Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 59372, 23 pages
Research Article

Numerical and Analytical Study of Optimal Low-Thrust Limited-Power Transfers between Close Circular Coplanar Orbits

Sandro da Silva Fernandes1 and Wander Almodovar Golfetto2

1Departamento de Matemática, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228-900, SP, Brazil
2Instituto de Aeronáutica e Espaço, Comando Geral de Tecnologia Aeroespacial, São José dos Campos 12228-904, SP, Brazil

Received 22 September 2006; Revised 18 April 2007; Accepted 20 May 2007

Academic Editor: José Manoel Balthazar

Copyright © 2007 Sandro da Silva Fernandes and Wander Almodovar Golfetto. 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 and analytical study of optimal low-thrust limited-power trajectories for simple transfer (no rendezvous) between close circular coplanar orbits in an inverse-square force field is presented. The numerical study is carried out by means of an indirect approach of the optimization problem in which the two-point boundary value problem, obtained from the set of necessary conditions describing the optimal solutions, is solved through a neighboring extremal algorithm based on the solution of the linearized two-point boundary value problem through Riccati transformation. The analytical study is provided by a linear theory which is expressed in terms of nonsingular elements and is determined through the canonical transformation theory. The fuel consumption is taken as the performance criterion and the analysis is carried out considering various radius ratios and transfer durations. The results are compared to the ones provided by a numerical method based on gradient techniques.