The Darboux point and the conjugate point on optimal deorbit for reentry trajectories
Abstract
The concept of the Darboux point at which an extremal loses its global optimality is extended to the case of discontinuous control. Using Contensou's domain of maneuverability, the condition for optimal switching at a corner is derived and the optimality of the trajectory in the neighborhood of a Darboux point is analyzed. The theory is applied to the problems of minimumfuel planar and noncoplanar deorbit from elliptical orbits for atmospheric entry at a prescribed angle. In each case, the globally optimal trajectory is assessed and it is found that in these nonlinear problems the Darboux point and the conjugate point are distinct. The global optimality is always lost before local optimality.
 Publication:

Lausanne International Astronautical Federation Congress
 Pub Date:
 October 1984
 Bibcode:
 1984laus.iafcR....V
 Keywords:

 Optimal Control;
 Orbital Position Estimation;
 Points (Mathematics);
 Reentry Trajectories;
 Trajectory Optimization;
 Elliptical Orbits;
 Orbit Calculation;
 Orbital Maneuvers;
 Trajectory Control;
 Astrodynamics