Holds the FFLib data structures and function definitions. More...

Classes
struct	alf_orb_data_s
	Alfriend orbital elements data structure. More...
struct	team_s
	Team data structure. More...
struct	state_s
	State data structure. More...
struct	geom_s
	Geometry data structure. More...
struct	ecc_geom_s
	Eccentric geometry data structure. More...
struct	ecc_geom_xy_s
	Eccentric geometry data structure (xy) More...
struct	window_s
	Time window data structure. More...
struct	plan_param_s
	Planning parameters data structure. More...
struct	constraints_s
	Constraints data structure. More...
struct	team_goals_s
	Team goals data structure. More...
struct	ecc_team_goals_s
	Eccentric team goals data structure. More...
struct	cost_s
	Cost estimate data structure. More...
struct	burn_s
	Burn data structure. More...
struct	maneuver_s
	Maneuver data structure. More...
struct	dv_command_s
	Delta-V command data structure. More...
struct	orientation_s
	Orientation data structure. More...
struct	assign_s
	Assignment data structure. More...
struct	coll_mon_data_s
	Collision monitor data. More...
Defines
#define	FF_J2 0.001082
	J2 perturbation is 0.001082.
#define	FF_TOL 1e-8
	Defines the default tolerance to use in comparing doubles.
#define	FF_MAX_ITER 100
	Defines the default value for maximum number of iterations.
#define	FF_MAX_BURNS 10
	Defines the maximum number of impulsive burns that can be included in a maneuver data structure.
#define	FF_MAX_MEMBERS 8
	Defines the maximum number of satellite members that can be on a given team.
#define	SC_OS_MACOSX
	Mac OS X.
#define	SC_OS_UNIX
	UNIX OS.
Typedefs
typedef struct alf_orb_data_s	alf_orb_data_t
	Alfriend orbital elements data structure.
typedef struct team_s	team_t
	Team data structure.
typedef struct state_s	state_t
	State data structure.
typedef struct geom_s	geom_t
	Geometry data structure.
typedef struct ecc_geom_s	ecc_geom_t
	Eccentric geometry data structure.
typedef struct ecc_geom_xy_s	ecc_geom_xy_t
	Eccentric geometry data structure (xy)
typedef struct window_s	window_t
	Time window data structure.
typedef struct plan_param_s	plan_param_t
	Planning parameters data structure.
typedef struct constraints_s	constraints_t
	Constraints data structure.
typedef struct team_goals_s	team_goals_t
	Team goals data structure.
typedef struct ecc_team_goals_s	ecc_team_goals_t
	Eccentric team goals data structure.
typedef struct cost_s	cost_t
	Cost estimate data structure.
typedef struct burn_s	burn_t
	Burn data structure.
typedef struct maneuver_s	maneuver_t
	Maneuver data structure.
typedef struct dv_command_s	dv_command_t
	Delta-V command data structure.
typedef struct orientation_s	orientation_t
	Orientation data structure.
typedef struct assign_s	assign_t
	Assignment data structure.
typedef struct coll_mon_data_s	coll_mon_data_t
	Collision monitor data.
typedef double(*	nr_function )(double x, double e, const ml_matrix &D, double dH)
	Newton-Raphson function.
Enumerations
enum	ff_error_codes { FF_NO_ERROR = 0, FF_NO_SOLN = 1, FF_MAX_ITER = 2, FF_BAD_VALUE = 3 }
	Error codes for invalid matrix operations. More...
enum	ff_formation_types { FF_IPLF = 1, FF_OOPLF_RGT = 2, FF_CIPE_REF_CENTER = 3, FF_CIPE_REF_ON = 4, FF_POS_PROJ_CIRC_REF_CENTER = 5, FF_POS_PROJ_CIRC_REF_ON = 6, FF_NEG_PROJ_CIRC_REF_CENTER = 7, FF_NEG_PROJ_CIRC_REF_ON = 8, FF_DUAL_PROJ_CIRC_REF_CENTER = 9, FF_DUAL_PROJ_CIRC_REF_ON = 10, FF_TETRA = 11 }
	Formation type enumerations. More...
Functions
maneuver_s	IterativeImpulsiveManeuver (state_t state, geom_t goals_circ, window_t window, plan_param_t param, bool &foundSoln)
	Computes the delta-v's required to implement a formation flying maneuver for a single spacecraft.(circular orbit)
maneuver_s	IterativeImpulsiveManeuver (state_t state, ecc_geom_t goals_ecc, window_t window, plan_param_t param, bool &foundSoln)
	Computes the delta-v's required to implement a formation flying maneuver for a single spacecraft. (eccentric orbit)
maneuver_s	ImpulsiveLPManeuver (state_t state, geom_t goals_circ, window_t window, plan_param_t param, double &maxDV)
	Plans an impulsive burn sequence (using simplex) to achieve the specified trajectory within the given time window. (circular orbit)
maneuver_s	ImpulsiveLPManeuver (state_t state, ecc_geom_t goals_ecc, window_t window, plan_param_t param, double &maxDV)
	Plans an impulsive burn sequence (using simplex) to achieve the specified trajectory within the given time window. (eccentric orbit)
maneuver_s	ImpulsiveManeuver (state_t state, geom_t goals, window_t window, plan_param_t param, double &maxDV)
	Plans an impulsive burn sequence (using closed-form equations) to achieve the specified trajectory within the given time window. For circular orbits only.
bool	OptimalInPlaneDeltaV (double nOrbMin, double nOrbMax, double a, double th0, double th1, double delta_a, double delta_th0, double delta_q1, double delta_q2, double &dV1, double &dV2, double &dV3, unsigned short &M, unsigned short &N)
	Computes the in-plane delta-v sequence for the given time window that achieves the desired element differences and results in the minimum total delta-v. For circular orbits only.
burn_t *	InPlane (alf_orb_data_t meas_elem, alf_orb_data_t delta_elem, double accNom, double dTMin, double nOrbMin, double nOrbMax, double horizon, double &t0, double &tF, unsigned short &nBurns)
	Computes the in-plane burn sequence for the given time window that achieves the desired element differences. For circular orbits only.
burn_t	OutOfPlane (alf_orb_data_t meas_elem, alf_orb_data_t delta_elem, double accNom, double dTMin, unsigned short &nBurns, double &th1)
	Compute the out-of-plane burn sequence for the given time window that achieves the desired element differences. For circular orbits only.
geom_t	AutoFormGeometry (state_t state, geom_t memberGoals[], int num, double minSepDist, double maxSepDist)
	Define new geometric goals for a single satellite, such that any semi-major axis difference is eliminated, any radial oscillation is eliminated, and the new trajectory maintains a minimum separation distance from all other known trajectories.
ecc_geom_t	AutoFormGeometry (state_t state, ecc_geom_t memberGoals[], int num, double minSepDist, double maxSepDist)
	Define new geometric goals for a single satellite, such that any semi-major axis difference is eliminated, any radial oscillation is eliminated, and the new trajectory maintains a minimum separation distance from all other known trajectories.
double	NearestOffset (double y0, double width, ml_matrix extrema, double minSepDistance, double maxSepDistance)
	Determine the nearest along-track offset for a trajectory that is safe such that the minimum and maximum required separation distances are respected.
ml_matrix	InitializeCostMatrix (team_goals_t teamGoals, int nRelatives)
	Given the team goals, initialize the cost matrix "f" with the right size.
ml_matrix	InitializeCostMatrix (ecc_team_goals_t teamGoals, int nRelatives)
	Given the team goals, initialize the cost matrix "f" with the right size.
int	PopulateCostMatrix (ml_matrix &f, cost_t costEstimate, team_goals_t teamGoals, ml_int_array relativeIDs)
	Fill in a single column of the cost matrix.
int	PopulateCostMatrix (ml_matrix &f, cost_t costEstimate, ecc_team_goals_t teamGoals, ml_int_array relativeIDs)
	Fill in a single column of the cost matrix.
void	CostMatrixRows (team_goals_t teamGoals, int index, int &a, int &b)
	Compute the starting and ending rows in the cost matrix that correspond to a give target state index.
void	CostMatrixRows (ecc_team_goals_t teamGoals, int index, int &a, int &b)
	Compute the starting and ending rows in the cost matrix that correspond to a give target state index.
cost_s	EstimateCost (alf_orb_data_t el0, alf_orb_data_t dEl, team_goals_t teamGoals, int memID, window_t window, double weight)
	Estimate the (weighted) cost to achieve all specified unique target states.
cost_s	FFEccEstimateCost (orb_data_t el0, const ml_matrix &xH0, ecc_team_goals_t teamGoals, int memID, window_t window, double weight, int nSPO)
	Estimate the (weighted) cost to achieve all specified unique target states.
team_goals_s	GenerateTeamGoals (alf_orb_data_t el0, int fType, double fSize, unsigned short nRels, int teamID, double angRes)
	Generate a set of team goals given the formation type and size.
ecc_team_goals_s	FFEccGenerateTeamGoals (orb_data_t el0, int fType, double fSize, unsigned short nRels, int teamID, double nu, const ml_matrix &eul)
	Generate a set of team goals given the formation type, size, location and orientation.
ecc_geom_xy_s *	FFEccTetrahedronGeometry (double nu, double d, const ml_matrix &eul)
	Compute the geometric goals for a formation that achieves a tetrahedron shape at a given true anomaly in an eccentric reference orbit.
geom_s	PCGoals (double R, double alpha0, double sgn, double y0)
	Generate the geometric goals for a projected circular formation.
void	SortTeamGoals (team_goals_t &teamGoals)
	Sort the team goals with fixed states listed before variable states.
void	SortTeamGoals (ecc_team_goals_t &teamGoals)
	Sort the team goals with fixed states listed before variable states.
assign_s	SetupAssignmentProblem (team_goals_t teamGoals, double orbFrac=1)
	Set up the assignment problem given the team goals by computing the number of fixed, variable and unique variable states, plus with the phases and indices of repeated variable states.
assign_s	SetupAssignmentProblem (ecc_team_goals_t teamGoals, double orbFrac=1)
	Set up the assignment problem given the team goals by computing the number of fixed, variable and unique variable states, plus with the phases and indices of repeated variable states.
int	RestrictIDSet (ml_int_array &relIDs, constraints_t constraints[], int numC)
	Restrict the set of relative IDs to respect the specified assignment constraints.
int	VerifyAssignmentParams (assign_t a, const ml_matrix &f)
	Check for inconsistencies in the assignment parameters.
int	PrivilegedAssignment (assign_t assign, const ml_matrix &f, int method, ml_int_array &optOrder, ml_matrix &optPhi, double &optCost)
	Assign N targets to N satellites one at a time, so that the satellite with the largest minimum cost is assigned its min-cost target first.
int	OptimalAssignment (assign_t assign, ml_matrix f, ml_int_array &optOrder, ml_matrix &optPhi, double &optCost)
	Assign N targets to N satellites so that the weighted sum of costs to reach all targets is minimized.
bool	EquallyPhased (const ml_matrix &phi, ml_int_array u, int Pu)
	Determine if the phase angles are equally phased.
ml_int_array	FindMinSet (ml_matrix &mat, double &minSum)
	Find the order in which to arrange the columns so that the matrix diagonal sum is minimized.
void	permute (ml_int_array arr, int start, int num, const ml_matrix &mat, double &cost, ml_int_array &best)
	Permute the supplied array, called recursively by FindMinSet.
void	LPCircular (const ml_matrix &x0, const ml_matrix &xF, double n, double duration, double dT, unsigned short constraintType, double maxConstraint, ml_matrix &aC, ml_matrix &t, bool &exitFlag)
	Computes the thrust trajectory to go from an initial state to a final state in Hills frame. For circular orbits.
void	LPEccentric (double e, double n, const ml_matrix &x0, const ml_matrix &xF, double nu0, double nuF, int nS, ml_matrix cW, unsigned short constraintType, double maxConstraint, ml_matrix &aC, ml_matrix &t, bool &exitFlag)
	Computes the thrust trajectory to go from an initial state to a final state in Hills frame. For eccentric orbits.
void	LPCircularTimeWeight (orb_data_t el0, const ml_matrix &xH0, geom_t goals, window_t window, int nSPO, ml_matrix &xHF, double &nOrbMvr)
	Determine the target state on the desired trajectory that gives the minimum time-weighted cost. For circular orbits.
void	LPEccentricTimeWeight (orb_data_t el0, const ml_matrix &xH0, ecc_geom_t goals, window_t window, int nSPO, ml_matrix &xHF, double &nOrbMvr)
	Determine the target state on the desired trajectory that gives the minimum time-weighted cost. For eccentric orbits.
void	GVEErrorDynamics (orb_data_t el0, ml_matrix &A, ml_matrix &B)
	Compute continuous-time dynamics for Gauss' variational equations.
void	LPEccentricGVE (orb_data_t el0, const ml_matrix &x0, const ml_matrix &xF, double MF, int nS, ml_matrix cW, unsigned short constraintType, double maxConstraint, ml_matrix &aC, ml_matrix &t, bool &exitFlag)
	Computes the thrust trajectory to go from an initial state to a final state in Hills frame. For eccentric orbits.
void	FFEccLinOrb (double n, double nu, double e, ml_matrix &a, ml_matrix &b, double dT)
	Compute the continous A,B matrices for linearized relative motion in an eccentric reference orbit, discretized with a zero-order hold with timestep dT. *sctlib (overload LinOrb)
ml_matrix	FFEccLinOrb (const ml_matrix &x, const ml_matrix &acc, double n, double nu, double e)
	Compute the right-hand-side for linearized relative motion in an eccentric reference orbit.
ml_matrix	FFEccProp (const ml_matrix &D, const ml_matrix &nu, double e, double dH)
	Compute Hills frame state at specified true anomaly given integration constants and eccentricity.
ml_matrix	FFEccProp (const ml_matrix &D, double nu, double e, double dH)
	Compute Hills frame state at specified true anomaly given integration constants and eccentricity.
double	FFEccDH (double nu0, double e)
	Compute integration constant dH for homogeneous solution to LTV differential equations of relative orbit motion. Found by setting H=0 at initial true anomaly.
void	FFEccGoals (double e, ecc_geom_t goals, ml_matrix &D, ml_matrix &xH)
	Compute integration constants and initial state from the geometric goals.
void	FFEccGoals (double e, ecc_geom_xy_t goals, ml_matrix &D, ml_matrix &xH)
	Compute integration constants and initial state from the geometric goals.
void	FFEccIntConst (const ml_matrix &xH0, double nu0, double e, ml_matrix &D, double &dH, ml_matrix &R)
	Compute integration constants for homogeneous solution to LTV differential equations of relative orbit motion.
ml_matrix	FFEccRMat (double nu, double e, double dH)
	Compute the state-transition matrix, R, given the eccentricity and true anomaly so that xH = R*D, where D is the vector of integration constants found from initial conditions.
ml_matrix	FFEccRMat (double nu, double e)
	Compute the state-transition matrix, R, given the eccentricity and true anomaly so that xH = R*D, where D is the vector of integration constants found from initial conditions. Here, the integration constant "dH" is computed using the first element of the "nu" matrix.
void	FFEccXExt (double e, const ml_matrix &D, double dH, double epsilon, int nMax, ml_matrix &x, ml_matrix &nu)
	Compute extreme x-values and associated true anomalies for given relative motion.
void	FFEccYExt (double e, const ml_matrix &D, double dH, double epsilon, int nMax, ml_matrix &y, ml_matrix &nu)
	Compute extreme y-values and associated true anomalies for given relative motion.
void	FFEccZExt (double e, const ml_matrix &D, double dH, double epsilon, int nMax, ml_matrix &z, ml_matrix &nu)
	Compute extreme z-values and associated true anomalies for given relative motion.
void	NuDot (double n, double e, double nu, double &nuDot, double &nuDotDot)
	Compute the time-derivative of the true anomaly. *sctlib.
double	FFEccDX (double nu, double e, const ml_matrix &D, double dH)
	Compute the first derivative of x with respect to true anomaly.
double	FFEccDY (double nu, double e, const ml_matrix &D, double dH)
	Compute the first derivative of y with respect to true anomaly.
double	FFEccDZ (double nu, double e, const ml_matrix &D, double dH)
	Compute the first derivative of z with respect to true anomaly.
double	FFEccDDX (double nu, double e, const ml_matrix &D, double dH)
	Compute the second derivative of x with respect to true anomaly.
double	FFEccDDY (double nu, double e, const ml_matrix &D, double dH)
	Compute the second derivative of y with respect to true anomaly.
double	FFEccDDZ (double nu, double e, const ml_matrix &D, double dH)
	Compute the second derivative of z with respect to true anomaly.
orb_data_t	Alfriend2El (alf_orb_data_t elA)
	Convert an Alfriend orbital element set into the standard orbital element set *sctlib.
alf_orb_data_t	El2Alfriend (orb_data_t el)
	Convert a standard orbital element set into the Alfriend orbital element set *sctlib.
alf_orb_data_t	El2Alfriend (orb_data_t el, double true_anom)
	Convert a standard orbital element set into the Alfriend orbital element set *sctlib.
alf_orb_data_s	add_elements (alf_orb_data_t el1, alf_orb_data_t el2)
	Add two sets of orbital elements *sctlib.
orb_data_s	add_elements (orb_data_t el1, orb_data_t el2)
	Add two sets of orbital elements *sctlib.
alf_orb_data_s	sub_elements (alf_orb_data_t el1, alf_orb_data_t el2)
	Subtract one element set from another.
orb_data_s	sub_elements (orb_data_t el1, orb_data_t el2)
	Subtract one element set from another.
double	CirclePhase (double beta)
	Compute the desired phase on a circle from the desired phase on the ellipse. The circle is superscribed about the ellipse.
double	EllipsePhase (double alpha)
	Compute the desired phase on an ellipse from the desired phase on the circle. The circle is superscribed about the ellipse.
alf_orb_data_t	OrbElemDiff (alf_orb_data_t el0, alf_orb_data_t el)
	Computes the differences between Alfriend orbital element vectors.
orb_data_t	OrbElemDiff (orb_data_t el0, orb_data_t el)
	Computes the differences between standard orbital element vectors.
alf_orb_data_t	Goals2DeltaElem (alf_orb_data_t el0, geom_t goals)
	Computes the desired element differences, given the geometric goals and the measured orbital elements.
geom_t	DeltaElem2Goals (alf_orb_data_t el0, alf_orb_data_t dEl)
	Computes the geoemtric goals, given the desired element differences and the measured orbital elements.
ml_matrix	DeltaElem2Hills (alf_orb_data_t elA, alf_orb_data_t dEl)
	Computes the Hills frame state from the element differences and reference elements.
alf_orb_data_s	Hills2DeltaElem (alf_orb_data_t el0, const ml_matrix &xH)
	Computes the element differences from the Hills frame state and reference elements.
geom_s	Hills2Goals (alf_orb_data_t el0, const ml_matrix &xH)
	Computes the geometric goals from the Hills frame state and reference elements.
ml_matrix	Goals2Hills (alf_orb_data_t el0, geom_t goals)
	Computes the Hills frame state from the geometric goals and reference elements.
orb_data_s	FFEccHills2DeltaElem (orb_data_t el0, const ml_matrix &xH)
	Computes the orbital element differences from the Hills frame state and the reference orbital elements.
alf_orb_data_s	FFEccHills2DeltaElem (alf_orb_data_t el0, const ml_matrix &xH)
	Computes the orbital element differences from the Hills frame state and the reference orbital elements.
ml_matrix	FFEccDeltaElem2Hills (alf_orb_data_t el0, alf_orb_data_t dEl)
	Convert element differences to Hills frame coordinates in an eccentric orbit.
ecc_geom_t	FFEccDeltaElem2Goals (alf_orb_data_t el0, alf_orb_data_t dEl)
	Convert element differences to eccentric geometric goals.
ml_matrix	FFEccGoals2Hills (double e, double nu, ecc_geom_t g, double n)
	Compute Hills frame state (in time-domain) given geometric goals and orbit data.
ml_matrix	FFEccGoals2Hills (double e, double nu, ecc_geom_xy_t g, double n)
	Compute Hills frame state (in time-domain) given geometric goals and orbit data.
ml_matrix	FFEccGoals2Hills (double e, double nu, ecc_geom_t g)
	Compute Hills frame state (in nu-domain) given geometric goals and orbit data.
ecc_geom_t	FFEccHills2Goals (double e, double nu, ml_matrix xH, double n)
	Compute geometric goals given Hills frame state (in time-domain) and orbit data.
ecc_geom_t	FFEccHills2Goals (double e, double nu, const ml_matrix &xH)
	Compute geometric goals given Hills frame state (in nu-domain) and orbit data.
void	Nu2TimeDomain (ml_matrix &x, double n, double e, double nu)
	Convert a relative orbit state from the nu-domain to the time-domain.
void	Time2NuDomain (ml_matrix &x, double n, double e, double nu)
	Convert a relative orbit state from the time-domain to the nu-domain.
ecc_geom_t	GeometryCirc2Ecc (double w, geom_t gCirc)
	Convert a circular geometry structure to an eccentric geometry structure.
geom_t	GeometryEcc2Circ (double w, ecc_geom_t gEcc)
	Convert an eccentric geometry structure to a circular geometry structure.
geom_t	RotateState (geom_t goals, double phi)
	Rotate a geometric goal set to the circular phase angle phi.
double	MeanAnom2TrueLat (double e, double w, double M)
	Convert mean anomlay to true latitude.
void	GetHillsMats (const ml_matrix &r0, const ml_matrix &v0, ml_matrix &A, ml_matrix &Adot)
	Computes the A and Adot matrices used for transformation to Hills frame.
void	AbsRelECI2Hills (ml_matrix r0, ml_matrix v0, ml_matrix dr, ml_matrix dv, ml_matrix &rH, ml_matrix &vH)
	Compute the relative position and velocity in Hills frame given an absolute ECI position & velocity and a relative inertial position & velocity.
alf_orb_data_t	Osc2Mean (alf_orb_data_t el, double J2)
	Transforms osculating orbital elements to mean orbital elements.
alf_orb_data_t *	ECI2MeanElements (const ml_matrix &xRefECI, const ml_matrix &xRelECI, double J2, alf_orb_data_t &elRefMean)
	Computes mean orbital elements and mean orbital element differences from reference and relative ECI position and velocity.
bool	AlignThruster (const ml_matrix &aH, const ml_matrix &bTh, ml_matrix &qHB)
	Computes desired Hills-to-body quaternion for a thruster firing. Rotation about thruster-axis is ignored.
bool	AlignThruster (const ml_matrix &aH, const ml_matrix &bTh, const ml_matrix &bST, const ml_matrix &r, const ml_matrix &v, double jD, double sep, ml_matrix &qHB)
	Computes desired Hills-to-body quaternion for a thruster firing such that the star tracker is pointed as far away as possible from the sun, earth and moon.
ml_matrix	Hills2Frenet (const ml_matrix &xH, const double &e, const double &nu, const double &n)
	Transforms from the Hills frame to the Frenet frame.
ml_matrix	HillsEqns (const ml_matrix &xH0, double n, double t)
	Closed form solution of relative orbital motion using Hills equations. For circular orbits only.
ml_matrix	FFEccHillsEqns (ml_matrix xH0, double nu0, const ml_matrix &nu, double e, double n)
	Compute Hills frame state (in time-domain) at future true anomaly(s). For eccentric or circular orbits.
ml_matrix	FFEccHillsEqns (const ml_matrix &xH0, double nu0, const ml_matrix &nu, double e)
	Compute Hills frame state (in nu-domain) at future true anomaly(s). For eccentric or circular orbits.
ml_matrix	DiscreteHills (const ml_matrix &x0, double n, const ml_matrix &aC, double dT)
	Compute the force relative trajectory from the initial state and time-history of applied accelerations. For circular orbits only.
ml_matrix	FFEccDiscreteHills (double e, double n, const ml_matrix &x0, double nu0, const ml_matrix &aC, const ml_matrix &t)
	Compute the force relative trajectory from the initial state and time-history of applied accelerations. For circular orbits only.
double	CollProbSet (double sigma, const ml_matrix &S, const ml_matrix &xc, const ml_matrix &Ssc, int n)
	Collision probability calculation using sets of ellipsoids.
ml_matrix	MonitoringAlg (ml_matrix &y, ml_matrix &t, ml_matrix &M, ml_matrix &nu, ml_matrix &accel, ml_matrix &aDiff, coll_mon_data_t d)
	Collision monitoring algorithm implementation used for both modes, monitoring and surveying.
ml_matrix	CollisionSurvey (ml_matrix &y, double t0, maneuver_t mvr1, maneuver_t mvr2[], int n_points, coll_mon_data_s d)
	Collision survey implementation which changes maneuvers to acceleration vectors and calls monitoring algorithm.
ml_matrix	DeltaElem2HillsMat (const ml_matrix &elA)
	Compute transformation matrix from delta elements to Hills.
ml_matrix	DeltaEl2AlfriendMat (orb_data_t el)
	Compute transformation matrix from standard differential elements to Alfriend differential elements.
double	distant_pt_ell (const ml_matrix &S, const ml_matrix &U, const ml_matrix &xc, const ml_matrix &x0, ml_matrix &x)
	Compute minimum distance from a distance point to an ellipsoid's surface.
double	Laguerre (const ml_matrix &a, double x_guess)
	Laguerre root finding algorithm adapted to real roots.
ml_matrix	GenerateTimeVector (orb_data_t d, const double tF, const int nPts, ml_matrix &M, ml_matrix &nu)
	Generate a time vector evenly spaced over true anomaly.
ml_matrix	ManeuverStruct2AccelVector (maneuver_t mvr, const ml_matrix &tProp)
	Compute a 3xN acceleration vector from a maneuver data structure.
bool	TeamLevels (team_t teams[], int num, ml_int_array &levels)
	Assign a hierarchical level to each team in the array.
int	IsRelative (int iD, team_t teams[], int num)
	Determine whether the given satellite ID is a relative of any team.
bool	FindUpperTeams (int kBot, team_t teams[], int num, ml_int_array &kUpper)
	Find teams above this one in the hierarchy.
double	TimeUntilTheta (double a, double w, double e, double theta0, double &theta1)
	Computes the time in seconds until the new latitude is reached from the original latitude.
void	AccelVector2ManeuverStruct (const ml_matrix &aC, ml_matrix t, double tRef, double nomAccel, double minSepTime, maneuver_t &mvr, ml_matrix &dV)
	Build a maneuver structure from acceleration and time vectors.
void	ManeuverStruct2AccelVector (maneuver_t mvr, double dT, ml_matrix &aC, ml_matrix &t)
	Compute a 3xN acceleration vector from a maneuver data structure.
ml_matrix	NOrbVector (window_t window)
	Compute a vector of maneuver durations (in orbits) from time window data.
ml_matrix	TargetTrueAnom (double e, double nu0, ml_matrix nOrb)
	Compute the future true anomaly (unwrapped) at the specified number of orbits after the initial true anomaly.
ml_matrix	Tetrahedron (double d, const ml_matrix &eul)
	Compute the 4 points of a regular tetrahedron, the surface area and volume.
double	vsum (const ml_matrix &a)
	Compute the sum of all elements in a row or column vector.
double	newton_raphson (nr_function f, nr_function df, double x, double epsilon, int &n_max, double e, const ml_matrix &D, const double &dH)
	Newton-Raphson (optimized for FFEccXExt and similar)
char *	matout (ml_matrix mat)
	Output a matrix to a string with higher precision than built-in "to_string" function.

Detailed Description

Enumeration Type Documentation

enum ff_error_codes

Enumerator:

FF_NO_ERROR	No error reported.
FF_NO_SOLN	No solution was found.
FF_MAX_ITER	The maximum number of iterations was reached.
FF_BAD_VALUE	Occurs when a supplied value is physically impossible (ie, SMA < 0).

enum ff_formation_types

Enumerator:

FF_IPLF	Equally spaced in-plane leader-follower.
FF_OOPLF_RGT	Equally spaced out-of-plane leader-follower with right ascen. diff. for repeated ground track
FF_CIPE_REF_CENTER	Equqlly phased centered in-plane ellipse, reference at center of ellipse.
FF_CIPE_REF_ON	Equqlly phased centered in-plane ellipse, reference on ellipse.
FF_POS_PROJ_CIRC_REF_CENTER	Equqlly phased positive-plane projected circle, reference at center of circle.
FF_POS_PROJ_CIRC_REF_ON	Equqlly phased positive-plane projected circle, reference on circle.
FF_NEG_PROJ_CIRC_REF_CENTER	Equqlly phased negative-plane projected circle, reference at center of circle.
FF_NEG_PROJ_CIRC_REF_ON	Equqlly phased negative-plane projected circle, reference on circle.
FF_DUAL_PROJ_CIRC_REF_CENTER	Equally phased dual-plane projected circle, reference at center of circle.
FF_DUAL_PROJ_CIRC_REF_ON	Equally phased dual-plane projected circle, reference on circle.
FF_TETRA	Repeating tetrahedron geometry at a specified true anomaly, any orientation.

Function Documentation

maneuver_s IterativeImpulsiveManeuver	(	state_t	state,
		geom_t	goals_circ,
		window_t	window,
		plan_param_t	param,
		bool &	foundSoln
	)

Computes the delta-v's required to implement a formation flying maneuver for a single spacecraft.(circular orbit)

(circular orbit)

Parameters:

state	Absolute and relative state information
goals_circ	Geometric goals for relative trajectory (circular)
window	Time window for the maneuver
param	Planning parameters for maneuver
foundSoln	Flag indicating whether a solution was found or not. Passed by reference.

Returns:: maneuver Maneuver data consisting of a series of impulsive burns

References orb_data_s::ecc, state_s::el, state_s::elA, plan_param_s::eTol, plan_param_s::maxDeltaV, orb_data_s::mean_anom, orb_data_s::perigee, orb_data_s::sma, and state_s::xH.

maneuver_s IterativeImpulsiveManeuver	(	state_t	state,
		ecc_geom_t	goals_ecc,
		window_t	window,
		plan_param_t	param,
		bool &	foundSoln
	)

Computes the delta-v's required to implement a formation flying maneuver for a single spacecraft. (eccentric orbit)

(eccentric orbit)

Parameters:

state	Absolute and relative state information
goals_ecc	Geometric goals for relative trajectory (eccentric)
window	Time window for the maneuver
param	Planning parameters for maneuver
foundSoln	Flag indicating whether a solution was found or not. Passed by reference.

Returns:: maneuver Maneuver data consisting of a series of impulsive burns

References orb_data_s::ecc, state_s::el, state_s::elA, plan_param_s::eTol, plan_param_s::maxDeltaV, orb_data_s::mean_anom, orb_data_s::perigee, orb_data_s::sma, and state_s::xH.

maneuver_s ImpulsiveLPManeuver	(	state_t	state,
		geom_t	goals_circ,
		window_t	window,
		plan_param_t	param,
		double &	maxDV
	)

Plans an impulsive burn sequence (using simplex) to achieve the specified trajectory within the given time window. (circular orbit)

For circular orbits.

Parameters:

state	Data structure of Orbit state
goals_circ	Data structure of geometric goal information
window	Data structure of commanded time window
param	Data structure of planning parameters
maxDV	The maximum delta-V of the sequence

Returns:: maneuver Maneuver data structure

References maneuver_s::achieve, orb_data_s::ecc, state_s::el, plan_param_s::eTol, plan_param_s::fNom, plan_param_s::horizon, state_s::mass, orb_data_s::mean_anom, plan_param_s::nSPOCoarse, plan_param_s::nSPOFine, orb_data_s::perigee, orb_data_s::sma, window_s::startTime, state_s::tM, TWO_PI, and state_s::xH.

maneuver_s ImpulsiveLPManeuver	(	state_t	state,
		ecc_geom_t	goals_ecc,
		window_t	window,
		plan_param_t	param,
		double &	maxDV
	)

Plans an impulsive burn sequence (using simplex) to achieve the specified trajectory within the given time window. (eccentric orbit)

For eccentric orbits.

Parameters:

state	Data structure of Orbit state
goals_ecc	Data structure of geometric goal information
window	Data structure of commanded time window
param	Data structure of planning parameters
maxDV	The maximum delta-V of the sequence. Passed by reference.

Returns:: maneuver Maneuver data structure

References maneuver_s::achieve, orb_data_s::ecc, state_s::el, plan_param_s::eTol, plan_param_s::fNom, plan_param_s::horizon, state_s::mass, orb_data_s::mean_anom, plan_param_s::nSPOCoarse, plan_param_s::nSPOFine, orb_data_s::perigee, orb_data_s::sma, window_s::startTime, state_s::tM, TWO_PI, and state_s::xH.

maneuver_s ImpulsiveManeuver	(	state_t	state,
		geom_t	goals,
		window_t	window,
		plan_param_t	param,
		double &	maxDV
	)

Plans an impulsive burn sequence (using closed-form equations) to achieve the specified trajectory within the given time window. For circular orbits only.

For circular orbits only.

Parameters:

state	Data structure of Orbit state
goals	Data structure of geometric goal information
window	Data structure of commanded time window
param	Data structure of planning parameters
maxDV	The maximum delta-V of the sequence

Returns:: maneuver Maneuver data structure

References maneuver_s::achieve, maneuver_s::burnData, burn_s::dT, plan_param_s::dTMin, burn_s::dV, orb_data_s::ecc, state_s::el, state_s::elA, plan_param_s::fNom, plan_param_s::horizon, maneuver_s::iD, burn_s::iD, alf_orb_data_s::inc, orb_data_s::inc, state_s::mass, MU_EARTH, maneuver_s::nBurns, window_s::nOrbMin, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::raan, alf_orb_data_s::sma, orb_data_s::sma, window_s::startTime, burn_s::t, maneuver_s::t0, maneuver_s::tF, window_s::timeWeightExp, state_s::tM, alf_orb_data_s::true_lat, TWO_PI, burn_s::uZ, and state_s::xH.

bool OptimalInPlaneDeltaV	(	double	nOrbMin,
		double	nOrbMax,
		double	a,
		double	th0,
		double	th1,
		double	delta_a,
		double	delta_th0,
		double	delta_q1,
		double	delta_q2,
		double &	dV1,
		double &	dV2,
		double &	dV3,
		unsigned short &	M,
		unsigned short &	N
	)

Computes the in-plane delta-v sequence for the given time window that achieves the desired element differences and results in the minimum total delta-v. For circular orbits only.

For circular orbits only.

Parameters:

nOrbMin	Minimum number of orbits the maneuver may last
nOrbMax	Maximum number of orbits the maneuver may last
a	Mean semi-major axis of reference [km]
th0	Latitude of reference at measurement [rad]
th1	Latitude at first burn [rad]
delta_a	Error in semi-major axis difference [km]
delta_th0	Error in latitude difference [rad]
delta_q1	Error in q1 difference
delta_q2	Error in q2 difference
dV1	First delta-v [km/s]. Passed by reference.
dV2	Second delta-v [km/s]. Passed by reference.
dV3	Third delta-v [km/s]. Passed by reference.
M	Number of half-orbits between burn 1 and burn 2. Passed by reference.
N	Number of half-orbits between burn 1 and burn 3. Passed by reference.

Returns:: Bool indicating status

References MU_EARTH, and PI.

burn_t* InPlane	(	alf_orb_data_t	meas_elem,
		alf_orb_data_t	delta_elem,
		double	accNom,
		double	dTMin,
		double	nOrbMin,
		double	nOrbMax,
		double	horizon,
		double &	t0,
		double &	tF,
		unsigned short &	nBurns
	)

Computes the in-plane burn sequence for the given time window that achieves the desired element differences. For circular orbits only.

For circular orbits only.

Parameters:

meas_elem	Reference orbital elements (Alfriend format)
delta_elem	Error in orbital element differences (Alfriend format)
accNom	Nominal acceleration [km/s/s]
dTMin	Minimum achievable burn duration [sec]
nOrbMin	Minimum number of orbits maneuver may last
nOrbMax	Maximum number of orbits maneuver may last
horizon	Minimum amount of time required prior to first burn [sec]
t0	First burn time [sec from meas time]. Passed by reference.
tF	Final burn time [sec from meas time]. Passed by reference.
nBurns	Number of burns required. Passed by reference.

Returns:: burn_t Burn Data structure

References burn_s::dT, burn_s::dV, MU_EARTH, PI, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::sma, burn_s::t, alf_orb_data_s::true_lat, TWO_PI, burn_s::uX, burn_s::uY, and burn_s::uZ.

burn_t OutOfPlane	(	alf_orb_data_t	meas_elem,
		alf_orb_data_t	delta_elem,
		double	accNom,
		double	dTMin,
		unsigned short &	nBurns,
		double &	th1
	)

Compute the out-of-plane burn sequence for the given time window that achieves the desired element differences. For circular orbits only.

For circular orbits only.

Parameters:

meas_elem	Reference orbital elements (Alfriend format)
delta_elem	Error in orbital element differences (Alfriend format)
accNom	Nominal acceleration [km/s/s]
dTMin	Minimum achievable burn duration [sec]
nBurns	Number of burns required. Passed by reference.
th1	Argument of latitude at which burn is applied. Passed by reference.

Returns:: burn_t Burn Data structure

References burn_s::dT, burn_s::dV, alf_orb_data_s::inc, MU_EARTH, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::raan, alf_orb_data_s::sma, burn_s::t, alf_orb_data_s::true_lat, TWO_PI, burn_s::uX, burn_s::uY, and burn_s::uZ.

geom_t AutoFormGeometry	(	state_t	state,
		geom_t	memberGoals[],
		int	num,
		double	minSepDist,
		double	maxSepDist
	)

Parameters:

state	Orbital state data structure
memberGoals	Geometric goals for all other members in the cluster
num	Number of samples to use
minSepDist	Minimum allowable separation distance between satellites
maxSepDist	Maximum allowable separation distance between satellites

Returns:: goals Geometric goals

References geom_s::aE, state_s::dEl, state_s::elA, alf_orb_data_s::sma, and geom_s::y0.

ecc_geom_t AutoFormGeometry	(	state_t	state,
		ecc_geom_t	memberGoals[],
		int	num,
		double	minSepDist,
		double	maxSepDist
	)

Parameters:

state	Orbital state data structure
memberGoals	Geometric goals for all other members in the cluster
num	Number of samples to use
minSepDist	Minimum allowable separation distance between satellites
maxSepDist	Maximum allowable separation distance between satellites

Returns:: goals Geometric goals

References state_s::dEl, orb_data_s::ecc, state_s::el, state_s::elA, orb_data_s::mean_anom, alf_orb_data_s::sma, ecc_geom_s::xMax, and ecc_geom_s::y0.

double NearestOffset	(	double	y0,
		double	width,
		ml_matrix	extrema,
		double	minSepDistance,
		double	maxSepDistance = `1e9`
	)

Parameters:

y0	Original along-track offset (on y-axis)
width	Width of trajectory on y-axis
extrema	Extrema pairs (min, max) on y-axis for N other trajectories
minSepDistance	Minimum separation distance between trajectories
maxSepDistance	Maximum separation distance between trajectories

Returns:: y0 Nearest along-track offset that meets separation objectives

ml_matrix InitializeCostMatrix	(	team_goals_t	teamGoals,
		int	nRelatives
	)

Parameters:

teamGoals	Team goals data structure
nRelatives	Number of relatives in the team

Returns:: f Cost matrix of the appropriate size, filled with zeros

References team_goals_s::constraints, team_goals_s::dPhi, team_goals_s::nU, TWO_PI, and constraints_s::variable.

ml_matrix InitializeCostMatrix	(	ecc_team_goals_t	teamGoals,
		int	nRelatives
	)

Parameters:

teamGoals	Team goals data structure
nRelatives	Number of relatives in the team

Returns:: f Cost matrix of the appropriate size, filled with zeros

References ecc_team_goals_s::constraints, ecc_team_goals_s::dPhi, constraints_s::nDuplicates, ecc_team_goals_s::nU, TWO_PI, and constraints_s::variable.

int PopulateCostMatrix	(	ml_matrix &	f,
		cost_t	costEstimate,
		team_goals_t	teamGoals,
		ml_int_array	relativeIDs
	)

Parameters:

f	Initial cost matrix
costEstimate	Cost estimate data structure supplied from a team member
teamGoals	Team goals data structure used to generate the cost estimates
relativeIDs	Array of member IDs for all relatives in the team

Returns:: f Updated cost matrix; col Index of the cost matrix column that was filled in. Returns -1 if the member ID occurs multiple times in the relativeIDs array. Returns -2 if the target index list has repeated elements. Returns -3 if the size of the cost estimate to be inserted does not match the size of the matrix

References cost_s::cost, cost_s::costLength, team_goals_s::dPhi, cost_s::memID, cost_s::nU, team_goals_s::nU, cost_s::targetIndex, and TWO_PI.

int PopulateCostMatrix	(	ml_matrix &	f,
		cost_t	costEstimate,
		ecc_team_goals_t	teamGoals,
		ml_int_array	relativeIDs
	)

Parameters:

f	Initial cost matrix
costEstimate	Cost estimate data structure supplied from a team member
teamGoals	Team goals data structure used to generate the cost estimates
relativeIDs	Array of member IDs for all relatives in the team

Returns:: f Updated cost matrix; col Index of the cost matrix column that was filled in. Returns -1 if the member ID occurs multiple times in the relativeIDs array. Returns -2 if the target index list has repeated elements. Returns -3 if the size of the cost estimate to be inserted does not match the size of the matrix

References cost_s::cost, cost_s::costLength, ecc_team_goals_s::dPhi, cost_s::memID, cost_s::nU, ecc_team_goals_s::nU, cost_s::targetIndex, and TWO_PI.

void CostMatrixRows	(	team_goals_t	teamGoals,
		int	index,
		int &	a,
		int &	b
	)

Compute the starting and ending rows in the cost matrix that correspond to a give target state index.

Parameters:

teamGoals	Team goals data structure
index	Target state index
a	Starting row. Passed by reference.
b	Ending row. Passed by reference.

References team_goals_s::constraints, team_goals_s::dPhi, team_goals_s::nU, TWO_PI, and constraints_s::variable.

void CostMatrixRows	(	ecc_team_goals_t	teamGoals,
		int	index,
		int &	a,
		int &	b
	)

Compute the starting and ending rows in the cost matrix that correspond to a give target state index.

Parameters:

teamGoals	Team goals data structure
index	Target state index
a	Starting row. Passed by reference.
b	Ending row. Passed by reference.

References ecc_team_goals_s::constraints, ecc_team_goals_s::dPhi, ecc_team_goals_s::nU, TWO_PI, and constraints_s::variable.

cost_s EstimateCost	(	alf_orb_data_t	el0,
		alf_orb_data_t	dEl,
		team_goals_t	teamGoals,
		int	memID,
		window_t	window,
		double	weight
	)

Parameters:

el0	Initial reference orbital elements (Alfriend format) [a,theta,i,q1,q2,W]
dEl	Initial orbital element differences (Alfriend format)
teamGoals	Team goals data structure defining desired relative motion for team
memID	Unique member ID
window	Time window data structure
weight	Scalar weight to be applied to all costs for this spacecraft

Returns:: costEstimate Data structure including weighted cost to achieve all specified unique target states.

References team_goals_s::constraints, cost_s::cost, cost_s::costLength, team_goals_s::dPhi, team_goals_s::geometry, alf_orb_data_s::inc, assign_s::M, cost_s::memID, MU_EARTH, window_s::nOrbMax, window_s::nOrbMin, constraints_s::nRestrict, cost_s::nU, team_goals_s::nU, assign_s::Pu, assign_s::Q, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::raan, constraints_s::restrictID, alf_orb_data_s::sma, cost_s::targetIndex, alf_orb_data_s::true_lat, and constraints_s::variable.

cost_s FFEccEstimateCost	(	orb_data_t	el0,
		const ml_matrix &	xH0,
		ecc_team_goals_t	teamGoals,
		int	memID,
		window_t	window,
		double	weight,
		int	nSPO
	)

Parameters:

el0	Initial reference orbital elements (Alfriend format) [a,theta,i,q1,q2,W]
xH0	Initial relative state, Hills frame
teamGoals	Team goals data structure defining desired relative motion for team
memID	Unique member ID
window	Time window data structure
weight	Scalar weight to be applied to all costs for this spacecraft
nSPO	Number of samples to use per orbit for LP algorithm

Returns:: costEstimate Data structure including weighted cost to achieve all specified unique target states.

References ecc_team_goals_s::constraints, cost_s::cost, cost_s::costLength, orb_data_s::ecc, ecc_team_goals_s::geometry, orb_data_s::mean_anom, cost_s::memID, window_s::nOrbMax, constraints_s::nRestrict, cost_s::nU, ecc_team_goals_s::nU, constraints_s::restrictID, orb_data_s::sma, cost_s::targetIndex, and TWO_PI.

team_goals_s GenerateTeamGoals	(	alf_orb_data_t	el0,
		int	fType,
		double	fSize,
		unsigned short	nRels,
		int	teamID,
		double	angRes
	)

Parameters:

el0	reference orbital elements [a,th,i,q1,q2,W]
fType	formation type
fSize	formation size
nRels	number of relatives in the team
teamID	unique integer team ID
angRes	angular resolution for discretized search with variable states [rad]

Returns:: teamGoals Team Goals data structure, with geometric goals for all unique states, and corresponding constraints

References geom_s::aE, geom_s::beta, team_goals_s::constraints, team_goals_s::dPhi, FF_CIPE_REF_CENTER, FF_CIPE_REF_ON, FF_DUAL_PROJ_CIRC_REF_CENTER, FF_DUAL_PROJ_CIRC_REF_ON, FF_IPLF, FF_NEG_PROJ_CIRC_REF_CENTER, FF_NEG_PROJ_CIRC_REF_ON, FF_OOPLF_RGT, FF_POS_PROJ_CIRC_REF_CENTER, FF_POS_PROJ_CIRC_REF_ON, team_goals_s::geometry, alf_orb_data_s::inc, constraints_s::nDuplicates, constraints_s::nRestrict, team_goals_s::nU, constraints_s::phase, SECS_TO_DAYS, alf_orb_data_s::sma, team_goals_s::teamID, TWO_PI, constraints_s::variable, geom_s::y0, geom_s::zInc, and geom_s::zLan.

ecc_team_goals_s FFEccGenerateTeamGoals	(	orb_data_t	el0,
		int	fType,
		double	fSize,
		unsigned short	nRels,
		int	teamID,
		double	nu,
		const ml_matrix &	eul
	)

Parameters:

el0	Orbital elements
fType	Formation type
fSize	Formation size
nRels	Number of relatives
teamID	Team ID
nu	True anomaly
eul	Euler angles

Returns:: Eccentric team goals

References ecc_team_goals_s::constraints, team_goals_s::constraints, ecc_team_goals_s::dPhi, orb_data_s::ecc, FF_TETRA, ecc_team_goals_s::geometry, team_goals_s::geometry, constraints_s::nDuplicates, constraints_s::nRestrict, team_goals_s::nU, ecc_team_goals_s::nU, ecc_geom_xy_s::nu_xy, ecc_geom_xy_s::nu_zMax, orb_data_s::perigee, constraints_s::phase, alf_orb_data_s::q1, alf_orb_data_s::q2, orb_data_s::sma, ecc_team_goals_s::teamID, constraints_s::variable, ecc_geom_xy_s::x, ecc_geom_xy_s::y, geom_s::y0, ecc_geom_xy_s::y0, and ecc_geom_xy_s::zMax.

ecc_geom_xy_s* FFEccTetrahedronGeometry	(	double	nu,
		double	d,
		const ml_matrix &	eul
	)

Parameters:

nu	True anomaly where tetrahedron occurs
d	Length of each side
eul	Euler angles defining the orientation

Returns:: g Geometric goals data structure

References ecc_geom_xy_s::nu_xy, ecc_geom_xy_s::nu_zMax, ecc_geom_xy_s::x, ecc_geom_xy_s::y, ecc_geom_xy_s::y0, and ecc_geom_xy_s::zMax.

geom_s PCGoals	(	double	R,
		double	alpha0,
		double	sgn,
		double	y0
	)

Parameters:

R	radius of the projected circle [km]
alpha0	angular offset around circle [rad]
sgn	orientation of plane
y0	along-track offset [km]

Returns:: g geomtric goals data structures

References geom_s::aE, geom_s::beta, geom_s::y0, geom_s::zInc, and geom_s::zLan.

void SortTeamGoals ( team_goals_t & teamGoals )

Parameters:

teamGoals Team goals data structure, supplied from ground. Passed by reference.

References team_goals_s::constraints, team_goals_s::geometry, team_goals_s::nU, and constraints_s::variable.

void SortTeamGoals ( ecc_team_goals_t & teamGoals )

Parameters:

teamGoals Team goals data structure, supplied from ground. Passed by reference.

References ecc_team_goals_s::constraints, ecc_team_goals_s::geometry, ecc_team_goals_s::nU, and constraints_s::variable.

assign_s SetupAssignmentProblem	(	team_goals_t	teamGoals,
		double	orbFrac
	)

Parameters:

teamGoals	Team goals data structure
orbFrac	fraction of orbit

Returns:: assign assignment parameters data structure

References geom_s::beta, team_goals_s::constraints, team_goals_s::dPhi, team_goals_s::geometry, assign_s::M, assign_s::N, constraints_s::nDuplicates, team_goals_s::nU, assign_s::P, constraints_s::phase, assign_s::phi, assign_s::Pu, assign_s::Q, TWO_PI, assign_s::u, and constraints_s::variable.

assign_s SetupAssignmentProblem	(	ecc_team_goals_t	teamGoals,
		double	orbFrac
	)

Parameters:

teamGoals	Team goals data structure
orbFrac	fraction of orbit

Returns:: assign assignment parameters data structure

References assign_s::M, assign_s::N, ecc_team_goals_s::nU, assign_s::P, assign_s::Pu, and assign_s::Q.

int RestrictIDSet	(	ml_int_array &	relIDs,
		constraints_t	constraints[],
		int	numC
	)

Parameters:

relIDs	Unique set of relative IDs. There must be no repeated IDs in this list.
constraints	Array of constraint data structures. Each one contains a list of IDs
numC	Number of constraint data structures.

Returns:: relIDs Updated set of relative IDs.; status If relIDs is not unique, the function immediately returns 0. Otherwise, it returns 1.

References constraints_s::nRestrict.

int VerifyAssignmentParams	(	assign_t	a,
		const ml_matrix &	f
	)

Parameters:

a	Assignment parameters structure
f	Cost matrix, with N columns for N satellites

Returns:: status 0 if all parameters consistent, negative integer for error -1 Cost matrix does not have N columns -2 P is greater than N -3 Pu is greater than P -4 Q is not positive -5 Phase vector "phi" is not the right length -6 Index vector "u" is not the right length -7 One or more elements of "u" is greater than P -8 One or more elements of "u" is not positive

References assign_s::N, assign_s::P, assign_s::phi, assign_s::Pu, assign_s::Q, and assign_s::u.

int PrivilegedAssignment	(	assign_t	assign,
		const ml_matrix &	f,
		int	method,
		ml_int_array &	optOrder,
		ml_matrix &	optPhi,
		double &	optCost
	)

Parameters:

assign	Assignment parameters, dictated by the team goals.
f	Cost matrix, with N columns for N satellites
method	Indicates whether to use the minimum cost (1) or the average cost (not 1) as the cost metric.
optOrder	The order in which the target states should be assigned to each satellite. Passed by reference.
optPhi	The corresponding phase angles associated with each target. Passed by reference.
optCost	The total cost to achieve all target states. Passed by reference.

Returns:: errorFlag Returns 0 if algorithm runs nominally. Returns a negative integer if an error is found with the supplied assignment structure.

References assign_s::N, assign_s::P, assign_s::phi, assign_s::Q, TWO_PI, and assign_s::u.

int OptimalAssignment	(	assign_t	assign,
		ml_matrix	f,
		ml_int_array &	optOrder,
		ml_matrix &	optPhi,
		double &	optCost
	)

Parameters:

assign	Assignment parameters data structure
f	Set of weighted cost vectors
optOrder	Optimal order of the target states. Passed by reference.
optPhi	Optimal phases for variable states. Passed by reference.
optCost	Total cost to achieve the optimal configuration. Passed by reference.

Returns:: status Indicates status of assignment parameters, <0 if poorly defined, 0 if okay.

References assign_s::N, assign_s::P, assign_s::phi, assign_s::Pu, assign_s::Q, TWO_PI, and assign_s::u.

bool EquallyPhased	(	const ml_matrix &	phi,
		ml_int_array	u,
		int	Pu
	)

Determine if the phase angles are equally phased.

Parameters:

phi	Phase angle array
u	Unique variable indices
Pu	Number of unique variable states

Returns:: Whether the variable states are equally phased

References PI, and TWO_PI.

ml_int_array FindMinSet	(	ml_matrix &	mat,
		double &	minSum
	)

Parameters:

mat	Matrix of costs. Passed by reference.
minSum	Minimum sum solution. Passed by reference.

Returns:: Array of matrix columns for optimal assignment.

void permute	(	ml_int_array	arr,
		int	num,
		int	start,
		const ml_matrix &	mat,
		double &	cost,
		ml_int_array &	best
	)

Parameters:

arr	Array to be permuted
num	Number of remaining rows to permute.
start	Starting row for current permutation.
mat	Matrix of costs. Passed by reference.
cost	Current cost.
best	Best cost thus far. Passed by reference.

void LPCircular	(	const ml_matrix &	x0,
		const ml_matrix &	xF,
		double	n,
		double	duration,
		double	dT,
		unsigned short	constraintType,
		double	maxConstraint,
		ml_matrix &	aC,
		ml_matrix &	t,
		bool &	exitFlag
	)

Computes the thrust trajectory to go from an initial state to a final state in Hills frame. For circular orbits.

For circular orbits.

Parameters:

x0	Initial state in Hill's frame
xF	Final state in Hill's frame
n	Reference orbit rate (rad/sec)
duration	Maneuver duration (secs)
dT	Thruster time step
constraintType	Flag [0: Equality; 1: Inequality constraint]
maxConstraint	Maximum constraint on u
aC	Commanded acceleration in Hill's frame
t	Time vector (secs)
exitFlag	Flag [0: No feasible solution; 1: Feasible solution]

void LPEccentric	(	double	e,
		double	n,
		const ml_matrix &	x0,
		const ml_matrix &	xF,
		double	nu0,
		double	nuF,
		int	nS,
		ml_matrix	cW,
		unsigned short	constraintType,
		double	maxConstraint,
		ml_matrix &	aC,
		ml_matrix &	t,
		bool &	exitFlag
	)

Computes the thrust trajectory to go from an initial state to a final state in Hills frame. For eccentric orbits.

For eccentric orbits.

Parameters:

e	Orbit eccentricity
n	Mean orbit rate (rad/sec)
x0	Initial state in Hill's frame
xF	Final state in Hill's frame
nu0	Initial true anomaly (rad)
nuF	Final true anomaly (rad)
nS	Number of samples to use for control vector
cW	Cost weighting vector
constraintType	Flag [0: Equality; 1: Inequality constraint]
maxConstraint	Maximum constraint on u
aC	Commanded acceleration in Hill's frame. Passed by reference.
t	Time vector (secs). Passed by reference.
exitFlag	Flag [0: No feasible solution; 1: Feasible solution]. Passed by reference.

void LPCircularTimeWeight	(	orb_data_t	el0,
		const ml_matrix &	xH0,
		geom_t	goals,
		window_t	window,
		int	nSPO,
		ml_matrix &	xHF,
		double &	nOrbMvr
	)

Determine the target state on the desired trajectory that gives the minimum time-weighted cost. For circular orbits.

For circular orbits.

Parameters:

el0	Initial orbital element set [a,i,W,w,e,M]
xH0	Initial state in Hill's frame
goals	Geometric goals data structure
window	Maneuver time window data structure, containing: nOrbMin Minimum number of orbits nOrbMax Maximum number of orbits nManeuvers Number of maneuvers to search over timeWeightExp Time-weighting exponent
nSPO	Number of samples to use for control vector (per orbit of maneuver duration)
xHF	Target Hills-frame state (at maneuver completion). Passed by reference.
nOrbMvr	Chosen maneuver duration (in orbits). Passed by reference.

References orb_data_s::ecc, orb_data_s::mean_anom, orb_data_s::perigee, PI, orb_data_s::sma, window_s::timeWeightExp, alf_orb_data_s::true_lat, and TWO_PI.

void LPEccentricTimeWeight	(	orb_data_t	el0,
		const ml_matrix &	xH0,
		ecc_geom_t	goals,
		window_t	window,
		int	nSPO,
		ml_matrix &	xHF,
		double &	nOrbMvr
	)

Determine the target state on the desired trajectory that gives the minimum time-weighted cost. For eccentric orbits.

For eccentric orbits.

Parameters:

el0	Initial orbital element set [a,i,W,w,e,M]
xH0	Initial state in Hill's frame
goals	Geometric goals data structure
window	Maneuver time window data structure, containing:
nSPO	Number of samples to use for control vector (per orbit of maneuver duration)
xHF	Target Hills-frame state (at maneuver completion). Passed by reference.
nOrbMvr	Chosen maneuver duration (in orbits). Passed by reference.

References orb_data_s::ecc, orb_data_s::mean_anom, orb_data_s::sma, and window_s::timeWeightExp.

void GVEErrorDynamics	(	orb_data_t	el0,
		ml_matrix &	A,
		ml_matrix &	B
	)

Parameters:

el0	Standard orbital elements
A	State dynamics. Passed by reference.
B	Input effect matrix. Passed by reference.

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

void LPEccentricGVE	(	orb_data_t	el0,
		const ml_matrix &	x0,
		const ml_matrix &	xF,
		double	MF,
		int	nS,
		ml_matrix	cW,
		unsigned short	constraintType,
		double	maxConstraint,
		ml_matrix &	aC,
		ml_matrix &	t,
		bool &	exitFlag
	)

Computes the thrust trajectory to go from an initial state to a final state in Hills frame. For eccentric orbits.

For eccentric orbits.

Parameters:

el0	Initial orbital elements
x0	Initial state in Hill's frame
xF	Final state in Hill's frame
MF	Final mean anomaly (rad)
nS	Number of samples to use for control vector
cW	Cost weighting vector
constraintType	Flag [0: Equality; 1: Inequality constraint]
maxConstraint	Maximum constraint on u
aC	Commanded acceleration in Hill's frame. Passed by reference.
t	Time vector (secs). Passed by reference.
exitFlag	Flag [0: No feasible solution; 1: Feasible solution]. Passed by reference.

References orb_data_s::ecc, orb_data_s::mean_anom, PI, and orb_data_s::sma.

void FFEccLinOrb	(	double	n,
		double	nu,
		double	e,
		ml_matrix &	a,
		ml_matrix &	b,
		double	dT
	)

Compute the continous A,B matrices for linearized relative motion in an eccentric reference orbit, discretized with a zero-order hold with timestep dT. *sctlib (overload LinOrb)

*sctlib (overload LinOrb)

Parameters:

n	Mean orbit rate [rad/s]
nu	True anomaly [rad]
e	Eccentricity
a	Plant matrix. Passed by reference.
b	Input matrix. Passed by reference.
dT	Time-step for discretization

ml_matrix FFEccLinOrb	(	const ml_matrix &	x,
		const ml_matrix &	acc,
		double	n,
		double	nu,
		double	e
	)

Compute the right-hand-side for linearized relative motion in an eccentric reference orbit.

Parameters:

x	State vector
acc	Acceleration vector
n	Mean orbit rate [rad/s]
nu	True anomaly [rad]
e	Eccentricity

Returns:: xDot

ml_matrix FFEccProp	(	const ml_matrix &	D,
		const ml_matrix &	nu,
		double	e,
		double	dH
	)

Parameters:

D	Integration constants computed from i.c.'s
nu	True anomaly [rad]
e	Eccentricity
dH	Integration constant found by setting H = 0 at nu0

Returns:: xH Hills frame state computed at nu

ml_matrix FFEccProp	(	const ml_matrix &	D,
		double	nu,
		double	e,
		double	dH
	)

Parameters:

D	Integration constants computed from i.c.'s
nu	True anomaly [rad]
e	Eccentricity
dH	Integration constant found by setting H = 0 at nu0

Returns:: xH Hills frame state computed at nu

double FFEccDH	(	double	nu0,
		double	e
	)

Compute integration constant dH for homogeneous solution to LTV differential equations of relative orbit motion. Found by setting H=0 at initial true anomaly.

Found by setting H=0 at initial true anomaly.

Parameters:

nu0	True Anomaly (at initial state) [rad]
e	Eccentricity

Returns:: dH Integration constant found by setting H = 0 at nu0

References PI.

void FFEccGoals	(	double	e,
		ecc_geom_t	goals,
		ml_matrix &	D,
		ml_matrix &	xH
	)

Parameters:

e	Eccentricity
goals	Eccentric geometric goals
D	Integration constants computed from i.c.'s. Passed by reference.
xH	Hills frame state at nu = 0. Passed by reference.

References ecc_geom_s::nu_xMax, ecc_geom_s::nu_zMax, PI, ecc_geom_s::xMax, ecc_geom_s::y0, and ecc_geom_s::zMax.

void FFEccGoals	(	double	e,
		ecc_geom_xy_t	goals,
		ml_matrix &	D,
		ml_matrix &	xH
	)

Parameters:

e	Eccentricity
goals	Eccentric geometric goals (xy)
D	Integration constants computed from i.c.'s. Passed by reference.
xH	Hills frame state at nu = 0. Passed by reference.

References ecc_geom_xy_s::nu_xy, ecc_geom_xy_s::nu_zMax, PI, ecc_geom_xy_s::x, ecc_geom_xy_s::y, ecc_geom_xy_s::y0, and ecc_geom_xy_s::zMax.

void FFEccIntConst	(	const ml_matrix &	xH0,
		double	nu0,
		double	e,
		ml_matrix &	D,
		double &	dH,
		ml_matrix &	R
	)

Parameters:

xH0	Initial state in Hills frame
nu0	True anomaly (at initial state) [rad]
e	Eccentricity
D	Vector of integration constants. Passed by reference.
dH	Integration constant found by setting H = 0 at nu0. Passed by reference.
R	State transition matrix. Passed by reference.

ml_matrix FFEccRMat	(	double	nu,
		double	e,
		double	dH
	)

Parameters:

nu	True Anomaly [rad]
e	Eccentricity
dH	Integration constant found by setting H = 0 at nu0

Returns:: matrix Transformation matrix for equation xH = R*D

References PI.

ml_matrix FFEccRMat	(	double	nu,
		double	e
	)

Compute the state-transition matrix, R, given the eccentricity and true anomaly so that xH = R*D, where D is the vector of integration constants found from initial conditions. Here, the integration constant "dH" is computed using the first element of the "nu" matrix.

Here, the integration constant "dH" is computed using the first element of the "nu" matrix.

Parameters:

nu	True Anomaly [rad]
e	Eccentricity

Returns:: matrix Transformation matrix for equation xH = R*D

References PI.

void FFEccXExt	(	double	e,
		const ml_matrix &	D,
		double	dH,
		double	epsilon,
		int	nMax,
		ml_matrix &	x,
		ml_matrix &	nu
	)

Parameters:

e	Eccentricity
D	Integration constants computed from i.c.'s
dH	Integration constant found by setting H = 0 at nu0
epsilon	Angular tolerance [rad]
nMax	Maximum number of iterations
x	Extreme values of radial oscillations [km]. Passed by reference.
nu	True anomaly where extreme values occur [rad]. Passed by reference.

References PI.

void FFEccYExt	(	double	e,
		const ml_matrix &	D,
		double	dH,
		double	epsilon,
		int	nMax,
		ml_matrix &	y,
		ml_matrix &	nu
	)

Parameters:

e	Eccentricity
D	Integration constants computed from i.c.'s
dH	Integration constant found by setting H = 0 at nu0
epsilon	Angular tolerance [rad]
nMax	Maximum number of iterations
y	Extreme values of along-track offsets [km]. Passed by reference.
nu	True anomaly where extreme along-track offsets occur [rad]. Passed by reference.

References PI.

void FFEccZExt	(	double	e,
		const ml_matrix &	D,
		double	dH,
		double	epsilon,
		int	nMax,
		ml_matrix &	z,
		ml_matrix &	nu
	)

Parameters:

e	Eccentricity
D	Integration constants computed from i.c.'s
dH	Integration constant found by setting H = 0 at nu0
epsilon	Angular tolerance [rad]
nMax	Maximum number of iterations
z	Extreme values of cross track amplitude [km]. Passed by reference.
nu	True anomaly where extreme amplitudes occur [rad]. Passed by reference.

References PI.

void NuDot	(	double	n,
		double	e,
		double	nu,
		double &	nuDot,
		double &	nuDotDot
	)

Compute the time-derivative of the true anomaly. *sctlib.

*sctlib

Parameters:

n	Mean orbit rate [rad/s]
e	Eccentricity
nu	True Anomaly [rad]
nuDot	Time derivative of true anomaly [rad/s]. Passed by reference.
nuDotDot	Second time derivative of true anomaly [rad/s]. Passed by reference.

double FFEccDX	(	double	nu,
		double	e,
		const ml_matrix &	D,
		double	dH
	)

Parameters:

nu	True anomaly [rad]
e	Eccentricity
D	Integration constants computed from i.c.'s
dH	Integration constant computed from H(nu0)=0

Returns:: dx First derivative of x with respect to true anomaly

double FFEccDY	(	double	nu,
		double	e,
		const ml_matrix &	D,
		double	dH
	)

Parameters:

nu	True anomaly [rad]
e	Eccentricity
D	Integration constants computed from i.c.'s
dH	Integration constant computed from H(nu0)=0

Returns:: dy First derivative of y with respect to true anomaly

double FFEccDZ	(	double	nu,
		double	e,
		const ml_matrix &	D,
		double	dH
	)

Parameters:

nu	True anomaly [rad]
e	Eccentricity
D	Integration constants computed from i.c.'s
dH	Integration constant computed from H(nu0)=0

Returns:: dz First derivative of x with respect to true anomaly

double FFEccDDX	(	double	nu,
		double	e,
		const ml_matrix &	D,
		double	dH
	)

Parameters:

nu	True anomaly [rad]
e	Eccentricity
D	Integration constants computed from i.c.'s
dH	Integration constant computed from H(nu0)=0

Returns:: ddx Second derivative of x with respect to true anomaly

double FFEccDDY	(	double	nu,
		double	e,
		const ml_matrix &	D,
		double	dH
	)

Parameters:

nu	True anomaly [rad]
e	Eccentricity
D	Integration constants computed from i.c.'s
dH	Integration constant computed from H(nu0)=0

Returns:: ddy Second derivative of y with respect to true anomaly

double FFEccDDZ	(	double	nu,
		double	e,
		const ml_matrix &	D,
		double	dH
	)

Parameters:

nu	True anomaly [rad]
e	Eccentricity
D	Integration constants computed from i.c.'s
dH	Integration constant computed from H(nu0)=0

Returns:: ddz Second derivative of z with respect to true anomaly

orb_data_t Alfriend2El ( alf_orb_data_t elA )

Parameters:

elA	Alfriend orbital elements [a,theta,i,q1,q2,W]

Returns:: el Standard orbital elements [a,i,W,w,e,M]

References orb_data_s::ecc, alf_orb_data_s::inc, orb_data_s::inc, orb_data_s::mean_anom, orb_data_s::perigee, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::raan, orb_data_s::raan, alf_orb_data_s::sma, orb_data_s::sma, orb_data_s::true_anom, and alf_orb_data_s::true_lat.

alf_orb_data_t El2Alfriend ( orb_data_t el )

Convert a standard orbital element set into the Alfriend orbital element set *sctlib.

Parameters:

el	Standard orbital elements [a,i,W,w,e,M]

Returns:: elA Alfriend orbital elements [a,theta,i,q1,q2,W]

References orb_data_s::ecc, orb_data_s::inc, alf_orb_data_s::inc, orb_data_s::mean_anom, orb_data_s::perigee, alf_orb_data_s::q1, alf_orb_data_s::q2, orb_data_s::raan, alf_orb_data_s::raan, orb_data_s::sma, alf_orb_data_s::sma, alf_orb_data_s::true_lat, and TWO_PI.

alf_orb_data_t El2Alfriend	(	orb_data_t	el,
		double	true_anom
	)

Convert a standard orbital element set into the Alfriend orbital element set *sctlib.

Parameters:

el	Standard orbital elements [a,i,W,w,e,M]
true_anom	True anomaly

Returns:: elA Alfriend orbital elements [a,theta,i,q1,q2,W]

References orb_data_s::ecc, orb_data_s::inc, alf_orb_data_s::inc, orb_data_s::perigee, alf_orb_data_s::q1, alf_orb_data_s::q2, orb_data_s::raan, alf_orb_data_s::raan, orb_data_s::sma, alf_orb_data_s::sma, alf_orb_data_s::true_lat, and TWO_PI.

alf_orb_data_s add_elements	(	alf_orb_data_t	el1,
		alf_orb_data_t	el2
	)

Add two sets of orbital elements *sctlib.

Parameters:

el1	First element set
el2	Second element set

Returns:: el Sum of two element sets (all angles are wrapped between -PI and +PI)

References alf_orb_data_s::inc, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::raan, alf_orb_data_s::sma, and alf_orb_data_s::true_lat.

orb_data_s add_elements	(	orb_data_t	el1,
		orb_data_t	el2
	)

Add two sets of orbital elements *sctlib.

epoch and orb_rate are not set.

Parameters:

el1	First element set
el2	Second element set

Returns:: el Sum of two element sets (all angles are wrapped between -PI and +PI)

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

alf_orb_data_s sub_elements	(	alf_orb_data_t	el1,
		alf_orb_data_t	el2
	)

Parameters:

el1	First element set
el2	Second element set, subtracted from first

Returns:: el Difference of two element sets (all angles are wrapped between -PI and +PI)

References alf_orb_data_s::inc, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::raan, alf_orb_data_s::sma, and alf_orb_data_s::true_lat.

orb_data_s sub_elements	(	orb_data_t	el1,
		orb_data_t	el2
	)

epoch and orb_rate are not set.

Parameters:

el1	First element set
el2	Second element set, subtracted from first

Returns:: el Difference of two element sets (all angles are wrapped between -PI and +PI)

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

double CirclePhase ( double beta )

Compute the desired phase on a circle from the desired phase on the ellipse. The circle is superscribed about the ellipse.

The circle is superscribed about the ellipse.

Parameters:

beta	Phase angle measured on ellipse [rad]

Returns:: alpha Phase angle measured on superscribed circle [rad]

References PI.

double EllipsePhase ( double alpha )

Compute the desired phase on an ellipse from the desired phase on the circle. The circle is superscribed about the ellipse.

The circle is superscribed about the ellipse.

Parameters:

alpha Phase angle measured on superscribed circle [rad]

Returns:: beta Phase angle measured on ellipse

References PI.

alf_orb_data_t OrbElemDiff	(	alf_orb_data_t	el0,
		alf_orb_data_t	el
	)

Parameters:

el0	Reference orbital elements (Alfriend format)
el	Secondary orbital elements (Alfriend format)

Returns:: dEl Orbital element difference

References alf_orb_data_s::inc, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::raan, alf_orb_data_s::sma, and alf_orb_data_s::true_lat.

orb_data_t OrbElemDiff	(	orb_data_t	el0,
		orb_data_t	el
	)

epoch and orb_rate are not set.

Parameters:

el0	Reference orbital elements (standard format)
el	Secondary orbital elements (standard format)

Returns:: dEl Orbital element difference

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

alf_orb_data_t Goals2DeltaElem	(	alf_orb_data_t	el0,
		geom_t	goals
	)

Parameters:

el0	Measured orbital elements (Alfriend format)
goals	Geometric goals data structure

Returns:: alf_orb_data_t Desired orbital element differences

geom_t DeltaElem2Goals	(	alf_orb_data_t	el0,
		alf_orb_data_t	dEl
	)

Parameters:

el0	Measured orbital elements (Alfriend format) [a,theta,i,q1,q2,W]
dEl	Desired orbital element differences

Returns:: goals Geometric goals

ml_matrix DeltaElem2Hills	(	alf_orb_data_t	elA,
		alf_orb_data_t	dEl
	)

Parameters:

elA	Reference orbital elements [Alfriend format]
dEl	Orbital element difference

Returns:: xH Hills frame position and velocity

References alf_orb_data_s::inc, MU_EARTH, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::raan, alf_orb_data_s::sma, and alf_orb_data_s::true_lat.

alf_orb_data_s Hills2DeltaElem	(	alf_orb_data_t	el0,
		const ml_matrix &	xH
	)

Parameters:

el0	Chief orbital elements in alfriend format
xH	Relative position and velocity in Hills frame

Returns:: alf_orb_data Orbital element difference in alfriend format

References alf_orb_data_s::inc, MU_EARTH, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::raan, RADIUS_EARTH, alf_orb_data_s::sma, and alf_orb_data_s::true_lat.

geom_s Hills2Goals	(	alf_orb_data_t	el0,
		const ml_matrix &	xH
	)

Parameters:

el0	Reference orbital elements
xH	Relative state in Hills frame

Returns:: goals Geometric goals

References geom_s::aE, geom_s::beta, MU_EARTH, alf_orb_data_s::sma, alf_orb_data_s::true_lat, geom_s::y0, geom_s::zInc, and geom_s::zLan.

ml_matrix Goals2Hills	(	alf_orb_data_t	el0,
		geom_t	goals
	)

Parameters:

el0	Reference orbital elements
goals	Geometric goals

Returns:: xH Relative state in Hills frame

References geom_s::aE, geom_s::beta, alf_orb_data_s::sma, alf_orb_data_s::true_lat, geom_s::y0, geom_s::zInc, and geom_s::zLan.

orb_data_s FFEccHills2DeltaElem	(	orb_data_t	el0,
		const ml_matrix &	xH
	)

[standard format]

Parameters:

el0	Reference orbital elements
xH	Relative position and velocity in Hills frame [km, km/s]

Returns:: dEl Orbital element differences

alf_orb_data_s FFEccHills2DeltaElem	(	alf_orb_data_t	el0,
		const ml_matrix &	xH
	)

[alfriend format]

Parameters:

el0	Reference orbital elements
xH	Relative position and velocity in Hills frame [km, km/s]

Returns:: dEl Orbital element differences

References orb_data_s::true_anom.

ml_matrix FFEccDeltaElem2Hills	(	alf_orb_data_t	el0,
		alf_orb_data_t	dEl
	)

Parameters:

el0	Reference orbital elements [Alfriend format]
dEl	Orbit element differences

Returns:: xH Relative state in Hills frame

ecc_geom_t FFEccDeltaElem2Goals	(	alf_orb_data_t	el0,
		alf_orb_data_t	dEl
	)

Parameters:

el0	Orbital elements [Alfriend format]
dEl	Orbital element differences

Returns:: goals Eccentric geometric data structure

References alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::sma, and alf_orb_data_s::true_lat.

ml_matrix FFEccGoals2Hills	(	double	e,
		double	nu,
		ecc_geom_t	g,
		double	n
	)

Parameters:

e	Eccentricity
nu	True anomaly [rad]
g	Data structure of geometric goals
n	Mean orbit rate [rad/s]

Returns:: xH Hills frame state

ml_matrix FFEccGoals2Hills	(	double	e,
		double	nu,
		ecc_geom_xy_t	g,
		double	n
	)

Parameters:

e	Eccentricity
nu	True anomaly [rad]
g	Data structure of geometric goals
n	Mean orbit rate [rad/s]

Returns:: xH Hills frame state

ml_matrix FFEccGoals2Hills	(	double	e,
		double	nu,
		ecc_geom_t	g
	)

Parameters:

e	Eccentricity
nu	True anomaly [rad]
g	Data structure of geometric goals

Returns:: xH Hills frame state

ecc_geom_t FFEccHills2Goals	(	double	e,
		double	nu,
		ml_matrix	xH,
		double	n
	)

Parameters:

e	Eccentricity
nu	True anomaly [rad]
xH	Hills frame state
n	Mean orbit rate [rad/s]

Returns:: g Data structure of geometric goals

References ecc_geom_s::nu_xMax, ecc_geom_s::nu_zMax, PI, ecc_geom_s::xMax, ecc_geom_s::y0, and ecc_geom_s::zMax.

ecc_geom_t FFEccHills2Goals	(	double	e,
		double	nu,
		const ml_matrix &	xH
	)

Parameters:

e	Eccentricity
nu	True anomaly [rad]
xH	Hills frame state

Returns:: g Data structure of geometric goals

References ecc_geom_s::nu_xMax, ecc_geom_s::nu_zMax, PI, ecc_geom_s::xMax, ecc_geom_s::y0, and ecc_geom_s::zMax.

void Nu2TimeDomain	(	ml_matrix &	x,
		double	n,
		double	e,
		double	nu
	)

Parameters:

x	Relative State in nu-domain. Passed by reference.
n	Mean orbit rate [rad/s]
e	Eccentricity
nu	True anomaly [rad]

void Time2NuDomain	(	ml_matrix &	x,
		double	n,
		double	e,
		double	nu
	)

Parameters:

x	Relative State in time-domain
n	Mean orbit rate [rad/s]
e	Eccentricity
nu	True anomaly [rad]
x	Relative State in nu-domain. Passed by reference.

ecc_geom_t GeometryCirc2Ecc	(	double	w,
		geom_t	gCirc
	)

Parameters:

w	Argument of perigee [rad]
gCirc	Geometry goals structure for circular orbits

Returns:: gEcc Geometry goals structure for Eccentric orbits

References geom_s::aE, geom_s::beta, ecc_geom_s::nu_xMax, ecc_geom_s::nu_zMax, PI, ecc_geom_s::xMax, geom_s::y0, ecc_geom_s::y0, geom_s::zInc, geom_s::zLan, and ecc_geom_s::zMax.

geom_t GeometryEcc2Circ	(	double	w,
		ecc_geom_t	gEcc
	)

Parameters:

w	Argument of perigee [rad]
gEcc	Geometry goals structure for Eccentric orbits

Returns:: gCirc Geometry goals structure for Circular orbits

References geom_s::aE, geom_s::beta, ecc_geom_s::nu_xMax, ecc_geom_s::nu_zMax, PI, ecc_geom_s::xMax, ecc_geom_s::y0, geom_s::y0, geom_s::zInc, geom_s::zLan, and ecc_geom_s::zMax.

geom_t RotateState	(	geom_t	goals,
		double	phi
	)

Parameters:

goals	Geometric goals data structure
phi	Circular phase angle

Returns:: goals New geometric data structure rotated to phi

References geom_s::beta, geom_s::zInc, and geom_s::zLan.

double MeanAnom2TrueLat	(	double	e,
		double	w,
		double	M
	)

Convert mean anomlay to true latitude.

Parameters:

e	Eccentricity
w	Argument of Perigee [rad]
M	Mean Anomaly [rad]

Returns:: theta True Latitude [rad]

References TWO_PI.

void GetHillsMats	(	const ml_matrix &	r0,
		const ml_matrix &	v0,
		ml_matrix &	A,
		ml_matrix &	Adot
	)

Parameters:

r0	Position, ECI frame
v0	Velocity, ECI frame
A	Rotation Matrix (position). Passed by reference.
Adot	Rotation Matrix (velocity). Passed by reference.

References orb_data_s::ecc, MU_EARTH, orb_data_s::sma, and orb_data_s::true_anom.

void AbsRelECI2Hills	(	ml_matrix	r0,
		ml_matrix	v0,
		ml_matrix	dr,
		ml_matrix	dv,
		ml_matrix &	rH,
		ml_matrix &	vH
	)

Parameters:

r0	Reference position in ECI frame
v0	Reference velocity in ECI frame
dr	Relative position in ECI frame
dv	Relative velocity in ECI frame
rH	Curvilinear Hills frame position [dR; r1*dTheta; dZ ]. Passed by reference.
vH	Curvilinear Hills frame velocity [dRDot; r1dThetaDot + r1DotdTheta; dZDot]. Passed by reference.

alf_orb_data_t Osc2Mean	(	alf_orb_data_t	el,
		double	J2
	)

Parameters:

el	Osculating orbital elements
J2	J2 perturbation

Returns:: el Mean orbital elements

References alf_orb_data_s::inc, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::raan, RADIUS_EARTH, alf_orb_data_s::sma, and alf_orb_data_s::true_lat.

alf_orb_data_t* ECI2MeanElements	(	const ml_matrix &	xRefECI,
		const ml_matrix &	xRelECI,
		double	J2,
		alf_orb_data_t &	elRefMean
	)

Parameters:

xRefECI	Reference position & velocity in ECI frame
xRelECI	Relative positions & velocities in ECI frame
J2	Size of J2 perturbation
elRefMean	Mean orbital elements of the reference orbit. Passed by reference.

Returns:: dElMean Mean orbital element differences

References orb_data_s::true_anom.

bool AlignThruster	(	const ml_matrix &	aH,
		const ml_matrix &	bTh,
		ml_matrix &	qHB
	)

Computes desired Hills-to-body quaternion for a thruster firing. Rotation about thruster-axis is ignored.

Rotation about thruster-axis is ignored.

Parameters:

aH	Unit Hills frame vector of applied acceleration
bTh	Unit body vector of Hall Effect Thruster nozzle
qHB	Desired ECI-to-body quaternion. Passed by reference.

Returns:: Always returns true. Output provided for compatibility with other AlignThruster function.

bool AlignThruster	(	const ml_matrix &	aH,
		const ml_matrix &	bTh,
		const ml_matrix &	bST,
		const ml_matrix &	r,
		const ml_matrix &	v,
		double	jD,
		double	sep,
		ml_matrix &	qHB
	)

Parameters:

aH	Unit Hills frame vector of applied acceleration
bTh	Unit body vector of Hall Effect Thruster nozzle
bST	Unit body vector of star tracker bore-sight
r	Position in ECI at burn time [km]
v	Velocity in ECI at burn time [km/s]
jD	Julian Date of burn time [JD]
sep	Required angular separation between bore-sight and bright body horizon [rad]
qHB	Desired ECI-to-body quaternion. Passed by reference.

Returns:: Flag indicating whether angular separation constraint is satisfied for all: sun, Earth, and moon

References PI.

ml_matrix Hills2Frenet	(	const ml_matrix &	xH,
		const double &	e,
		const double &	nu,
		const double &	n
	)

Transforms from the Hills frame to the Frenet frame.

Parameters:

xH	(6,1) Relative position and velocity in Hills-frame
e	(1,1) Orbit eccentricity
nu	(1,1) True anomaly (rad)
n	(1,1) Mean orbit rate (rad/s)

Returns:: xF (6,1) Relative position and velocity in Frenet-frame

ml_matrix HillsEqns	(	const ml_matrix &	xH0,
		double	n,
		double	t
	)

Closed form solution of relative orbital motion using Hills equations. For circular orbits only.

For circular orbits only.

Parameters:

xH0	Initial state in Hills frame
n	Orbital Rate (rad/s)
t	Time (sec)

Returns:: X State

ml_matrix FFEccHillsEqns	(	ml_matrix	xH0,
		double	nu0,
		const ml_matrix &	nu,
		double	e,
		double	n
	)

Compute Hills frame state (in time-domain) at future true anomaly(s). For eccentric or circular orbits.

For eccentric or circular orbits

Parameters:

xH0	Initial Hills frame state
nu0	True anomaly (at initial state) [rad]
nu	True anomaly (at new state) [rad]
e	Eccentricity
n	Mean orbit rate [rad/s]

Returns:: xH New Hills frame state at nu (with nu-derivatives)

ml_matrix FFEccHillsEqns	(	const ml_matrix &	xH0,
		double	nu0,
		const ml_matrix &	nu,
		double	e
	)

Compute Hills frame state (in nu-domain) at future true anomaly(s). For eccentric or circular orbits.

For eccentric or circular orbits

Parameters:

xH0	Initial Hills frame state
nu0	True anomaly (at initial state) [rad]
nu	True anomaly (at new state) [rad]
e	Eccentricity

Returns:: xH New Hills frame state at nu (with nu-derivatives)

ml_matrix DiscreteHills	(	const ml_matrix &	x0,
		double	n,
		const ml_matrix &	aC,
		double	dT
	)

Compute the force relative trajectory from the initial state and time-history of applied accelerations. For circular orbits only.

For circular orbits only.

Parameters:

x0	Initial state
n	Reference orbit rate (rad/sec)
aC	Commanded accelerations
dT	Thruster sampling time

Returns:: xS State trajectory

ml_matrix FFEccDiscreteHills	(	double	e,
		double	n,
		const ml_matrix &	x0,
		double	nu0,
		const ml_matrix &	aC,
		const ml_matrix &	t
	)

Compute the force relative trajectory from the initial state and time-history of applied accelerations. For circular orbits only.

For circular orbits only.

Parameters:

e	Eccentricity
n	Mean orbit rate (rad/sec)
x0	Initial relative state
nu0	Initial true anomaly
aC	Commanded accelerations
t	Time vector (final time corresponds to final state)

Returns:: xS Discrete Hills state

double CollProbSet	(	double	sigma,
		const ml_matrix &	S,
		const ml_matrix &	xc,
		const ml_matrix &	Ssc0,
		int	n
	)

Collision probability calculation using sets of ellipsoids.

The units of the inputs should all be consistent, for example km and km2. Only the position of the ellipsoid shold be input.

Parameters:

sigma	Standard deviations of input ellipsoid, ex. 1.0 or 2.0
S	Ellipsoid matrix, 3x3, [length2]
xc	Ellipsoid center, 3x1, [length]
Ssc0	Hard-body ellipsoid for single spacecraft [length2]
n	Number of shells in computation

Returns:: prob Probability of a collision

References PI.

ml_matrix MonitoringAlg	(	ml_matrix &	y,
		ml_matrix &	t,
		ml_matrix &	M,
		ml_matrix &	nu,
		ml_matrix &	accel,
		ml_matrix &	aDiff,
		coll_mon_data_s	d
	)

Collision monitoring algorithm implementation used for both modes, monitoring and surveying.

Requires an acceleration matrix for each relative spacecraft, which will be zero for monitoring. The differential accelerations aDiff may not be zero or else the data output will be corrupted. Currently only the first element of aDiff is used to scale Q assuming that it is a worst-case representation. The function GenerateTimeVector can be used to create t, M, and nu given the total time window.

Parameters:

y	Relative state, 6xm
t	Time vector (sec), 1xn
M	Mean anomaly, 1xn
nu	True anomaly, 1xn
accel	Stacked relative accleration vectors, 3mxn
aDiff	Differential accelerations, 3x1
d	Collision monitoring data structure

Returns:: Probability, mxn

References orb_data_s::ecc, coll_mon_data_s::el_ref, alf_orb_data_s::inc, coll_mon_data_s::lenSC, orb_data_s::mean_anom, coll_mon_data_s::nPts, orb_data_s::perigee, coll_mon_data_s::Pmin, alf_orb_data_s::q1, alf_orb_data_s::q2, alf_orb_data_s::raan, coll_mon_data_s::S0, coll_mon_data_s::sigma, orb_data_s::sma, alf_orb_data_s::sma, coll_mon_data_s::Ssc, and alf_orb_data_s::true_lat.

ml_matrix CollisionSurvey	(	ml_matrix &	y,
		double	t0,
		maneuver_t	mvr1,
		maneuver_t	mvr2[],
		int	n_points,
		coll_mon_data_s	d
	)

Parameters:

y	Relative state (6,n). Passed by reference.
t0	Current time (MET)
mvr1	Maneuver data structure for self
mvr2	Maneuver structure array for relative spacecraft, must be [n]
n_points	Number of points for time vector
d	Collision monitor data structure

Returns:: Probability matrix, one row per relative

References coll_mon_data_s::el_ref, maneuver_s::nBurns, and maneuver_s::tF.

ml_matrix DeltaElem2HillsMat ( const ml_matrix & elA )

Compute transformation matrix from delta elements to Hills.

Parameters:

elA	Reference orbital elements [Alfriend format]

Returns:: m Transformation matrix

References MU_EARTH.

ml_matrix DeltaEl2AlfriendMat ( orb_data_t el )

Compute transformation matrix from standard differential elements to Alfriend differential elements.

Parameters:

el	Reference orbit data

Returns:: T Transformation matrix

References orb_data_s::ecc, orb_data_s::mean_anom, and orb_data_s::perigee.

double distant_pt_ell	(	const ml_matrix &	S,
		const ml_matrix &	U,
		const ml_matrix &	xc,
		const ml_matrix &	x0,
		ml_matrix &	x
	)

Compute minimum distance from a distance point to an ellipsoid's surface.

Parameters:

S	Singular value matrix of ellipsoid (3,3)
U	Rotation matrix of ellipsoid (3,3)
xc	Center of ellipsoid (3,1)
x0	Outside point (3D) (3,1)
x	Point on the ellipsoid (3,1)

Returns:: Distance

double Laguerre	(	const ml_matrix &	a,
		double	x_guess
	)

Laguerre root finding algorithm adapted to real roots.

Parameters:

a	Vector containing the coefficients of the polynomial, a[i] x^i
x_guess	Initial guess for the root

Returns:: Root

ml_matrix GenerateTimeVector	(	orb_data_t	d,
		const double	tF,
		const int	nPts,
		ml_matrix &	M,
		ml_matrix &	nu
	)

Also returns the corresponding mean and true anomaly vectors.

Parameters:

d	Orbit elements data
tF	Final time
nPts	Number of points per orbit
M	Matrix for returning mean anomaly vector
nu	Matrix for returning true anomaly vector

Returns:: Time vector

References orb_data_s::ecc, orb_data_s::mean_anom, PI, orb_data_s::sma, and TWO_PI.

ml_matrix ManeuverStruct2AccelVector	(	maneuver_t	mvr,
		const ml_matrix &	tProp
	)

Compute a 3xN acceleration vector from a maneuver data structure.

Parameters:

mvr	Maneuver data structure, containing an array of burn data structures
tProp	Time history to use for acceleration vector [sec]

Returns:: aC 3xN acceleration matrix [km/s/s]

References maneuver_s::burnData, burn_s::dT, burn_s::dV, maneuver_s::nBurns, burn_s::t, burn_s::uX, burn_s::uY, and burn_s::uZ.

bool TeamLevels	(	team_t	teams[],
		int	num,
		ml_int_array &	levels
	)

Parameters:

teams	Array of team data structures.
num	Number of team data structures.
levels	Array of team hierarchical team levels. Passed by reference.

Returns:: circular Flag indicating whether the supplied team organization is circular (true) or not (false).

int IsRelative	(	int	iD,
		team_t	teams[],
		int	num
	)

Determine whether the given satellite ID is a relative of any team.

Parameters:

iD	Unique integer ID of the satellite being checked.
teams[]	Array of team data structures.
num	Number of team data structures.

Returns:: kTeam Index of the team for which it is a relative (counts from 1). Returns 0 if not a relative.

References team_s::memID.

bool FindUpperTeams	(	int	kBot,
		team_t	teams[],
		int	num,
		ml_int_array &	kUpper
	)

Find teams above this one in the hierarchy.

Parameters:

kBot	Index of team to consider. Find all teams above this one.
teams	Array of team data structures.
num	Number of team data structures.
kUpper	Array of team indices that are above this one in the hierarchy. Passed by reference.

Returns:: circular Flag indicating whether the supplied team organization is circular (true) or not (false).

double TimeUntilTheta	(	double	a,
		double	w,
		double	e,
		double	theta0,
		double &	theta1
	)

Parameters:

a	Semi-major axis [km]
w	Argument of perigee [rad]
e	Eccentricity
theta0	Initial true latitude [rad]
theta1	Final true latitude [rad]

Returns:: dT Elapsed time between initial and final true latitude; theta1 Updated value for final latitude (increased by 2*PI if originally less than initial latitude)

References TWO_PI.

void AccelVector2ManeuverStruct	(	const ml_matrix &	aC,
		ml_matrix	t,
		double	tRef,
		double	nomAccel,
		double	minSepTime,
		maneuver_t &	mvr,
		ml_matrix &	dV
	)

Parameters:

aC	3xN acceleration matrix. [km/s/s]
t	Time vector in seconds, starting at 0.
tRef	Reference time in seconds, [MET]. This is added to the time vector "t" after differencing to avoid numerical rounding errors.
nomAccel	Nominal acceleration in [km/s]. Each burn is assumed to apply this acceleration. This relates the burn duration to the delta-v magnitude.
minSepTime	Minimum allowable separation time between end of one burn and beginning of next. Multiple burns closer together than this will be grouped into a single burn.
mvr	Maneuver data structure with burn info. Passed by reference.
dV	Non-zero delta-v magnitudes. Passed by reference.

References maneuver_s::burnData, burn_s::dT, burn_s::dV, FF_TOL, maneuver_s::iD, burn_s::iD, maneuver_s::nBurns, burn_s::t, maneuver_s::t0, maneuver_s::tF, burn_s::uX, burn_s::uY, and burn_s::uZ.

void ManeuverStruct2AccelVector	(	maneuver_t	mvr,
		double	dT,
		ml_matrix &	aC,
		ml_matrix &	t
	)

Parameters:

mvr	Maneuver data structure, containing an array of burn data structures
dT	Time-step to use in creating the acceleration time-history [sec]
aC	3xN acceleration matrix [km/s/s]. Passed by reference.
t	1xN+1 time vector [sec]. Passed by reference.

References maneuver_s::burnData, burn_s::dT, burn_s::dV, maneuver_s::nBurns, burn_s::t, burn_s::uX, burn_s::uY, and burn_s::uZ.

ml_matrix NOrbVector ( window_t win )

Parameters:

win	Time window data structure

Returns:: nOrb Vector of maneuver durations (in orbits) to consider in planning

References window_s::nManeuvers, window_s::nOrbMax, and window_s::nOrbMin.

ml_matrix TargetTrueAnom	(	double	e,
		double	nu0,
		ml_matrix	nOrb
	)

Parameters:

e	Eccentricity
nu0	Initial true anomaly [rad]
nOrb	Number of orbits into the future to evaluate the true anomaly

Returns:: nuF Target true anomay at future times, unwrapped [rad]

References TWO_PI.

ml_matrix Tetrahedron	(	double	d,
		const ml_matrix &	eul
	)

Parameters:

d	Distance of each side.
eul	Euler angles for rotating the tetrahedron. [rad]

Returns:: p 3x4 matrix containing the [x;y;z]' coordinates of each point.

char* matout ( ml_matrix mat )

Output a matrix to a string with higher precision than built-in "to_string" function.

Parameters:

mat	Matrix to convert to a string.

Returns:: String representation of the matrix in "MATLAB readable" format

sc_formation.h File Reference

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