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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 854967, 15 pages
Research Article

A Simple Time Domain Collocation Method to Precisely Search for the Periodic Orbits of Satellite Relative Motion

National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi’an 710072, China

Received 1 May 2014; Revised 10 July 2014; Accepted 13 August 2014; Published 25 September 2014

Academic Editor: Vivian Martins Gomes

Copyright © 2014 Xiaokui Yue 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.


A numerical approach for obtaining periodic orbits of satellite relative motion is proposed, based on using the time domain collocation (TDC) method to search for the periodic solutions of an exact nonlinear relative model. The initial conditions for periodic relative orbits of the Clohessy-Wiltshire (C-W) equations or Tschauner-Hempel (T-H) equations can be refined with this approach to generate nearly bounded orbits. With these orbits, a method based on the least-squares principle is then proposed to generate projected closed orbit (PCO), which is a reference for the relative motion control. Numerical simulations reveal that the presented TDC searching scheme is effective and simple, and the projected closed orbit is very fuel saving.