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A Note on the Nonlinear Stability of Equilibrium Points in the Planar Equilateral Restricted Mass-Unequal Four-Body Problem

José Alejandro Zepeda Ramírez

Dept. de Física, UAM–Iztapalapa, 09340 Iztapalapa, Mexico City, Mexico

E-mail Address: alex.zepeda.r@gmail.com

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Martha Alvarez-Ramírez

Dept. de Matemáticas, UAM–Iztapalapa, 09340 Iztapalapa, Mexico City, Mexico

E-mail Address: mar@xanum.uam.mx

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Antonio García

Dept. de Matemáticas, UAM–Iztapalapa, 09340 Iztapalapa, Mexico City, Mexico

E-mail Address: agar@xanum.uam.mx

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https://doi.org/10.1142/S0218127422500298Cited by:1 (Source: Crossref)

Abstract

This note follows up on the study in the paper [Zepeda Ramírez et al., 2021], where we investigate the nonlinear stability of equilibrium points for the planar restricted equilateral four-body problem for the specific values of masses $m_{1} = 0.01$ $m_{1} = 0.01$ and $0.99$ $0.99$ of the primary, fixed on the horizontal axis. We give an improvement of the previous results.

Keywords:

References

Meyer, K. R. & Offin, D. C. [2017] Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, 3rd edition, Applied Mathematical Sciences, Vol. 90 (Springer, Cham). Crossref, Google Scholar
Zepeda Ramírez, J. A., Alvarez-Ramírez, M. & García, A. [2021] “ Nonlinear stability of equilibrium points in the planar equilateral restricted mass-unequal four-body problem,” Int. J. Bifurcation and Chaos 31, 2130031-1–15. Link, Web of Science, Google Scholar