A note on the nonlinear stability of equilibrium points in the planar equilateral restricted mass-unequal four-body problem. (English) Zbl 1492.70011
Summary: This note follows up on the study in the paper [the authors, Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 11, Article ID 2130031, 15 p. (2021; Zbl 1477.70019)], where we investigate the nonlinear stability of equilibrium points for the planar restricted equilateral four-body problem for the specific values of masses \(m_1=0.01\) and \(0.99\) of the primary, fixed on the horizontal axis. We give an improvement of the previous results.
MSC:
| 70F10 | \(n\)-body problems |
| 37N05 | Dynamical systems in classical and celestial mechanics |
| 70H14 | Stability problems for problems in Hamiltonian and Lagrangian mechanics |
Citations:
Zbl 1477.70019References:
| [1] | Meyer, K. R. & Offin, D. C. [2017] Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, 3rd edition, , Vol. 90 (Springer, Cham). · Zbl 1372.70002 |
| [2] | 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 Chaos31, 2130031-1-15. · Zbl 1477.70019 |
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