The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2 : 1 Resonance. (16th January 2012) - Sampaio, Jarbas Cordeiro; Vilhena de Moraes, Rodolpho; da Silva Fernandes, Sandro
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 harmonicsJ 20 andJ 40 and the tesseral harmonicsJ 22 andJ 42 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.