From the circular to the spatial elliptic restricted three-body problem

  • J. F. Palacián
  • P. Yanguas
Conference paper


We deal with the study of the spatial restricted three-body problem in the case where the small particle is far from the primaries, that is, the so-called comet case. We consider the circular problem, apply double averaging and compute the relative equilibria of the reduced system. It appears that, in the circular problem, we find not only part of the equilibria existing in the elliptic case, but also new ones. These critical points are in correspondence with periodic and quasiperiodic orbits and invariant tori of the non-averaged Hamiltonian. We explain carefully the transition between the circular and the elliptic problems. Moreover, from the relative equilibria of elliptic type, we obtain invariant 3-tori of the original system.


Spatial restricted three-body problem Averaging Relative equilibria Stability Bifurcations Invariant tori 


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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • J. F. Palacián
    • 1
  • P. Yanguas
    • 1
  1. 1.Departamento de Matemática e InformáticaUniversidad Pública de NavarraPamplonaSpain

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