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Mathematical Problems in Engineering
Volume 2012, Article ID 405870, 22 pages
Research Article

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.


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 𝐽20 and 𝐽40 and the tesseral harmonics 𝐽22 and 𝐽42 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.