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Equilibrium stability in the triangular restricted four-body problem with non-spherical primaries

Author

Listed:
  • Moneer, Eman M.
  • Allawi, Yazan
  • Elaissi, Samira
  • Dubeibe, Fredy L.
  • Zotos, Euaggelos E.

Abstract

This paper investigates the Lagrangian configuration of the restricted four-body problem in which the three primaries are non-spherical, specifically either prolate or oblate. By using various standard numerical methods, the positions of equilibrium points and their linear stability and dynamical type were determined. The impact of mass and shape of the primaries on the system’s equilibrium points and their linear stability were systematically explored by discretizing the parameter space for the non-sphericity parameter within a specified interval. The study revealed that the system always has an even number of equilibrium points, ranging from 8 to 22. Linearly stable points always exist, except for the case where there are 10 equilibrium points, where all the points are unstable.

Suggested Citation

  • Moneer, Eman M. & Allawi, Yazan & Elaissi, Samira & Dubeibe, Fredy L. & Zotos, Euaggelos E., 2023. "Equilibrium stability in the triangular restricted four-body problem with non-spherical primaries," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008342
    DOI: 10.1016/j.chaos.2023.113933
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    References listed on IDEAS

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    1. Muhammad, Shah & Duraihem, Faisal Zaid & Zotos, Euaggelos E., 2021. "On the equilibria of the restricted four-body problem with triaxial rigid primaries - I. Oblate bodies," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Suraj, Md Sanam & Aggarwal, Rajiv & Mittal, Amit & Meena, Om Prakash & Asique, Md Chand, 2020. "On the spatial collinear restricted four-body problem with non-spherical primaries," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    3. Martha à lvarez-Ramírez & Claudio Vidal, 2009. "Dynamical Aspects of an Equilateral Restricted Four-Body Problem," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-23, March.
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    Cited by:

    1. Moneer, Eman M. & Elaissi, Samira & Dubeibe, Fredy L. & Zotos, Euaggelos E., 2023. "Investigating the impact of non-spherical bodies and three-body interactions on equilibrium dynamics in the circular restricted three-body problem," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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