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
- General Physics and Astronomy
- Applied Mathematics