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

• Published in: Results in physics Vol. 31; p. 104961
• Main Authors: Li, Xu, Qian, Ying-Jing, Yang, Xiao-Dong, Zhang, Wei
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2021; Elsevier
• Subjects: Bifurcation; Resonant orbit; Restricted three-body problem; Stability; Restricted three-body problem; Bifurcation; Resonant orbit; Stability
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2021.104961

•Shooting method is applied to compute the exterior resonant families.•Distribution of eigenvalues, stability curves are presented for the 1:2 and 2:3 resonant families.•Some critical points, corresponding to period-doubling and tangent bifurcations, are found. 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.