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Invariant Manifolds of Spatial Restricted Three-Body Problems: the Lunar Case

In: New Advances in Celestial Mechanics and Hamiltonian Systems

Author

Listed:
  • Jesús Palacián

    (Universidad Pública de Navarra, Departamento de Matemática e Informática)

  • Patricia Yanguas

    (Universidad Pública de Navarra, Departamento de Matemática e Informática)

Abstract

New periodic orbits of three-dimensional restricted three-body problems are computed using a technique based on normal forms calculations. The system is formulated as a Hamiltonian perturbation of the two-body problem. Up to a certain order of approximation, the departure Hamiltonian is transformed into simpler ones, by extending the integrals of its principal part to the whole systems using different Lie transformations. Therefore, the resulting normal forms are reduced through invariant theory and the corresponding relative equilibria are determined. Finally, the transformations are inverted to recover the associated higher-dimensional invariant sets of the initial Hamiltonian.

Suggested Citation

  • Jesús Palacián & Patricia Yanguas, 2004. "Invariant Manifolds of Spatial Restricted Three-Body Problems: the Lunar Case," Springer Books, in: J. Delgado & E. A. Lacomba & J. Llibre & E. Pérez-Chavela (ed.), New Advances in Celestial Mechanics and Hamiltonian Systems, pages 199-224, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-9058-7_13
    DOI: 10.1007/978-1-4419-9058-7_13
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