| Contents |
| We introduce a new problem: the Sitnikov Problem with restriction to a circle, that is two bodies with positive masses (primaries) follow elliptic Keplerian orbits on a fixed plane and a third massless body (secondary) restricted to move on a circle, passing through the center of mass of the primaries orthogonally. In this talk we assume eccentricity zero for the primaries and we take as a parameter the ratio between the radii of the circle followed by the primaries and the circle of the secondary.
We begin showing that the introduced statement is the link between another two problems already studied: the classical Sitnikov problem (when primaries follow circular paths) and the 2-body problem on the circle. After we determine two equilibria: the origin and the opposite in the circle. We analyze the stability of each equilibrium. Particularly, we will show the alternation of the stability for the latter equilibrium as the parameter varies. |
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