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.
Partial Support has been given by Spanish Ministry of Education and Science (DGCY Project # ESP99-1074-C02-01)
Partial Support has been given by Spanish Ministry of Education and Science (DGCY Project # PB98-1576)
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Palacián, J., Yanguas, P. (2004). Invariant Manifolds of Spatial Restricted Three-Body Problems: the Lunar Case. In: Delgado, J., Lacomba, E.A., Llibre, J., Pérez-Chavela, E. (eds) New Advances in Celestial Mechanics and Hamiltonian Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9058-7_13
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DOI: https://doi.org/10.1007/978-1-4419-9058-7_13
Publisher Name: Springer, Boston, MA
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