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Regular and Chaotic Dynamics, 2021, Volume 26, Issue 4, Pages 402–438
DOI: https://doi.org/10.1134/S1560354721040067
(Mi rcd1123)
 

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
References:
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.
Funding agency Grant number
Fondo Nacional de Desarrollo Científico y Tecnológico 11180776
1180288
J. Andrade was supported by project Fondecyt 11180776, C. Vidal was supported by project Fondecyt 1180288.
Bibliographic databases:
Document Type: Article
MSC: 70F07, 70G60, 37D40
Language: English
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
Citation in format AMSBIB
\Bibitem{AndVidSie21}
\by Jaime Andrade, Claudio Vidal, Claudio Sierpe
\paper Stability of the Relative Equilibria in the Two-body Problem on the Sphere
\jour Regul. Chaotic Dyn.
\yr 2021
\vol 26
\issue 4
\pages 402--438
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\crossref{https://doi.org/10.1134/S1560354721040067}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85112137526}
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