Optimal altitude-constrained low-thrust transfer between inclined Circular Orbits

Abstract

The reformulated Edelbaum problem of the minimum-time low-thrust transfer between inclined circular orbits is further extended in order to constrain the intermediate orbits during the transfer to remain below a given altitude. The minimum-time problem involving an inequality constraint on the orbital velocity is shown to be equivalent to one involving an equality constraint in terms of the thrust yaw angle representing the control variable that is optimized resulting in the minimum-time solution. The transfers are shown to comprise an initial unconstrained arc followed by a constrained arc where the altitude remains constant while pure inclination change is effected, and terminating by a final unconstrained arc with simultaneous altitude and inclination changes as during the first arc.