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Dynamics of a particle in a gravitational field of a homogeneous annulus disk

  • Angelo Alberti
  • Claudio Vidal
Original Article

Abstract

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.

Keywords

Gravitational attraction of a particle by a homogeneous annulus disk Symmetries Dynamics Circular Solutions 

Mathematics Subject Classifications

70F15 37N05 

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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de PernambucoRecife-PeBrasil
  2. 2.Departamento de Matemática, Facultad de CienciasUniversidad del Bio BioConcepción, VIII-RegiónChile

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