/*
 * lambert.h -- Lambert transfer orbit solver
 *
 * Solves Lambert's problem: given two position vectors and a
 * time of flight, find the orbit connecting them.
 *
 * Uses the Universal Variable formulation with Stumpff functions,
 * handling elliptic, parabolic, and hyperbolic transfers uniformly.
 *
 * Reference:
 *   Bate, Mueller & White, "Fundamentals of Astrodynamics" (1971)
 *   Battin, "An Introduction to the Methods of Astrodynamics" (1999)
 *   Curtis, "Orbital Mechanics for Engineering Students" (2014)
 *
 * All units: AU, days, AU/day. Gravitational parameter is Gauss's
 * constant squared (k^2 = GM_sun in AU^3/day^2).
 *
 * Thread-safe: no static mutable state.
 */

#ifndef PG_ORBIT_LAMBERT_H
#define PG_ORBIT_LAMBERT_H

#ifdef __cplusplus
extern "C" {
#endif

/*
 * Result of a Lambert transfer orbit solution.
 * All velocities in AU/day.
 */
typedef struct lambert_result
{
    double  v1[3];          /* departure velocity vector (AU/day) */
    double  v2[3];          /* arrival velocity vector (AU/day) */
    double  sma;            /* semi-major axis (AU), negative for hyperbolic */
    int     converged;      /* 1 if solver converged, 0 otherwise */
} lambert_result;

/*
 * Solve Lambert's problem.
 *
 * r1[3]:    departure position (AU, heliocentric ecliptic J2000)
 * r2[3]:    arrival position (AU, heliocentric ecliptic J2000)
 * tof_days: time of flight in days (must be > 0)
 * mu:       gravitational parameter (AU^3/day^2), use GAUSS_K2 for Sun
 * prograde: 1 for prograde (short way), 0 for retrograde (long way)
 * result:   output lambert_result
 *
 * Returns 1 on success, 0 on failure.
 */
int lambert_solve_uv(const double r1[3], const double r2[3],
                     double tof_days, double mu, int prograde,
                     lambert_result *result);

#ifdef __cplusplus
}
#endif

#endif /* PG_ORBIT_LAMBERT_H */