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On the analysis of the geometry of escape in the 3D (4+2)-body ring problem

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  • Boureghda, Zahra
  • Martínez-Belda, M.C.
  • Navarro, Juan F.

Abstract

The aim of this paper is to reveal new insights into the escape dynamics of the (4+2)-body ring problem in three dimensions through a numerical exploration, based on a new computational method. By means of a new surface of section, adequate to the symmetries of the problem, we determine the impact of the mass ratio and the Jacobi constant parameters on the geometry of the basins of escape and their connections with the distribution of the times of escape towards the different opening windows. In addition, thanks to a special selection of the initial conditions, we are able to visualize in a surface the location of the basins of escape whereas the system under study is of dimension six. The results show that the size and location of the basins of escape depend on the mass ratio parameter, and their characteristics seem to follow a pattern managed by this parameter. We hope that our investigation will reveal new challenges and prospective researches for more numerical explorations in the escape dynamics of the three-dimensional (N+2)-body ring problem.

Suggested Citation

  • Boureghda, Zahra & Martínez-Belda, M.C. & Navarro, Juan F., 2024. "On the analysis of the geometry of escape in the 3D (4+2)-body ring problem," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924010063
    DOI: 10.1016/j.chaos.2024.115454
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