Coordinate transformation functions. More...

Functions
ml_matrix	az_el_range_range_rate_to_rv (const ml_matrix &q_radar_to_hills, double az, double el, double range, double range_dot)
	Converts az, el, range and range rate to exact r and approximate v.
ml_matrix	q_from_u (const ml_matrix &u_catalog, const ml_matrix &u_meas)
	Returns a quaternion given at least 3 matching vectors.
double	q_to_angle (const ml_matrix &quaternion)
	Returns value of the angle from the quaternion in radians.
ml_matrix	q_to_vec (const ml_matrix &quaternion)
	Returns the value of the vector from quaternion.
ml_matrix	au_to_q (double angle, double unit_vec[3])
	Compute quaternion from angle and unit vector, array format.
ml_matrix	au_to_q (double angle, const ml_matrix &unit_vec)
	Compute quaternion from angle and unit vector, matrix format.
double	q_to_au (const ml_matrix &quaternion, ml_matrix &unit_vec)
	Compute angle and unit vector from quaternion.
ml_matrix	eul_to_mat (const ml_matrix &euler)
	Convert 3-2-1 Euler angle sequence to a matrix that transforms in the direction of the rotation.
ml_matrix	eul_to_q (const ml_matrix &euler)
	Convert 3-2-1 Euler angle sequence to a quaternion that transforms in the direction of the rotation.
ml_matrix	delta_eul_to_q (const ml_matrix &q, const ml_matrix &euler)
	Apply a 3-2-1 Euler angle sequence to a quaternion that transforms in the direction of the rotation.
ml_matrix	rot_mat_x (const double &a)
	Generate a rotation matrix for angular rotation about the x axis.
ml_matrix	rot_mat_y (const double &a)
	Generate a rotation matrix for angular rotation about the y axis.
ml_matrix	rot_mat_z (const double &a)
	Generate a rotation matrix for angular rotation about the z axis.
ml_matrix	mat_to_q (const ml_matrix &mat)
	Convert a matrix to a quaternion.
ml_matrix	mat_to_eul (const ml_matrix &mat, const ml_matrix &euler)
	Convert a matrix to an Euler angle sequence.
ml_matrix	u_to_q (const ml_matrix &vec1, const ml_matrix &vec2)
	Computes the quaternion which aligns one vector with a second.
ml_matrix	perpendicular (const ml_matrix &vec)
	Computes the perpendicular vector.
ml_matrix	q_error (const ml_matrix &q_ref, const ml_matrix &q_meas)
	Finds the small error between two quaternions and converts them into an angle vector.
ml_matrix	qb_to_i_dot (const ml_matrix &quaternion, const ml_matrix &w)
	Calculates the derivative of the body to inertial quaternion.
ml_matrix	qi_to_b_dot (const ml_matrix &quat, const ml_matrix &w)
	Calculates the derivative of the inertial to body quaternion.
ml_matrix	qeb_re_ub_to_az_el (const ml_matrix &qEB, const ml_matrix &rE, const ml_matrix &vB)
	Calculate azimuth & elevation angle from ECI to body quaternion, position, and boresight vector.
ml_matrix	mat_eci_to_lvlh (const ml_matrix &pos, const ml_matrix &vel)
	Generate the matrix that transforms from ECI to LVLH coordinates.
ml_matrix	q_eci_to_lvlh (const ml_matrix &pos, const ml_matrix &vel)
	Generate the quaternion that transforms from ECI to LVLH coordinates.
ml_matrix	mat_eci_to_hills (const ml_matrix &r, const ml_matrix &v)
	Generate the matrix that transforms from ECI to Hills coordinates.
ml_matrix	q_eci_to_hills (const ml_matrix &r, const ml_matrix &v)
	Generate the quaternion that transforms from ECI to Hills coordinates.
ml_matrix	eci_to_hills (const ml_matrix &x0, const ml_matrix &x1)
	Transform from two ECI states to one relative state in Hills-frame.
ml_matrix	hills_to_eci (const ml_matrix &x0, const ml_matrix &xH)
	Transform from a relative state in Hills-frame to an absolute ECI state.
ml_matrix	q_to_ra_dec (const ml_matrix &quaternion, const ml_matrix &uu)
	Compute right ascension and declination from a quaterion.
ml_matrix	u_to_ra_dec (const ml_matrix &unit_vec)
	Computes right ascension and declination from a unit vector.
ml_matrix	u_to_ra_dec (const ml_matrix &unit_vec, bool normalize)
	Computes right ascension and declination from a unit vector and normalizes the result.
ml_matrix	ra_dec_to_q (const ml_matrix &uu, double ra, double dec)
	Compute a quaternion from right ascension and declination.
ml_matrix	ra_dec_to_u (double ra, double dec)
	Calculate a unit vector from right ascension and declination.
ml_matrix	ra_dec_to_u (const ml_matrix &ra, const ml_matrix &dec)
	Calculate a unit vector from right ascension and declination.
ml_matrix	az_el_to_q (ml_matrix az, ml_matrix el)
	Compute a quaternion from azimuth and elevation.
ml_matrix	az_el_to_q (double az, double el)
	Compute a quaternion from azimuth and elevation.
ml_matrix	qslerp (const ml_matrix &quat1, const ml_matrix &quat2, double t)
	Interpolates between two quaternions.
ml_matrix	lat_lon_alt_to_pos (double lat, double lon, double h, double f=FLATTENING_FACTOR, double a=RADIUS_EARTH)
	Compute EF position vector from latitude, longitude, and altitude.
ml_matrix	lat_lon_to_pos (double lat, double lon, double f, double a, bool is_geodetic)
	Converts latitude and longitude to r for an ellipsoidal planet.
ml_matrix	lat_lon_to_pos (double lat, double lon, double f=FLATTENING_FACTOR, double a=RADIUS_EARTH, int type=0)
	Converts latitude and longitude to r for an ellipsoidal planet.
ml_matrix	pos_to_lat_lon_alt (const ml_matrix &efPos, double f=FLATTENING_FACTOR, double a=RADIUS_EARTH, double tolerance=1.0e-6)
	Compute latitude, longitude, and altitude from EF position vector.
void	cart_to_sph (const ml_matrix &x, const ml_matrix &y, const ml_matrix &z, ml_matrix &r, ml_matrix &theta, ml_matrix &phi)
	Converts cartesian coordinates to spherical.
ml_matrix	cart_to_sph (const ml_matrix &x)
	Converts cartesian coordinates to spherical. Stacked form.
void	sph_to_cart (const ml_matrix &r, const ml_matrix &theta, const ml_matrix &phi, ml_matrix &x, ml_matrix &y, ml_matrix &z)
	Convert spherical coordinates to cartesian.
ml_matrix	RPhiTheta2Cart (const ml_matrix &r)
	Computes the transformation matrix from an r, phi, theta frame to cartesian.
ml_matrix	CameraToECI (double az, double el, double tt, const ml_matrix &qECIToBody, const ml_matrix &mBaseToBody)
	Computes the transformation matrix from a camera frame with 3 rotations to the body frame.
ml_matrix	eci_to_ned (const ml_matrix &r, int opt, double f=FLATTENING_FACTOR)
	Computes the transformation matrix or quaternion from a eciframe to the North East Down (NED) frame.
ml_matrix	u_to_az_el (const ml_matrix &u)
	Computes the azimuth and elevation of a unit vector.
ml_matrix	az_el_to_u (double az, double el)
	Computes u from azimuth and elevation of a unit vector.
ml_matrix	az_el_to_u (const ml_matrix &az, const ml_matrix &el)
	Compute a unit vector from azimuth and elevation.
ml_matrix	q_from_dq (const ml_matrix &q, const ml_matrix &dX)
	Computes q as the product of q and a delta quaternion.
ml_matrix	dq_from_dX (const ml_matrix &dX)
	Delta quaternion from a 3 vector.
ml_matrix	r_lvlh_to_eci (const ml_matrix &r_eci, const ml_matrix &v_eci, const ml_matrix &r)
	LVLH position to ECI.
ml_matrix	v_lvlh_to_eci (const ml_matrix &r_eci, const ml_matrix &v_eci, const ml_matrix &v)
	ECI position to LVLH.
ml_matrix	r_eci_to_lvlh (const ml_matrix &r_eci, const ml_matrix &v_eci, const ml_matrix &r)
	LVLH position to ECI.
ml_matrix	v_eci_to_lvlh (const ml_matrix &r_eci, const ml_matrix &v_eci, const ml_matrix &v)
	ECI position to LVLH.
ml_matrix	x_lvlh_to_eci (const ml_matrix &r_eci, const ml_matrix &v_eci, const ml_matrix &x)
	LVLH state to ECI.
ml_matrix	x_eci_to_lvlh (const ml_matrix &r_eci, const ml_matrix &v_eci, const ml_matrix &x)
	ECI state to LVLH.
ml_matrix	x_lvlh_to_eci (const ml_matrix &x_eci, const ml_matrix &x)
	ECI state to LVLH.
ml_matrix	x_eci_to_lvlh (const ml_matrix &x_eci, const ml_matrix &x)
	ECI state to LVLH.
ml_matrix	LLAToECEF (const ml_matrix &lla, double rP=RADIUS_EARTH)
	Compute ECEF position from latitude, longitude, altitude.
ml_matrix	small_angles_to_q (const ml_matrix &angle)
	Convert small angles to a quaternion.
ml_matrix	spice_to_3_by_3 (const ml_matrix &m, int k=1)
	Convert SPICE rotation matrix to 3x3.

Detailed Description

Function Documentation

ml_matrix az_el_range_range_rate_to_rv	(	const ml_matrix &	q_radar_to_hills,
		double	az,
		double	el,
		double	range,
		double	range_dot
	)

Parameters:

az	Azimuth
el	Elevation
range	Range
range_dot	Range rate

Returns:: state [r;v]

ml_matrix q_from_u	(	const ml_matrix &	u_catalog,
		const ml_matrix &	u_meas
	)

Parameters:

u_catalog	A 3xn matrix of catalog unit vectors
u_meas	A 3xn matrix of measured unit vectors

Returns:: The quaternion.

double q_to_angle ( const ml_matrix & quaternion )

Parameters:

quaternion The quaternion.

Returns:: The angle from the quaternion in radians.

References PI, and TWO_PI.

ml_matrix q_to_vec ( const ml_matrix & quaternion )

Parameters:

quaternion The quaternion.

Returns:: The vector from the quaternion.

ml_matrix au_to_q	(	double	angle,
		double	unit_vec[3]
	)

Parameters:

angle
unit_vec

Returns:: The quaternion computed from the provided angle and unit vector.

ml_matrix au_to_q	(	double	angle,
		const ml_matrix &	unit_vec
	)

Parameters:

angle
unit_vec

Returns:: The quaternion computed from the provided angle and unit vector.

double q_to_au	(	const ml_matrix &	quaternion,
		ml_matrix &	unit_vec
	)

Parameters:

quaternion	The quaternion.
unit_vec	The unit vector will be returned in this matrix.

Returns:: The angle computed from the quaternion, measured in radians.

ml_matrix eul_to_mat ( const ml_matrix & euler )

Parameters:

euler (3,1) The Euler angle sequence to be converted.

Returns:: The matrix which transforms in the direction of the rotation.

ml_matrix delta_eul_to_q	(	const ml_matrix &	q,
		const ml_matrix &	euler
	)

Apply a 3-2-1 Euler angle sequence to a quaternion that transforms in the direction of the rotation.

Parameters:

euler	(3,1) The Euler angle sequence to be converted.
q	(4,1) The original quaternion.

Returns:: The matrix which transforms in the direction of the rotation.

ml_matrix rot_mat_x ( const double & a )

Generate a rotation matrix for angular rotation about the x axis.

Parameters:

a	Angle of rotation (rad)

Returns:: The rotation matrix.

ml_matrix rot_mat_y ( const double & a )

Generate a rotation matrix for angular rotation about the y axis.

Parameters:

a	Angle of rotation (rad)

Returns:: The rotation matrix.

ml_matrix rot_mat_z ( const double & a )

Generate a rotation matrix for angular rotation about the z axis.

Parameters:

a	Angle of rotation (rad)

Returns:: The rotation matrix.

ml_matrix mat_to_q ( const ml_matrix & mat )

Convert a matrix to a quaternion.

Wrapper for the MatrixLib function q_from_mat.

Parameters:

mat	(3,3) The matrix to be converted.

Returns:: The quaternion generated from the provided matrix.

ml_matrix mat_to_eul	(	const ml_matrix &	mat,
		const ml_matrix &	euler
	)

Wrapper for the MatrixLib function q_mat_to_eul.

Parameters:

mat	(3,3)
euler	(3,1)

Returns:: Returns the Euler angle sequence generated from the provided matrix.

ml_matrix u_to_q	(	const ml_matrix &	vec1,
		const ml_matrix &	vec2
	)

Computes the quaternion which aligns one vector with a second.

This is not a unique solution.

Wrapper for the MatrixLib function q_from_u.

Parameters:

vec1	(3,1) Starting vector.
vec2	(3,1) Ending vector.

Returns:: Quaternion which rotates vec1 into vec2

ml_matrix perpendicular ( const ml_matrix & vec )

Wrapper for the MatrixLib function q_perpendicular.

Parameters:

vec	(3,1) The vector.

Returns:: Returns the perpendicular to the given vector.

ml_matrix q_error	(	const ml_matrix &	q_ref,
		const ml_matrix &	q_meas
	)

This routine gives the correct sign when both vectors transform from frame a to frame b and frame b is the body frame. If the convention is reversed you must reverse the sign.

Parameters:

q_ref	(4,1) Reference quaternion.
q_meas	(4,1) Measured quaternion.

Returns:: (3,1) Vector of small angular errors.

ml_matrix qb_to_i_dot	(	const ml_matrix &	quaternion,
		const ml_matrix &	w
	)

Calculates the derivative of the body to inertial quaternion.

Parameters:

quaternion	(4,1) The quaternion, should be a column vector
w	(3,1) The anglular velocity, a 3 element column vector

Returns:: (4,1) Derivative of the body to inertial quaternion.

ml_matrix qi_to_b_dot	(	const ml_matrix &	quat,
		const ml_matrix &	w
	)

Calculates the derivative of the inertial to body quaternion.

Parameters:

quat	(4,1) The quaternion, should be a column vector.
w	(3,1) The angular rate, a 3 element column vector.

Returns:: (4,1) Derivative of the inertial to body quaternion.

ml_matrix qeb_re_ub_to_az_el	(	const ml_matrix &	qEB,
		const ml_matrix &	rE,
		const ml_matrix &	vB
	)

Calculate azimuth & elevation angle from ECI to body quaternion, position, and boresight vector.

Azimuth angle is measured clockwise from north to the projection of the boresight vector onto the east-north plane. Elevation angle is the "angle off nadir", the angular distance between the nadir vector and the boresight vector. Adapted by KenW from Joe Mueller's QEB_RE_UB_to_AzEl.m matlab code in /Contracts/NavyReconfigure/Matlab

Parameters:

qEB	(4,1) ECI to spacecraft body coordinate frame quaternion
rE	(3,1) ECI position of spacecraft
vB	(3,1) boresight vector defined in body frame

Returns:: (2,1) matrix containing azimuth angle in (1,1) and elevation angle in (2,1)

ml_matrix mat_eci_to_lvlh	(	const ml_matrix &	pos,
		const ml_matrix &	vel
	)

For LVLH coordinates; z is in the -r direction y is in the - rxv direction x completes the set

Parameters:

pos	(3,1) Position vectors
vel	(3,1) Velocity vectors

Returns:: (4,n) The quaternions that transform from ECI to LVLH coordinates.

ml_matrix q_eci_to_lvlh	(	const ml_matrix &	pos,
		const ml_matrix &	vel
	)

Parameters:

pos	(3,1) Position vector
vel	(3,1) Velocity vector

Returns:: (4,n) The quaternions that transform from ECI to LVLH coordinates.

ml_matrix mat_eci_to_hills	(	const ml_matrix &	r,
		const ml_matrix &	v
	)

For Hills coordinates; x is in the + r direction z is in the + rxv direction y completes the set (aligned with velocity for circular orbits)

Parameters:

r	(3,1) Position vector
v	(3,1) Velocity vector

Returns:: q (4,1) Quaternion

ml_matrix q_eci_to_hills	(	const ml_matrix &	r,
		const ml_matrix &	v
	)

Parameters:

r	(3,1) Position vector
v	(3,1) Velocity vector

Returns:: q (4,1) Quaternion

ml_matrix eci_to_hills	(	const ml_matrix &	x0,
		const ml_matrix &	x1
	)

Parameters:

x0	(6,1) ECI position and velocity of reference orbit
x1	(6,1) ECI position and velocity of secondary orbit

Returns:: xH (6,1) Relative position and velocity in Hills-frame

ml_matrix hills_to_eci	(	const ml_matrix &	x0,
		const ml_matrix &	xH
	)

Parameters:

x0	(6,1) ECI position and velocity of reference orbit
xH	(6,1) Relative position and velocity in Hills-frame

Returns:: x1 (6,1) ECI position and velocity of secondary orbit

ml_matrix q_to_ra_dec	(	const ml_matrix &	quaternion,
		const ml_matrix &	uu
	)

Compute right ascension and declination from a quaterion.

Parameters:

quaternion	(4,1) The quaternion (inertial to body).
uu	(3,1) unit vector in the body frame.

Returns:: The right ascension and declination.

ml_matrix u_to_ra_dec ( const ml_matrix & unit_vec )

Computes right ascension and declination from a unit vector.

Parameters:

unit_vec (3,n) Unit vector(s)

Returns:: rADec (2,n) stacked vector(s) of right ascension (top) and declination (bot)

ml_matrix u_to_ra_dec	(	const ml_matrix &	unit_vec,
		bool	normalize
	)

Computes right ascension and declination from a unit vector and normalizes the result.

Parameters:

unit_vec	(3,n) Unit vector(s)
normalize	Flag indicating whether the return vector should be normalized.

Returns:: rADec (2,n) stacked vector(s) of right ascension (top) and declination (bot)

References TWO_PI.

ml_matrix ra_dec_to_q	(	const ml_matrix &	uu,
		double	ra,
		double	dec
	)

If right ascension and declination are defined in frame a, and u is fixed in frame b, q transforms from frame a to b such that u lies along the vector determined by (rA,dec) in frame a.

Parameters:

uu	(3,1) unit vector
ra	(1) Right ascension [rad]
dec	(1) Declination [rad]

Returns:: (4,1) Quaternion

ml_matrix ra_dec_to_u	(	double	ra,
		double	dec
	)

Parameters:

ra	(1) Right ascension [rad]
dec	(1) Declination [rad]

Returns:: A unit vector(3,1) computed from the provided right ascension and declination.

ml_matrix ra_dec_to_u	(	const ml_matrix &	ra,
		const ml_matrix &	dec
	)

Parameters:

ra	(1,n) Right ascension [rad]
dec	(1,n) Declination [rad]

Returns:: A unit vector computed from the provided right ascension and declination.

ml_matrix az_el_to_q	(	ml_matrix	az,
		ml_matrix	el
	)

Compute a quaternion from azimuth and elevation.

Parameters:

az	Is the azimuth (angle about +z from +x)
el	is the elevation (angle about +y from +x)

Returns:: (4,n) The quaternion from base to rotated frame.

ml_matrix az_el_to_q	(	double	az,
		double	el
	)

Compute a quaternion from azimuth and elevation.

Parameters:

az	Is the azimuth (angle about +z from +x)
el	is the elevation (angle about +y from +x)

Returns:: (4,1) The quaternion from base to rotated frame.

ml_matrix qslerp	(	const ml_matrix &	quat1,
		const ml_matrix &	quat2,
		double	t
	)

Parameters:

quat1	(4,1)
quat2	(4,1)
t	(1) between 0 to 1

Returns:: (4,1) Interpolated quaternion

ml_matrix lat_lon_alt_to_pos	(	double	lat,
		double	lon,
		double	h,
		double	f,
		double	a
	)

Parameters:

lat	Latitude in radians.
lon	Longitude in radians.
h	Distance above the subsatellite point.
f	Flattening factor
a	Equatorial radius

Returns:: (3,1) The EF position vector.

ml_matrix lat_lon_to_pos	(	double	lat,
		double	lon,
		double	f,
		double	a,
		bool	is_geodetic
	)

Parameters:

lat	Latitude in radians.
lon	Longitude in radians.
f	Flattening factor
a	Equatorial radius
is_geodetic	true for geodetic

Returns:: (3,1) The EF position vector.

ml_matrix lat_lon_to_pos	(	double	lat,
		double	lon,
		double	f,
		double	a,
		int	type
	)

Parameters:

lat	Latitude in radians.
lon	Longitude in radians.
f	Flattening factor
a	Equatorial radius
type	0 for Geodetic

Returns:: The EF position vector.

ml_matrix pos_to_lat_lon_alt	(	const ml_matrix &	efPos,
		double	f,
		double	a,
		double	tolerance
	)

Parameters:

efPos	ECEF position (km)
f	Flattening factor
a	Equatorial radius
tolerance	Tolerance for the iteration

Returns:: (3,1) lat (radians), lon (radians), altitude (km)

References PI.

void cart_to_sph	(	const ml_matrix &	x,
		const ml_matrix &	y,
		const ml_matrix &	z,
		ml_matrix &	r,
		ml_matrix &	theta,
		ml_matrix &	phi
	)

Individual vector form.

Parameters:

x
y
z
r
theta
phi

ml_matrix cart_to_sph ( const ml_matrix & x )

Converts cartesian coordinates to spherical. Stacked form.

Stacked matrix form.

Parameters:

x	Position state [x;y;z]

Returns:: r New coordinates [r;theta;phi]

void sph_to_cart	(	const ml_matrix &	r,
		const ml_matrix &	theta,
		const ml_matrix &	phi,
		ml_matrix &	x,
		ml_matrix &	y,
		ml_matrix &	z
	)

Convert spherical coordinates to cartesian.

Individual vector form.

Parameters:

r
theta
phi
x
y
z

ml_matrix RPhiTheta2Cart ( const ml_matrix & r )

Computes the transformation matrix from an r, phi, theta frame to cartesian.

In an RPT frame, r is the radial direction, phi is 'east', and theta is in the direction of co-elevation. When theta is zero the r vector is in the xy-plane.

Parameters:

r	Position vector

Returns:: cRPT2Cart Transformation matrix

ml_matrix CameraToECI	(	double	az,
		double	el,
		double	tt,
		const ml_matrix &	qECIToBody,
		const ml_matrix &	mBaseToBody
	)

Computes the transformation matrix from a camera frame with 3 rotations to the body frame.

Parameters:

az	Azimuth (rad)
el	Elevation (rad)
tt	Turntable angle (rad)
qECIToBody	Quaternion from ECI to Body
mBaseToBody	Transformation matrix from Camera base to body

Returns:: mCameraToECI Transformation matrix

ml_matrix eci_to_ned	(	const ml_matrix &	r,
		int	opt,
		double	f
	)

Computes the transformation matrix or quaternion from a eciframe to the North East Down (NED) frame.

Reference: Stevens, B.L., Lewis, F.L. , Aircraft Control and Simulation, John Wiley & Sons, 1992, p. 36.

Parameters:

r	ECI position vector (km)
opt	0 output quaternion 1 output matrix (rad)
f	Flattening factor

Returns:: qECIToNED or mECIToNED Transformation quaternion or matrix

ml_matrix u_to_az_el ( const ml_matrix & u )

Computes the azimuth and elevation of a unit vector.

Parameters:

u	Unit vector

Returns:: [az;el]

ml_matrix az_el_to_u	(	double	az,
		double	el
	)

Computes u from azimuth and elevation of a unit vector.

Parameters:

az	Azimuth
el	Elevation

Returns:: Unit vector

ml_matrix az_el_to_u	(	const ml_matrix &	az,
		const ml_matrix &	el
	)

Compute a unit vector from azimuth and elevation.

Parameters:

az	is the azimuth (angle about +z from +x)
el	is the elevation (angle about +y from +x)

Returns:: The unit vector.

ml_matrix q_from_dq	(	const ml_matrix &	q,
		const ml_matrix &	dX
	)

Computes q as the product of q and a delta quaternion.

Parameters:

q	Quaternion
dX	Delta quaternion

Returns:: Quaternion

ml_matrix dq_from_dX ( const ml_matrix & dX )

Delta quaternion from a 3 vector.

Parameters:

dX	Delta quaternion

Returns:: Quaternion

ml_matrix r_lvlh_to_eci	(	const ml_matrix &	r_eci,
		const ml_matrix &	v_eci,
		const ml_matrix &	r
	)

LVLH position to ECI.

Parameters:

r_eci	Position vector of reference center in the ECI frame
v_eci	Velocity vector of reference center in the ECI frame
r	Position vector in lvlh frame

Returns:: Position vector in the eci frame

ml_matrix v_lvlh_to_eci	(	const ml_matrix &	r_eci,
		const ml_matrix &	v_eci,
		const ml_matrix &	v
	)

ECI position to LVLH.

Parameters:

r_eci	Position vector of reference center in the ECI frame
v_eci	Velocity vector of reference center in the ECI frame
v	Position vector in lvlh frame

Returns:: Position vector in the eci frame

ml_matrix r_eci_to_lvlh	(	const ml_matrix &	r_eci,
		const ml_matrix &	v_eci,
		const ml_matrix &	r
	)

LVLH position to ECI.

Parameters:

r_eci	Position vector of reference center in the ECI frame
v_eci	Velocity vector of reference center in the ECI frame
r	Position vector in eci frame

Returns:: Position vector in the lvlh frame

ml_matrix v_eci_to_lvlh	(	const ml_matrix &	r_eci,
		const ml_matrix &	v_eci,
		const ml_matrix &	v
	)

ECI position to LVLH.

Parameters:

r_eci	Position vector of reference center in the ECI frame
v_eci	Velocity vector of reference center in the ECI frame
v	Position vector in eci frame

Returns:: Position vector in the lvlh frame

ml_matrix x_lvlh_to_eci	(	const ml_matrix &	r_eci,
		const ml_matrix &	v_eci,
		const ml_matrix &	x
	)

LVLH state to ECI.

Parameters:

r_eci	Position vector of reference center in the ECI frame
v_eci	Velocity vector of reference center in the ECI frame
x	[r;v] in lvlh frame

Returns:: Position vector in the eci frame

ml_matrix x_eci_to_lvlh	(	const ml_matrix &	r_eci,
		const ml_matrix &	v_eci,
		const ml_matrix &	x
	)

ECI state to LVLH.

Parameters:

r_eci	Position vector of reference center in the ECI frame
v_eci	Velocity vector of reference center in the ECI frame
x	[r;v] in eci frame

Returns:: Position vector in the eci frame

ml_matrix x_lvlh_to_eci	(	const ml_matrix &	x_eci,
		const ml_matrix &	x
	)

ECI state to LVLH.

Parameters:

x_eci	Velocity vector of reference center in the ECI frame
x	[r;v] in lvlh frame

Returns:: Position vector in the eci frame

ml_matrix x_eci_to_lvlh	(	const ml_matrix &	x_eci,
		const ml_matrix &	x
	)

ECI state to LVLH.

Parameters:

x_eci	State vector of reference center in the ECI frame [r;v]
x	[r;v] in eci frame

Returns:: State in the eci frame

ml_matrix LLAToECEF	(	const ml_matrix &	lla,
		double	rP
	)

Compute ECEF position from latitude, longitude, altitude.

Assumes a spherical planet. Can handle an array of positions.

Parameters:

lla	(3xn) Latitude [rad], longitude [rad], altitude [km]
rP	Radius of planet (for Earth: 6378.14) [km]

Returns:: ECEF position vector [km]

ml_matrix small_angles_to_q ( const ml_matrix & angle )

Parameters:

angle Angle vector

Returns:: Equivalent quaternion

ml_matrix spice_to_3_by_3	(	const ml_matrix &	m,
		int	k
	)

Convert SPICE rotation matrix to 3x3.

Parameters:

m	SPICE 9-by-1 rotation matrix (column major)
k	Column

Returns:: 3-by-3 matrix Planet fixed to ECI

sc_coord.h File Reference

Functions

Detailed Description

Function Documentation