Dynamics of an isosceles problem generated by a perturbation of Euler's collinear solution

2025/01/07 by Karine Santos, Santos, Karine
Engineering · Physics and Astronomy · #Dynamical Systems (math.DS) #Elasticity and Wave Propagation #FOS: Mathematics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2501.03517

openalex publication_date 2025/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a study of the isosceles problem resulting by a perturbation of Euler's collinear solution under Newtonian gravitational attraction of three bodies in space. After the Hamiltonian was obtained, a circumference of relative equilibria points was found. The original system was subsequently reduced to another system with two degrees of freedom, periodic in the time, where there is now a single point of equilibrium. Linear and parametric stability were discussed in this simplified model of the three-body problem.

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