Stability interchanges in a curved Sitnikov problem

Luis Franco-Pérez, Marian Gidea, Mark Levi, Ernesto Pérez-Chavela

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4 Scopus citations

Abstract

We consider a curved Sitnikov problem, in which an infinitesimal particle moves on a circle under the gravitational influence of two equal masses in Keplerian motion within a plane perpendicular to that circle. There are two equilibrium points, whose stability we are studying. We show that one of the equilibrium points undergoes stability interchanges as the semi-major axis of the Keplerian ellipses approaches the diameter of that circle. To derive this result, we first formulate and prove a general theorem on stability interchanges, and then we apply it to our model. The motivation for our model resides with the n-body problem in spaces of constant curvature.

Original languageEnglish (US)
Article number1056
Pages (from-to)1056-1079
Number of pages24
JournalNonlinearity
Volume29
Issue number3
DOIs
StatePublished - Feb 12 2016

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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    Franco-Pérez, L., Gidea, M., Levi, M., & Pérez-Chavela, E. (2016). Stability interchanges in a curved Sitnikov problem. Nonlinearity, 29(3), 1056-1079. [1056]. https://doi.org/10.1088/0951-7715/29/3/1056