The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2？:？1 Resonance

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 20 and 40 and the tesseral harmonics 22 and 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.