Astrophysics and Space Science

, Volume 338, Issue 1, pp 23–33 | Cite as

Computation of families of periodic orbits and bifurcations around a massive annulus

  • E. TresacoEmail author
  • A. Elipe
  • A. Riaguas
Original Article


This paper studies the main features of the dynamics around a planar annular disk. It is addressed an appropriated closed expression of the gravitational potential of a massive disk, which overcomes the difficulties found in previous works in this matter concerning its numerical treatment. This allows us to define the differential equations of motion that describes the motion of a massless particle orbiting the annulus. We describe the computation methods proposed for the continuation of uni-parametric families of periodic orbits, these algorithms have been applied to analyze the dynamics around a massive annulus by means of a description of the main families of periodic orbits found, their bifurcations and linear stability.


Periodic orbits Bifurcation of families Solid annulus disk potential 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Centro Universitario de la DefensaZaragozaSpain
  2. 2.Grupo de Mecánica Espacial—IUMAUniversidad de ZaragozaZaragozaSpain
  3. 3.Dept. de Matemática AplicadaUniversidad de ValladolidSoriaSpain

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