Reconfiguration Optimization of Relative Motion Between Elliptical Orbits Using Lyapunov-Floquet Transformation

This article investigates the reconfiguration optimization of the formation flying in elliptical orbits. Based on the Tschauner'Hempel equations, the time-varying system has been reduced to a time-independent one by Lyapunov'Floquet transformation without losing its relative motion characteristics. A geometric configuration invariant of the formation is introduced and general relative configurations are considered as linear combinations of essential components in proportion to this invariant. Benefitting from the evolution of the configuration invariant, the reconfiguration optimization is converted into an optimal parameter selection problem and the transfer trajectory is parameterized by a functional integral. In particular, the indirect method of optimal control based on the reduced dynamics avoids the time-varying derivative of costate variables, which simplifies the optimization problem. The numerical results of both low-thrust and impulsive reconfigurations verify the effectiveness of the reconfiguration optimization based on the reduced relative dynamics.