Optimal Trajectories for Hypervelocity Flight

This paper discusses optimal trajectories for hypervelocity flight of interest in aeroassisted orbital transfer. Both coplanar orbital transfer and noncoplanar orbital transfer are studied. More precisely, the GEO-to-LEO transfer, the HEO-to-LEO transfer, and the LEO-to-LEO transfer are considered in connection with a spacecraft which is controlled during the atmospheric pass via the angle of attack (coplanar case) or via the angle of attack and the angle of bank (noncoplanar case). Within the framework of classical optimal control, the following problems are studied: (P1) minimize the energy required for orbital transfer; (P4) maximize the time of flight during the atmospheric portion of the trajectory; and (P5) minimize the time integral of the square of the path inclination. Within the framework of minimax optimal control, the following problem is studied: (Q1) minimize the peak heating rate. Numerical solutions for Problems (P1), (P4), (P5), (Q1) are obtained by means of the sequential gradient - restoration algorithm for optimal control problems. The engineering implications of the results obtained are discussed. In particular, it is shown that the nearly-grazing solution [namely, the trajectory solving Problem (P5)] is a useful engineering compromise between energy requirements and aerodynamic heating requirements.