Orbital transfer trajectory optimization

Abstract

Recent developments in astronautical engineering have led to the adoption of low thrust rocket engines for spacecraft. Optimizing the orbital transfers for low thrust engines is significantly more complicated than optimizing transfers for impulsive engines because a continuous control law must be found and long integrations are necessary to determine whether the control law works or not. Previous work on optimizing low thrust orbital transfers has led to the development of control laws for continuous thrusting including the effects of oblateness, multiple attracting bodies, eclipses, and solar cell degradation. The current work adds to this by developing control laws for optimal coasting and for variable specific impulse at constant power. The Hamiltonian method is used to develop the optimal control laws and physical interpretations are given to each term in the Hamiltonian. Application of the optimal coasting control law to transfers from LEO to GEO indicate that small amounts of coasting can significantly reduce the fuel needed for a transfer.