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Optimization of Low-Thrust Transfer Trajectory Based on Averaging Method

Optimization of low-thrust transfer trajectory is one of the most difficult problems in low-thrust technique research. In this paper, based on the averaging method, an analytical control law has been developed for optimal-fuel transfer trajectory. Firstly, the small parameters have been divided from the motion equation by variable substitution. Secondly, averaging method is utilized to calculate the increment of orbital parameters in an orbital period by integral operation, and then based on the Pontryagin's theory, the analytical control law is presented. Finally, numerical result is presented for optimal-fuel mission transfer from LEO to GEO.