The invariant manifold structure of the spatial Hill's problem

G. Gómez; M. Marcote; J. M. Mondelo

doi:https://doi.org/10.1080/14689360412331313039

The invariant manifold structure of the spatial Hill's problem

G. Gómez, M. Marcote, J. M. Mondelo

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

36 Citations (Scopus)

Abstract

The paper studies the invariant manifolds of the spatial Hill's problem associated to the two liberation points. A combination of analytical and numerical tools allow the normalization of the Hamiltonian and the computation of periodic and quasi-periodic (invariant tori) orbits. With these tools, it is possible to give a complete description of the center manifolds, association to the liberation points, for a large set of energy values. A systematic exploration of the homoclinic and heteroclinic connections between the center manifolds of the liberation points is also given.

Original language	English
Pages (from-to)	115-147
Journal	Dynamical Systems
Volume	20
DOIs	https://doi.org/10.1080/14689360412331313039
Publication status	Published - 1 Mar 2005

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N2 - The paper studies the invariant manifolds of the spatial Hill's problem associated to the two liberation points. A combination of analytical and numerical tools allow the normalization of the Hamiltonian and the computation of periodic and quasi-periodic (invariant tori) orbits. With these tools, it is possible to give a complete description of the center manifolds, association to the liberation points, for a large set of energy values. A systematic exploration of the homoclinic and heteroclinic connections between the center manifolds of the liberation points is also given.

AB - The paper studies the invariant manifolds of the spatial Hill's problem associated to the two liberation points. A combination of analytical and numerical tools allow the normalization of the Hamiltonian and the computation of periodic and quasi-periodic (invariant tori) orbits. With these tools, it is possible to give a complete description of the center manifolds, association to the liberation points, for a large set of energy values. A systematic exploration of the homoclinic and heteroclinic connections between the center manifolds of the liberation points is also given.

U2 - https://doi.org/10.1080/14689360412331313039

DO - https://doi.org/10.1080/14689360412331313039

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EP - 147

JO - Dynamical Systems

JF - Dynamical Systems

SN - 1468-9367

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