Optimal trajectories for hypervelocity flight

Optimal trajectories for hypervelocity flight of interest in aeroassisted orbital transfer are discussed. Both coplanar and noncoplanar transfer are studied. More precisely, the geosynchronous-earth-orbit-, high-earth orbit- and low-earth-orbit-to-low earth-orbit transfers are considered in connection with a spacecraft that is controlled during the atmospheric pass by the angle of attack (coplanar case) or by the angle of attack and the angle of bank (noncoplanar case). Within the framework of classical optimal control, the following problems are studied: minimize the energy required for orbital transfer; maximize the time of flight during the atmospheric portion of the trajectory; and minimize the time integral of the square of the path inclination. Within the framework of minimax optimal control, the problem studied is to minimize the peak rate. Numerical solutions for the problems are obtained by means of the sequential gradient-restoration algorithm. The engineering implications of the results are discussed.