Stability and bifurcation analyses for exterior resonant families in Earth-Moon system

Abstract

In this work, stability and bifurcation analyses for exterior resonant orbit families have been investigated for a test spacecraft around Earth-Moon system. The initial states are obtained for certain resonance ratio orbits in the two-body problem. The shooting method is applied to compute the true resonant orbits families based on the planar circular restricted three-body problem. By means of numerical approach, the 1:2 and 2:3 families of resonant orbits are studies, and the distribution of eigenvalues, stability curves are presented. Inparticular, some critical points, corresponding to period-doubling and tangent bifurcations, are found in the stability curves. The bifurcation and stability analyses show overall features of the resonant orbits. This study may provide alternative orbital design ideas.