Dynamics of a particle in a gravitational field of a homogeneous annulus disk
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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.
KeywordsGravitational attraction of a particle by a homogeneous annulus disk Symmetries Dynamics Circular Solutions
Mathematics Subject Classifications70F15 37N05
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- Alberti, A.: Dinâmica de uma partícula no potencial de um fio circular homogêneo. Master thesis, Departamento de Matemática—UFPE (2003)Google Scholar
- Azevêdo, C., Cabral, H., Ontaneda, P.: On the Fixed Homogeneous Circle Problem. ArXiv: math.DS/0307329v5 (2005)Google Scholar
- Kellog O.D. (1929). Fundations of the Potential Theory. Dover Publications, Inc., New York Google Scholar
- Vidal, C., Alberti, A.: Periodic solutions of a particle in a potential field of a planar massive annulus. Preprint (2006)Google Scholar