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Published in:
2015 | OriginalPaper | Chapter
Quasi-Periodic Almost-Collision Motions in the Spatial Three-Body Problem
Authors : Jesús F. Palacián, Flora Sayas, Patricia Yanguas
Published in: Extended Abstracts Spring 2014
Publisher: Springer International Publishing
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Abstract
We deal with the spatial three-body problem in the various regimes where the Hamiltonian is split as the sum of two Keplerian systems plus a small perturbation. This is a region of the phase space \(T^{{\ast}}\mathbb{R}^{6}\) where the perturbation is small [3], the so called perturbing region \(\mathcal{P}_{\varepsilon,n}\). In particular, we prove the existence of quasi-periodic motions where the inner particles describe bounded near-rectilinear trajectories whereas the outer particle follows an orbit lying near the invariable plane. These motions fill in five-dimensional invariant tori. Moreover, the inner particles move in orbits either near an axis perpendicular to the invariable plane or near the invariable plane.