dvec3 >	m_v1
std::vector< glm::dvec3 >	m_v2
std::vector< int >	m_iters
std::vector< double >	m_x
double	m_s
double	m_c
double	m_lambda
int	m_Nmax
bool	m_has_converged
int	m_multi_revs
bool	cw

Detailed Description

This class represent a Lambert's problem. When instantiated it assumes a prograde orbit (unless otherwise stated) and evaluates all the solutions up to a maximum number of multiple revolutions. After the object is instantiated the solutions can be retreived using the appropriate getters. Note that the number of solutions will be N_max*2 + 1, where N_max is the maximum number of revolutions.

NOTE: The class has been tested extensively via monte carlo runs checked with numerical propagation. Compared to the previous Lambert Solver in the keplerian_toolbox it is 1.7 times faster (on average as defined by lambert_test.cpp). With respect to Gooding algorithm it is 1.3 - 1.5 times faster (zero revs - multi revs). The algorithm is described in detail in the publication below and its original with the author.

Author

Dario Izzo (dario.izzo AT googlemail.com)

Constructor & Destructor Documentation

Izzo()

cqsp::common::systems::lambert::Izzo::Izzo	(	const glm::dvec3 &	r1,
		const glm::dvec3 &	r2,
		const double &	tof = 3.1415926535 / 2,
		const double &	mu = 1.,
		const bool	cw = false,
		const int &	multi_revs = 5
	)

Constructs and solves a Lambert problem.

Parameters

[in]	R1	first cartesian position
[in]	R2	second cartesian position
[in]	tof	time of flight
[in]	mu	gravity parameter
[in]	cw	when 1 a retrograde orbit is assumed
[in]	multi_revs	maximum number of multirevolutions to compute

Member Function Documentation

dTdx()

void cqsp::common::systems::lambert::Izzo::dTdx ( double &  DT, double &  DDT, double &  DDDT, const double  x0, const double  tof  )

private

get_iters()

const std::vector< int > & cqsp::common::systems::lambert::Izzo::get_iters

(

)

const

Returns

an std::vector containing the iterations taken to compute each one of the solutions

get_mu()

const double & cqsp::common::systems::lambert::Izzo::get_mu

(

)

const

Returns

the gravitational parameter

get_Nmax()

int cqsp::common::systems::lambert::Izzo::get_Nmax

(

)

const

Returns

the maximum number of revolutions. The number of solutions to the problem will be Nmax*2 +1

get_r1()

const glm::dvec3 & cqsp::common::systems::lambert::Izzo::get_r1

(

)

const

Returns

a 3-d array with the cartesian components of r1

get_r2()

const glm::dvec3 & cqsp::common::systems::lambert::Izzo::get_r2

(

)

const

Returns

a 3-d array with the cartesian components of r2

get_tof()

const double & cqsp::common::systems::lambert::Izzo::get_tof

(

)

const

Returns

the time of flight

get_v1()

const std::vector< glm::dvec3 > & cqsp::common::systems::lambert::Izzo::get_v1

(

)

const

Returns

an std::vector containing 3-d arrays with the cartesian components of the velocities at r1 for all 2N_max+1 solutions

get_v2()

const std::vector< glm::dvec3 > & cqsp::common::systems::lambert::Izzo::get_v2

(

)

const

Returns

an std::vector containing 3-d arrays with the cartesian components of the velocities at r2 for all 2N_max+1 solutions

get_x()

const std::vector< double > & cqsp::common::systems::lambert::Izzo::get_x

(

)

const

Gets the x variable for each solution found (0 revs, 1,1,2,2,3,3 .... N,N)

Returns

the x variables in an std::vector

householder()

int cqsp::common::systems::lambert::Izzo::householder ( const double  T, double &  x0, const int  N, const double  eps, const int  iter_max  )

private

hypergeometricF()

double cqsp::common::systems::lambert::Izzo::hypergeometricF ( double  z, double  tol  )

private

solve()

void cqsp::common::systems::lambert::Izzo::solve

(

)

x2tof()

void cqsp::common::systems::lambert::Izzo::x2tof ( double &  tof, const double  x0, const int  N  )

private

x2tof2()

void cqsp::common::systems::lambert::Izzo::x2tof2 ( double &  tof, const double  x0, const int  N  )

private

Member Data Documentation

cw

bool cqsp::common::systems::lambert::Izzo::cw

private

m_c

double cqsp::common::systems::lambert::Izzo::m_c

private

m_has_converged

bool cqsp::common::systems::lambert::Izzo::m_has_converged

private

m_iters

std::vector<int> cqsp::common::systems::lambert::Izzo::m_iters

private

m_lambda

double cqsp::common::systems::lambert::Izzo::m_lambda

private

m_multi_revs

int cqsp::common::systems::lambert::Izzo::m_multi_revs

private

m_Nmax

int cqsp::common::systems::lambert::Izzo::m_Nmax

private

m_s

double cqsp::common::systems::lambert::Izzo::m_s

private

m_v1

std::vector<glm::dvec3> cqsp::common::systems::lambert::Izzo::m_v1

private

m_v2

std::vector<glm::dvec3> cqsp::common::systems::lambert::Izzo::m_v2

private

m_x

std::vector<double> cqsp::common::systems::lambert::Izzo::m_x

private

mu

const double cqsp::common::systems::lambert::Izzo::mu

private

r1

const glm::dvec3 cqsp::common::systems::lambert::Izzo::r1

private

r2

const glm::dvec3 cqsp::common::systems::lambert::Izzo::r2

private

tof

const double cqsp::common::systems::lambert::Izzo::tof

private

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The documentation for this class was generated from the following files:

• /github/workspace/src/common/systems/maneuver/lambert/izzo.h
• /github/workspace/src/common/systems/maneuver/lambert/izzo.cpp