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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年3月17日

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  • Karine Santos

摘要

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.