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International Journal of Aerospace Engineering
Volume 2017, Article ID 9234905, 10 pages
Research Article

A Shape-Based Method for Continuous Low-Thrust Trajectory Design between Circular Coplanar Orbits

1National Key Laboratory of Aerospace Flight Dynamics, Xi’an, Shaanxi 710072, China
2School of Astronautics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China

Correspondence should be addressed to Qun Fang; nc.ude.upwn@gnafq

Received 16 December 2016; Accepted 22 March 2017; Published 10 April 2017

Academic Editor: Paul Williams

Copyright © 2017 Qun Fang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The shape-based method can provide suitable initial guesses for trajectory optimization, which are useful for quickly converging a more accurate trajectory. Combined with the optimal control theory, an optimized shape-based method using the finite Fourier series is proposed in this paper. Taking the flight time-fixed case and the time-free case into account, respectively, the optimized shape-based method, which considers the first-order optimal necessary conditions, can guarantee that not only an orbit designed during the preliminary phase is optimal, but also the thrust direction is not constrained to be tangential. Besides, the traditional shape-based method using the finite Fourier series, in which the thrust direction is constrained to be tangential, is developed for the time-free case in this paper. The Earth-Mars case and the LEO-GEO case are used to verify the optimized shape-based method’s feasibility for time-fixed and time-free continuous low-thrust trajectory design between circular coplanar orbits, respectively. The optimized shaped-based method can design a lower cost trajectory.