IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i12p1992-d1680618.html
   My bibliography  Save this article

The Influence of the Mass Ratio and the Jacobi Constant on the Probability of Escape in the 3D (4+2)-Body Ring Problem

Author

Listed:
  • Zahra Boureghda

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Mari Carmen Martínez-Belda

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Juan F. Navarro

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

Abstract

The dynamics of escape in the ( N + 2 ) -body ring problem exhibits a limited supply of research that involves the investigation in the three-dimensional scenario. In this paper, we introduce a new method based on the use of a spherical surface of section to analyze the probability of escape in the ( 4 + 2 ) -body ring problem in three dimensions. Our analysis reveals perplexing results regarding the impact of the mass ratio, β , and the Jacobi constant, C , parameters on this escape probability. In order to delineate the different effects exerted by these parameters, we incorporate into the system three increasing values of β and four values of C for each value of β , that show different behaviors in the distribution of the escaping orbits.

Suggested Citation

  • Zahra Boureghda & Mari Carmen Martínez-Belda & Juan F. Navarro, 2025. "The Influence of the Mass Ratio and the Jacobi Constant on the Probability of Escape in the 3D (4+2)-Body Ring Problem," Mathematics, MDPI, vol. 13(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1992-:d:1680618
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/12/1992/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/12/1992/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1992-:d:1680618. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.