sc_suborb.h File Reference

Suborbital utility functions. More...

Go to the source code of this file.

Functions
bool	azimuth_launch_angle (double lat0, double lon0, double latF, double lonF, double jd, double tof, bool deg, double &az, double &inc, double &ra, double &m0, double &mF)
	Compute the azimuth angle at the launch site for an orbital plane that intersects the launch location and the target location. More...
ml_matrix	ecef_to_eci (double loc_sid_time)
	Compute the transformation matrix from ECEF to ECI. More...
ml_matrix	eci_to_orbit_plane (const ml_matrix &r, const ml_matrix &n)
	Compute the rotation matrix from ECI to orbit plane. More...
ml_matrix	lla_to_ecef (const ml_matrix &lla, double rP)
	Convert from LLA to ECEF. More...
ml_matrix	ecef_to_lla (const ml_matrix &ecef, double rP)
	Convert from ECEF to LLA. More...
void	suborb_distance (double lat0, double lon0, double latF, double lonF, double &angleDist, double &range)
	Compute the minimum angular distance around the Earth that connects two points. More...
void	suborb_lambert (double tFDes, double h0, double hF, double angleDist, double tol, double maxIter, double &gamma, double &v, double &tF)
	Find initial velocity and flight path angle that gives desired distance. More...
void	suborb_velocity (double gamma, double h0, double hF, double angleDist, double &v, double &tF)
	Compute initial velocity and flight time for a suborb trajectory. More...
ml_matrix	orbit_normal_from_elements (double inc, double ra)
	Computes the orbit normal from inclination and right ascension. More...
void	optimal_intercept (const ml_matrix &rA0, const ml_matrix &vA0, const ml_matrix &lla0, double jd0, double minDist, double vBurnout, double &vDes, double &gammaDes, double &t0F, ml_matrix &llaF, double &tLaunch, double &jdLaunch)
	Computes the optimal intercept time and velocity. More...
ml_matrix	adjust_eci_for_time (double jD0, double jDF, const ml_matrix &ECI0)
	Computes the optimal intercept time and velocity. More...

Function Documentation

azimuth_launch_angle()

bool azimuth_launch_angle	(	double	lat0,
		double	lon0,
		double	latF,
		double	lonF,
		double	jd,
		double	tof,
		bool	deg,
		double &	az,
		double &	inc,
		double &	ra,
		double &	m0,
		double &	mF
	)

NOTE: the target longitude can be increased by accounting for the anticipated time of flight, and noting the Earth's rate of rotation during that time.

NOTE: the local azimuth angle may need to be modified to account for Earth's rotation.

Reference: Aydin, "Orbit Selection and EKV Guidance for Space-based ICBM Intercept", Masters Thesis, Naval Post-Graduate School, 2005.

Accepts lat/lon in degrees or radians; returns outputs in same format. Input 'deg' specifies input/output format.

Parameters

lat0	initial latitude
lon0	initial longitude
latF	final latitude
lonF	final longitude
jd	Julian date (if negative, do not adjust with the jd)
tof	time of flight
deg	flag for are the lat/lon in degrees?
az	azimuth (returned)
inc	inclination (returned)
ra	right ascension (returned)
m0	initial mean anomaly (returned)
mF	final mean anomaly (returned)

ecef_to_eci()

ml_matrix ecef_to_eci

(

double

loc_sid_time

)

Parameters

loc_sid_time

local sidereal time

Returns

3x3 rotation matrix

Referenced by optimal_intercept().

eci_to_orbit_plane()

ml_matrix eci_to_orbit_plane	(	const ml_matrix &	r,
		const ml_matrix &	n
	)

This function takes a position vector and orbit normal vector in ECI and returns the rotation matrix that rotates from the ECI frame to the orbital plane. In the orbital plane, the y vector is aligned with r, the z vector is aligned with n, and x completes the right-hand system.

Parameters

r	3x1 position vector in ECI frame
n	3x1 normal vector in ECI frame

Returns

3x3 rotation matrix from ECI to orbital plane

lla_to_ecef()

ml_matrix lla_to_ecef	(	const ml_matrix &	lla,
		double	rP
	)

Parameters

lla	3x1 matrix, [lat (rad); lon (rad); ht (km)]
rP	Radius of the planet

Returns

ecef matrix [x; y; z] (km)

Referenced by optimal_intercept().

ecef_to_lla()

ml_matrix ecef_to_lla	(	const ml_matrix &	ecef,
		double	rP
	)

Parameters

ecef	matrix [x; y; z] (km)
rP	rP

Returns

lla matrix [lat (rad); lon (rad); ht (km)]

Referenced by optimal_intercept().

suborb_distance()

void suborb_distance	(	double	lat0,
		double	lon0,
		double	latF,
		double	lonF,
		double &	angleDist,
		double &	range
	)

Reference: Zarchan, P. (2002) Tactical and Strategic suborb Guidance, 4th Edition, pp. 239-244.

Parameters

lat0	initial latitude (rad)
lon0	initial longitude (rad)
latF	final latitude (rad)
lonF	final longitude (rad)
angleDist	angular distance of flight around Earth (rad) (returned)
range	corresponding range along Earth's surface (km) (returned)

Referenced by optimal_intercept().

suborb_lambert()

void suborb_lambert	(	double	tFDes,
		double	h0,
		double	hF,
		double	angleDist,
		double	tol,
		double	maxIter,
		double &	gamma,
		double &	v,
		double &	tF
	)

Given initial and final altitudes, the desired time of flight, and the desired angular distance to fly around the globe, this routine conducts an iterative search for the initial flight path angle using the Lambert method.

References: Zarchan, P. (2002) Tactical and Strategic suborb Guidance, 4th Edition, pp. 239-244.

Parameters

tFDes	desired time of flight (sec)
h0	initial altitude (km)
hF	final altitude (km)
angleDist	angular distance of flight around Earth (rad)
tol	tolerance for converging to tFDes (0 = default (1e-3))
maxIter	maximum number of iterations (0 = default (100))
gamma	initial flight path angle (rad) (returned)
v	initial velocity required (km/s) (returned)
tF	flight time (sec) (returned)

References suborb_velocity().

Referenced by optimal_intercept().

suborb_velocity()

void suborb_velocity	(	double	gamma,
		double	h0,
		double	hF,
		double	angleDist,
		double &	v,
		double &	tF
	)

Given an initial altitude and flight path angle for the suborb, compute the required velocity for it to hit the target. The target is located at a given altitude and a specified angular distance (around the Earth) away from the suborb.

References: Zarchan, P. (2002) Tactical and Strategic suborb Guidance, 4th Edition, pp. 239-244.

Parameters

gamma	initial flight path angle (rad)
h0	initial altitude (km)
hF	final altitude (km)
angleDist	angular distance of flight around Earth (rad)
v	initial velocity required (km/s) (returned)
tF	flight time (sec) (returned)

Referenced by suborb_lambert().

orbit_normal_from_elements()

ml_matrix orbit_normal_from_elements	(	double	inc,
		double	ra
	)

Computes the orbit normal from inclination and right ascension.

Reference: Bate, R.R., et. al. Fundamentals of Astrodynamics, p 82.

Parameters

inc	inclination (rad)
ra	right ascension (rad)

Returns

a 3x1 orbit normal vector

optimal_intercept()

void optimal_intercept	(	const ml_matrix &	rA0,
		const ml_matrix &	vA0,
		const ml_matrix &	lla0,
		double	jd0,
		double	minDist,
		double	vBurnout,
		double &	vDes,
		double &	gammaDes,
		double &	t0F,
		ml_matrix &	llaF,
		double &	tLaunch,
		double &	jdLaunch
	)

Parameters

rA0	(3,1) Estimated ECI position of adversarial suborb [km]
vA0	(3,1) Estimated ECI velocity of adversarial suborb [km]
lla0	(3,1) Latitude, longitude, altitude of interceptor
jd0	Initial Juian date at time of state estimate
minDist	Minimum allowable distance from target to intercept location [km]
vBurnout	Maximum attainable burnout velocity of the interceptor [km/s]
vDes	(Return value) Desired burnout velocity [km/s]
gammaDes	(Return value) Desired initial flight path angle (at burnout) [rad]
t0F	(Return value) Desired time of flight [sec]
llaF	(Return value) (3,1) Target position as latitude, longitude, altitude
tLaunch	(Return value) Time until launch [sec]
jdLaunch	(Return value) Julian date for launch

References ecef_to_eci(), ecef_to_lla(), lla_to_ecef(), suborb_distance(), and suborb_lambert().

adjust_eci_for_time()

ml_matrix adjust_eci_for_time	(	double	jD0,
		double	jDF,
		const ml_matrix &	ECI0
	)

Parameters

jD0	Initial Juian date at time of state estimate
jDF	Final Juian date at time of state estimate
ECI0	Transformation matrix

Returns

Transformed matrix