Optimizing an Ascent Trajectory of a Small Spacecraft Launched by an Air-based Two-Stage Rocket

In this paper we have considered the problem of optimizing the ascent trajectory of a small spacecraft launched by an air-based two-stage rocket. The control is provided by the angle of attack and thrust of the engines while a restriction on the angle of attack is introduced. The thrust of engines at active trajectory phases is considered to be constant. The optimum control criterion is the maximum of the finite mass. To determine the optimal control programs, we have applied Pontryagin's maximum principle. We have conducted the analysis of the parameters of the trajectory and rocket flight modes. We have also calculated the payload mass launched into low-earth orbit.