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Dynamical Properties of Body with Variable Mass in a Fifth-degree Hénon–Heiles System

Astronomy Reports volume 66, pages 64–74 (2022)Cite this article

Abstract

The aim of this work is to investigate the motion properties of the infinitesimal body in the frame of the fifth-degree generalized Hénon–Heiles (GHH) potential. We determine the equations of motion of the infinitesimal body, where its mass varies according to the Jeans law, within the framework of the GHH potential. We illustrate numerically the positions of stationary points and their stability, and we found that all these points are unstable. Further, the dynamical features such as Poincaré surfaces of section, the trajectory allocations, the basins of attraction, the permitted and prohibited regions of motion are studied for each stationary point.

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ACKNOWLEDGMENTS

Authors are thankful to the anonymous referee for the valuable comments by which we succeeded to improve our manuscript at this end.

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Authors and Affiliations

  1. Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), 11421, Cairo, Helwan, Egypt

    Elbaz I. Abouelmagd

  2. International Center for Advanced Interdisciplinary Research (ICAIR), Sangam Vihar, New Delhi, India

    Abdullah A. Ansari

Authors
  1. Elbaz I. Abouelmagd
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  2. Abdullah A. Ansari
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Correspondence to Elbaz I. Abouelmagd or Abdullah A. Ansari.

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Abouelmagd, E.I., Ansari, A.A. Dynamical Properties of Body with Variable Mass in a Fifth-degree Hénon–Heiles System. Astron. Rep. 66, 64–74 (2022). https://doi.org/10.1134/S1063772922010012

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  • DOI: https://doi.org/10.1134/S1063772922010012

Keywords:

  • fifth-order
  • mass variation effect
  • generalized Hénon–Heiles model
  • Poincaré surfaces of section
  • trajectories