On the stability of the Lagrangian homographic solutions in a curved       three-body problem on $\mathbb{S}^2$

Regina Martínez; Carles Simó

doi:10.3934/dcds.2013.33.1157

Article Contents

2013, Volume 33, Issue 3: 1157-1175. Doi: 10.3934/dcds.2013.33.1157

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On the stability of the Lagrangian homographic solutions in a curved three-body problem on $\mathbb{S}^2$

Regina Martínez^1, and
Carles Simó^2,

1.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona
2.
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona

Received: April 30, 2011

Revised: October 31, 2011

Published: February 2013

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Abstract

The problem of three bodies with equal masses in $\mathbb{S}^2$ is known to have Lagrangian homographic orbits. We study the linear stability and also a "practical'' (or effective) stability of these orbits on the unit sphere.

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Mathematics Subject Classification: Primary: 70F07, 70H12; Secondary: 34D08, 37J25.

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