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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 405870, 22 pages
doi:10.1155/2012/405870
The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2 : 1 Resonance
1Departamento de Matemática, Universidade Estadual Paulista (UNESP), 12516-410 Guaratinguetá-SP, Brazil
2Instituto de Ciência e Tecnologia, Universidade Federal de São Paulo (UNIFESP), 12231-280 São José dos Campos, SP, Brazil
3Departamento de Matemática, Instituto Tecnológico de Aeronáutica (ITA), 12228-900 São José dos Campos, SP, Brazil
Received 7 July 2011; Accepted 27 September 2011
Academic Editor: Silvia Maria Giuliatti Winter
Copyright © 2012 Jarbas Cordeiro Sampaio 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.
Abstract
The orbital dynamics of synchronous satellites is studied. The 2 : 1 resonance is considered; in other words, the satellite completes two revolutions while the Earth completes one. In the development of the geopotential, the zonal harmonics and and the tesseral harmonics and are considered. The order of the dynamical system is reduced through successive Mathieu transformations, and the final system is solved by numerical integration. The Lyapunov exponents are used as tool to analyze the chaotic orbits.