Optimization of space vehicle combined orbital plane change maneuver on the basis of pontryagin’s maximum principle

The task of optimizing the space vehicle combined orbital plane change maneuver with the aim of maximizing its final mass is considered in the paper. Burst of power is used for the vehicle’s exit from the initial low earth orbit and subsequent re-entry. Starting from atmospheric entry till the end of the orbital plane change with the entry in the final orbit the angle of attack, the air-path bank angle and the fuel-flow rate are used as controls. Limitations for the angle of attack, fuel-flow rate, adiabatic recovery temperature, longitudinal and vertical load factor are introduced. The successive linearization method is used to determine the optimal control programs. Solving the optimization task is exemplified by a hypothetical space vehicle. The results of modeling space vehicle motion are presented. The changes in the determined “aerodynamic” (angle of attack and air-path bank angle) and “motion” (fuel-flow rate) controls with increasing the angle of orbital plane change are discussed with and without account of the key limitation on the modes of motion – maximum adiabatic recovery heating temperature.