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Analysis on nonlinear dynamics of two first-order resonances in a three-body system

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Abstract

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.

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Acknowledgements

The authors gratefully acknowledge the support of National Natural Science Foundation of China (NNSFC) through grant Nos. 11832002, the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Bei**g Municipality (PHRIHLB), the research foundation of Huainan Normal University (2020XJZD007).

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Authors and Affiliations

  1. Bei**g Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Bei**g University of Technology, Bei**g, 100124, People’s Republic of China

    Yi Zhou & Wei Zhang

  2. School of Finance and Mathematics, Huainan Normal University, Anhui, 232038, People’s Republic of China

    Yi Zhou

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  1. Yi Zhou
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Correspondence to Wei Zhang.

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Zhou, Y., Zhang, W. Analysis on nonlinear dynamics of two first-order resonances in a three-body system. Eur. Phys. J. Spec. Top. 231, 2289–2306 (2022). https://doi.org/10.1140/epjs/s11734-022-00428-6

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  • DOI: https://doi.org/10.1140/epjs/s11734-022-00428-6

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