## 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 language | English (US) |
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Article number | 1056 |

Pages (from-to) | 1056-1079 |

Number of pages | 24 |

Journal | Nonlinearity |

Volume | 29 |

Issue number | 3 |

DOIs | |

State | Published - Feb 12 2016 |

## All Science Journal Classification (ASJC) codes

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