Analysis on nonlinear dynamics of two first-order resonances in a three-body system
Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, 100124, Beijing, People’s Republic of China
2 School of Finance and Mathematics, Huainan Normal University, 232038, Anhui, People’s Republic of China
Accepted: 20 December 2021
Published online: 11 January 2022
This paper focuses on the analysis on the nonlinear dynamics of two first-order 2:3 external and 3:2 internal mean motion resonances (MMRs) for three-body formed by two massive bodies, namely planet and star, and one test particle of the negligible mass. A detailed analysis of the phase space structure is given by computing Poincaré map of the planar circular restricted three-body model. It is found that the eccentricity and initial location, namely the semimajor axis and phase, of the massless particle significantly affect the steady state of the resonant orbits. The transition mechanisms are obtained for the number of the stable islands. The width- and height-variation trends of the stable islands are analyzed. The stable and chaotic domains are obtained by the resonance space. Our results may be instructive for understanding the dynamics of the resonant bodies and the evolution of the resonant orbits.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2022