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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/123692
Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem
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The Augmented Hill Three-Body problem is an extension of the classical Hill problem that, among other applications, has been used to model the motion of a solar sail around an asteroid. This model is a 3 degrees of freedom (3DoF) Hamiltonian system that depends on four parameters. This paper describes the bounded motions (periodic orbits and invariant tori) in an extended neighbourhood of some of the equilibrium points of the model. An interesting feature is the existence of equilibrium points with a 1:1 resonance, whose neighbourhood we also describe. The main tools used are the computation of periodic orbits (including their stability and bifurcations), the reduction of the Hamiltonian to centre manifolds at equilibria, and the numerical approximation of invariant tori. It is remarkable how the combination of these techniques allows the description of the dynamics of a 3DoF Hamiltonian system.
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FARRÉS BASIANA, Ariadna, JORBA I MONTE, Àngel and MONDELO GONZÁLEZ, José María. Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem. Celestial Mechanics and Dynamical Astronomy. 2017. Vol. 129, num. 25-55. ISSN 0923-2958. [consulted: 13 of June of 2026]. Available at: https://hdl.handle.net/2445/123692