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Parametric Stability in a P+2-Body Problem

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Abstract

We consider a planar restricted \(P+2\)-body problem where P bodies of equal masses located at the vertices of a regular polygon move in an homographic elliptic orbit and an additional mass is fixed at the center of the polygon. We study the equilibrium of the infinitesimal mass that lies on the half-line from the center of the polygon through the midpoint of its side, outside the unit circle. We study the parametric stability of this equilibrium constructing the boundary curves of the stability/instability regions in the plane of the parameters.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Sergipe, Av. Marechal Rondon, S/n, Jardim Roza Elze, São Cristovão, SE, Brazil

    Gerson Cruz Araujo

  2. Departamento de Matemática, Universidade Federal de Pernambuco/PVNS Universidade Federal de Sergipe, Itabaiana, Brazil

    Hildeberto E. Cabral

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  1. Gerson Cruz Araujo
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  2. Hildeberto E. Cabral
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Correspondence to Gerson Cruz Araujo.

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Araujo, G.C., Cabral, H.E. Parametric Stability in a P+2-Body Problem. J Dyn Diff Equat 30, 719–742 (2018). https://doi.org/10.1007/s10884-017-9570-x

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  • DOI: https://doi.org/10.1007/s10884-017-9570-x

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