IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v134y2020ics0960077920301065.html
   My bibliography  Save this article

Basins of convergence of equilibrium points in the restricted three-body problem with modified gravitational potential

Author

Listed:
  • Zotos, Euaggelos E.
  • Chen, Wei
  • Abouelmagd, Elbaz I.
  • Han, Huiting

Abstract

This article aims to investigate the points of equilibrium and the associated convergence basins in the restricted problem with two primaries, with a modified gravitational potential. In particular, for one of the primary bodies, we add an external gravitational term of the form 1/r3, which is very common in general relativity and represents a gravitational field much stronger than the classical Newtonian one. Using the well-known Newton–Raphson iterator we numerically locate the position of the points of equilibrium, while we also obtain their linear stability. Furthermore, for the location of the points of equilibrium, we obtain semi-analytical functions of both the mass parameter and the transition parameter. Finally, we demonstrate how these two variable parameters affect the convergence dynamics of the system as well as the fractal degree of the basin diagrams. The fractal degree is derived by computing the (boundary) basin entropy.

Suggested Citation

  • Zotos, Euaggelos E. & Chen, Wei & Abouelmagd, Elbaz I. & Han, Huiting, 2020. "Basins of convergence of equilibrium points in the restricted three-body problem with modified gravitational potential," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
  • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301065
    DOI: 10.1016/j.chaos.2020.109704
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920301065
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2020.109704?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vincent, Aguda Ekele & Abouelmagd, Elbaz I. & Perdios, Efstathios A. & Kalantonis, Vassilis S., 2024. "Numerical exploration of the quantized Hill problem dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Yadav, Arun Kumar & Kushvah, Badam Singh & Dolas, Uday, 2021. "Controlling the libration point orbits for CRTBP with non-ideal solar sail and albedo effect," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Abouelmagd, Elbaz I. & Alshaery, A.A. & Gao, Fabao, 2024. "New dynamical system for circular satellites relative motion," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

    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:eee:chsofr:v:134:y:2020:i:c:s0960077920301065. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.