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On the dynamics of the equilateral restricted four-body problem with Kerr-like primaries

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  • Alhowaity, Sawsan
  • Suraj, Md Sanam
  • Dubeibe, Fredy L.
  • Idrisi, M. Javed

Abstract

The dynamical behavior of the restricted four-body problem with Kerr-like primaries is investigated numerically. We analyze the positions and linear stability of the equilibrium points and further classify them into index-I and index-II saddle points by evaluating the number of positive eigenvalues of the Hessian matrix of the effective potential. Our results show that the equilibrium points lose linear stability beyond a critical value of the rotation parameter. In addition, we perform a systematic and detailed classification of phase space trajectories. The initial conditions are categorized into three main types: (i) bounded regular orbits, (ii) escaping orbits, and (iii) collision orbits, based on a thorough numerical analysis. Each initial condition is color-coded according to its orbital outcome, yielding visual representations referred to as orbit type diagrams (OTDs). The results reveal a high degree of complexity in the system’s dynamical behavior. In particular, the structure of the escape basins exhibits a strong dependence on the total orbital energy. Fractal basin boundaries are observed across all escape regimes, indicating a complex interplay between the system’s energy levels and the geometry of the escape channels.

Suggested Citation

  • Alhowaity, Sawsan & Suraj, Md Sanam & Dubeibe, Fredy L. & Idrisi, M. Javed, 2025. "On the dynamics of the equilateral restricted four-body problem with Kerr-like primaries," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925006812
    DOI: 10.1016/j.chaos.2025.116668
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    References listed on IDEAS

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    1. 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).
    2. 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).
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    1. Idrisi, M. Javed & Ullah, M. Shahbaz, 2025. "Elliptic concentric restricted five-body problem: application to binary star systems with circumbinary planets," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).

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