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Dynamics of a particle in a gravitational field of a homogeneous annulus disk. (English) Zbl 1330.70071

Summary: We formulate the problem of an infinitesimal particle moving in the space under the influence of the gravitational force induced by a homogeneous annulus disk fixed on a plane. We compute using different coordinates and in terms of an elliptic integral the potential associated to this problem. Also we study the symmetries of the associated potential. After that, we look at the dynamics in some particular cases, namely: in the line perpendicular to the plane that contains the annulus disk and passes through the center of the ring and on the plane that contains the massive annulus.

MSC:

70F15 Celestial mechanics
37N05 Dynamical systems in classical and celestial mechanics
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References:

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