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On the fixed homogeneous circle problem

C. Azevedo·H. Cabral·P. Ontaneda
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Abstract

We give some results about the dynamics of a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. Our main results concern (1) singularities and (2) the dynamics in the plane that contains the circle. The study presented here is purely analytic.

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C. Azevedo, H. Cabral, P. Ontaneda. 2005-03-23. On the fixed homogeneous circle problem. https://arxiv.org/abs/math/0307329

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