Orbit mechanics, including Keplerian, spherical and cartesian elements. More...

Classes
struct	orb_data_s
	Structure for storing orbit data. More...
struct	gps_data_s
	Data structure for the GPS model. More...
struct	gps_orb_out_s
	Structure for storing the orbit data output of the GPS Model. More...
Typedefs
typedef struct orb_data_s	orb_data_t
	Structure for storing orbit data.
typedef struct gps_data_s	gps_data_t
	Data structure for the GPS model.
typedef struct gps_orb_out_s	gps_orb_out_t
	Structure for storing the orbit data output of the GPS Model.
Functions
void	el_to_rv (const orb_data_t &data, ml_matrix &pos, ml_matrix &vel)
	Converts orbital elements to r and v for an elliptic orbit.
orb_data_t	rv_to_el (const ml_matrix &pos, const ml_matrix &vel, double mu=MU_EARTH)
	Converts position and velocity vectors to Keplerian orbital elements.
double	rv_to_sma (double r_mag, double v_mag, double mu=MU_EARTH)
	Computes the semimajor axis given position and velocity.
double	mean_to_true (double ecc, double mean)
	Computes the true anomaly from the mean anomaly.
double	mean_to_ecc (double ecc, double mean)
	Generate the eccentric anomaly from the mean anomaly and the eccentricity.
double	ecc_to_true (double ecc, double hyp)
	Computes the true anomaly from the eccentric or hyperbolic anomaly.
double	ecc_to_mean (double ecc, double hyp)
	Converts eccentric anomaly to mean anomaly.
double	true_to_mean (double ecc, double nu)
	Converts true anomaly to mean anomaly.
double	mean_to_true_abs (double ecc, double mean_anom)
	Converts mean anomaly to true without wrapping.
double	true_to_ecc (double ecc, double nu)
	Converts true anomaly to eccentric or hyperbolic anomaly.
double	rarp_to_ecc (double ap, double per)
	Compute the eccentricity from apogee and perigee radii.
double	rarp_to_sma (double ap, double per)
	Computes the semi major axis from apogee and perigee radii.
double	slr (double ecc, double sma)
	Compute the semi-latus rectum.
ml_matrix	cp_to_i (double inc, double raan, double w)
	Converts the transformation matrix from the perifocal frame to the inertial frame.
double	orb_rate (double r, double a, double mu=MU_EARTH)
	Compute the orbital rate for non-circular orbits, or distance units other than [km].
double	orb_rate (double r)
	Compute the orbital rate for circular orbits and distance units in [km].
double	period (double a, double mu=MU_EARTH)
	Compute the orbital period.
void	lin_orb (double n, ml_matrix &a, ml_matrix &b, double dt)
	Computes the linearized orbit equations.
void	rv_orb_gen (const ml_matrix &el, const ml_matrix &t, ml_matrix &r, ml_matrix &v, double mu=MU_EARTH)
	Generate an orbit by propagating Keplerian elements.
void	rv_orb_gen (const orb_data_t &el, const ml_matrix &t, ml_matrix &r, ml_matrix &v, double mu=MU_EARTH)
	Generate an orbit by propagating Keplerian elements.
ml_matrix	cart_orb_rhs (const ml_matrix &x)
	Computes the right-hand-side of the unforced orbit equations about a mass point in cartesian coordinates.
ml_matrix	cart_orb_rhs (const ml_matrix &x, const ml_matrix &a)
	Right hand side of the cartesion equations of motion.
ml_matrix	satellite_visibility (const ml_matrix &from_pos, const ml_matrix &targets, double horizon_angle, double radius)
	Compute satellite visibility.
ml_matrix	planetary_accelerations (const ml_matrix &pos, double jd, int center)
	Compute perturbations due to other planets aside from the center.
ml_matrix	acc_planet (const ml_matrix &pos, double mu, const ml_matrix &rho)
	Acceleration due to a planet on a spacecraft within the sphere of influence of another body.
ml_matrix	orbit_acquisition_dv (ml_matrix &t, const orb_data_t &elI, const orb_data_t &elF, double smaTol=0.5, double incTol=1e-3, double raTol=1e-3)
	Compute delta-v sequence to acquire orbit.
double	phase_change_dv (double a0, double deltaA, double kTarget, double mu)
	Compute delta-v for a phase change.
ml_matrix	gps_satellite (double jD)
	GPS Satellite.

Detailed Description

Function Documentation

void el_to_rv	(	const orb_data_t &	data,
		ml_matrix &	pos,
		ml_matrix &	vel
	)

Converts orbital elements to r and v for an elliptic orbit.

Parameters:

data	Orbital elements for the satellite.
pos	position "r" matrix to be returned (km).
vel	velocity "v" matrix to be returned (km/s).

References orb_data_s::ecc, orb_data_s::inc, orb_data_s::mean_anom, MU_EARTH, orb_data_s::perigee, orb_data_s::raan, and orb_data_s::sma.

orb_data_t rv_to_el	(	const ml_matrix &	pos,
		const ml_matrix &	vel,
		double	mu
	)

Parameters:

pos	position "r" matrix for the satellite (km).
vel	velocity "v" matrix for the satellite (km/s).
mu	gravitational constant for the central body of the orbit pair (km^3/sec^2)

Returns:: The Keplerian orbital elements for the satellite.

References orb_data_s::ecc, orb_data_s::inc, orb_data_s::mean_anom, orb_data_s::orb_rate, orb_data_s::perigee, PI, orb_data_s::raan, orb_data_s::sma, orb_data_s::true_anom, and TWO_PI.

double rv_to_sma	(	double	r_mag,
		double	v_mag,
		double	mu
	)

Computes the semimajor axis given position and velocity.

Parameters:

r_mag	Position magnitude (length).
v_mag	Velocity magnitude (length/s).
mu	Gravitational parameter (length^3/s^2).

Returns:: Semimajor axis (length).

double mean_to_true	(	double	ecc,
		double	mean_anom
	)

Parameters:

ecc	Eccentricity.
mean_anom	Mean anomaly (rad).

Returns:: True anomaly (rad).

double mean_to_ecc	(	double	ecc,
		double	mean_anom
	)

Parameters:

ecc	Eccentricity.
mean_anom	Mean anomaly (rad).

Returns:: Eccentric anomaly (rad).

double ecc_to_true	(	double	ecc,
		double	hyp
	)

Parameters:

ecc	Eccentricity.
hyp	Hyperbolic anomaly (rad0.

Returns:: True anomaly (rad).

double ecc_to_mean	(	double	ecc,
		double	hyp
	)

Parameters:

ecc	Eccentricity.
hyp	Hyperbolic anomaly (rad).

Returns:: Mean anomaly (rad).

double true_to_mean	(	double	ecc,
		double	nu
	)

Parameters:

ecc	Eccentricity.
nu	True anomaly (rad).

Returns:: Mean anomaly (rad).

double mean_to_true_abs	(	double	ecc,
		double	mean_anom
	)

Converts mean anomaly to true without wrapping.

Parameters:

ecc	Eccentricity in radians.
mean_anom	Mean anomaly in radians.

Returns:: The true anomaly in radians.

References PI, and TWO_PI.

double true_to_ecc	(	double	ecc,
		double	nu
	)

Parameters:

ecc	Eccentricity in radians.
nu	True anomaly in radians.

Returns:: The eccentric or hyperbolic anomaly in radians.

double rarp_to_ecc	(	double	ap,
		double	per
	)

Parameters:

ap	Apogee radius.
per	Perigee radius.

Returns:: Eccentricity.

double rarp_to_sma	(	double	ap,
		double	per
	)

Computes the semi major axis from apogee and perigee radii.

Parameters:

ap	Apogee radius.
per	Perigee radius.

Returns:: The semi-major axis.

double slr	(	double	ecc,
		double	sma
	)

Parameters:

ecc	Eccentricity.
sma	Semi major axis (or perigee radius for parabola).

Returns:: Semi-latus rectum.

ml_matrix cp_to_i	(	double	inc,
		double	raan,
		double	w
	)

Parameters:

inc	Inclination (rad).
raan	Right ascension of the ascending node (rad).
w	Argument of perigee (rad).

Returns:: The inertial frame (3,3) transformation matrix.

double orb_rate	(	double	r,
		double	sma,
		double	mu
	)

Parameters:

r	Radius
sma	Semi major axis (inf for parabola)
mu	Gravitational parameter

Returns:: w Angular velocity

double orb_rate ( double r )

Parameters:

r Radius

Returns:: w Angular velocity (rad/s)

References MU_EARTH.

double period	(	double	a,
		double	mu
	)

Compute the orbital period.

The units for a and mu must be consistent, for example [km] and [km3/s2]. FLT_MAX is substituted for infinity.

Parameters:

a	Semi-major axis
mu	Gravitation parameter, default is Earth

Returns:: p Orbital period (s)

References TWO_PI.

void lin_orb	(	double	n,
		ml_matrix &	a,
		ml_matrix &	b,
		double	dt
	)

If value of dT is not equal to -1 it will generate the discrete time equations.

Parameters:

n	(1) orbit rate (rad/s).
a	(6,6) State transition matrix.
b	(6,3) Input matrix.
dt	(1) Time step (s).

void rv_orb_gen	(	const ml_matrix &	el,
		const ml_matrix &	t,
		ml_matrix &	pos,
		ml_matrix &	vel,
		double	mu
	)

Parameters:

el	(6,1) Elements vector [a,i,W,w,e,M]
t	(1,n) Times from 0 to � (sec)
pos	(3,n) Position vectors for times t
vel	(3,n) Velocity vectors for times t
mu	(1,1) Gravitational potential

References orb_data_s::ecc, orb_data_s::inc, orb_data_s::mean_anom, orb_data_s::perigee, orb_data_s::raan, and orb_data_s::sma.

void rv_orb_gen	(	const orb_data_t &	el,
		const ml_matrix &	t,
		ml_matrix &	pos,
		ml_matrix &	vel,
		double	mu
	)

Overloaded for calling with elements of type "orb_data_s"

Parameters:

el	(6,1) Elements vector [a,i,W,w,e,M]
t	(1,n) Times from 0 to � (sec)
pos	(3,n) Position vectors for times t
vel	(3,n) Velocity vectors for times t
mu	(1,1) Gravitational potential

References orb_data_s::ecc, orb_data_s::inc, orb_data_s::mean_anom, orb_data_s::perigee, orb_data_s::raan, and orb_data_s::sma.

ml_matrix cart_orb_rhs ( const ml_matrix & x )

Parameters:

x	(6,1) State [x;y;z;dx/dt;dy/dt;dz/dt], pos: (km), vel: (km/s)

Returns:: xDot (6,1) State derivative

References MU_EARTH.

ml_matrix cart_orb_rhs	(	const ml_matrix &	x,
		const ml_matrix &	a
	)

Parameters:

x	(6,1) Current state vector, pos: (km), vel: (km/s).
a	(3,1) Acceleration vector (km/s/s).

Returns:: xDot (6,1) State derivative.

References MU_EARTH.

ml_matrix satellite_visibility	(	const ml_matrix &	from_pos,
		const ml_matrix &	targets,
		double	horizon_angle,
		double	radius
	)

Parameters:

from_pos	Position of the viewing satellite.
targets	Positions of possibly visible satellites.
horizon_angle	Angle above horizon for visibility
radius	Planet radius.

Returns:: A ml_int_array with "1" for each visible satellite and "0" for each that is not visible.

ml_matrix planetary_accelerations	(	const ml_matrix &	pos,
		double	jd,
		int	center
	)

Currently only handles the earth, moon and sun.

Parameters:

pos	(3,1) Position vector wrt center
jd	(1,1) Julian Date
center	1 for Earth and 2 for Moon

Returns:: (3,1) Acceleration

References MU_EARTH, MU_MOON, and MU_SUN.

ml_matrix acc_planet	(	const ml_matrix &	pos,
		double	mu,
		const ml_matrix &	rho
	)

Parameters:

pos	(3,1) Vector of the spacecraft from the central body
mu	(1) Planet's gravitational parameter
rho	(3,:) Vector of the planet from the central body

Returns:: (3,1) Acceleration

ml_matrix orbit_acquisition_dv	(	ml_matrix &	t,
		const orb_data_t &	elI,
		const orb_data_t &	elF,
		double	smaTol,
		double	incTol,
		double	raTol
	)

Compute delta-v sequence to acquire orbit.

Inclination and right ascension correction are a single burn. Semi-major axis correction is a two-burn Hohmann transfer set. The conditions for performing a SMA correction are: 1. The SMA error exceeds the tolerance, AND 2. a) The final SMA is smaller than the initial, OR b) Both the inc. and r.a. error are within tolerance. The times will include the wait time for the necessary Hohmann phasing.

Parameters:

t	delta-V time (output)
elI	Initial orbital elements
elF	Final orbital elements
smaTol	Tolerance on semi-major axis
incTol	Tolerance on inclination
raTol	Tolerance on right ascension

Returns:: Matrix of delta-V's (3xn)

References orb_data_s::inc, orb_data_s::mean_anom, orb_data_s::perigee, PI, orb_data_s::raan, and orb_data_s::sma.

double phase_change_dv	(	double	a0,
		double	deltaA,
		double	kTarget,
		double	mu
	)

Compute delta-v for a phase change.

Parameters:

a0	(1,1) Initial semi-major axis
deltaA	(1,1) Phase change
kTarget	(1,1) Number of revolutions
mu	(1,1) Planet's gravitational parameter

Returns:: (1,1) Delta-v

References PI.

sc_orbit.h File Reference

Classes

Typedefs

Functions

Detailed Description

Function Documentation