Abstract:
Numerous orbits exist in the solar system or in astrodynamic with very peculiar motions. Their common feature is that they consist of two moons or satellites around a central attractor which are in co-orbital motions with almost equal semi major axes. In spite of analytical theories and numerical investigations developed to describe their long-term dynamics, so far very few rigorous long-time stability results in this setting have been obtained even in the restricted three-body problem.
Actually, the nearly equal semi major axes of the moons implies also nearly equal orbital periods (or 1:1 mean motion resonance), and this last point prevent the application of the usual Hamiltonian perturbation theory for the three body problem.
Adapting the idea of Arnol'd to a resonant case, hence by an application of KAM theory to the planar three-body problem, we provide a rigorous proof of existence of a large measure set of Lagrangian invariant tori supporting quasi-periodic co-orbital motions, hence stable over infinite times.
In collaboration with L. Biasco, L. Chierchia, A. Pousse, P. Robutel.
Il seminario si svolgerà in presenza presso il Dipartimento di Matematica e Fisica, Lungotevere Dante 376, aula M1.
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