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Stability of the Relative Equilibria in the Two-body Problem on the Sphere
Jaime Andradea, Claudio Vidala, Claudio Sierpeb a Grupo de Investigación en Sistemas Dinámicos y Aplicaciones-GISDA,
Departamento de Matemática, Facultad de Ciencias,
Universidad del Bío-Bío, Casilla 5-C, Concepción, VIII-Región, Chile
b Departamento de Matemática, Facultad de Ciencias,
Universidad del Bío-Bío, Casilla 5-C, Concepción, VIII-Región, Chile
Abstract:
We consider the 2-body problem in the sphere $\mathbb{S}^2$. This problem is modeled by a Hamiltonian system with $4$ degrees of freedom and, following the approach given in [4], allows us to reduce the study to a system of $2$ degrees of freedom. In this work we will use theoretical tools such as normal forms and some nonlinear stability results on Hamiltonian systems for demonstrating a series of results that will correspond to the open problems proposed in [4] related to the nonlinear stability of the relative equilibria. Moreover, we study the existence of Hamiltonian pitchfork and center-saddle bifurcations.
Keywords:
two-body-problem on the sphere, Hamiltonian formulation, normal form, resonance,
nonlinear stability.
Citation:
Jaime Andrade, Claudio Vidal, Claudio Sierpe, “Stability of the Relative Equilibria in the Two-body Problem on the Sphere”, Regul. Chaotic Dyn., 26:4 (2021), 402–438
Linking options:
https://www.mathnet.ru/eng/rcd1123 https://www.mathnet.ru/eng/rcd/v26/i4/p402
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Abstract page: | 93 | References: | 20 |
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