On Action-angle coordinates and the Poincaré Coordinates
Féjoz, Jacques (2013), On Action-angle coordinates and the Poincaré Coordinates, Regular and Chaotic Dynamics, 18, 6, p. 708-723. http://dx.doi.org/10.1134/S1560354713060105
TypeArticle accepté pour publication ou publié
Journal nameRegular and Chaotic Dynamics
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Abstract (EN)This article is a review of two related classical topics of Hamiltonian systems and celestial mechanics. The first section deals with the existence and construction of action-angle coordinates, which we describe emphasizing the role of the natural adiabatic invariants ''$\oint_\gamma p\, dq$''. The second section is the construction and properties of the Poincaré coordinates in the Kepler problem, adapting the principles of the former section, in an attempt to use known first integrals more directly than Poincaré did.
Subjects / Keywordsperturbation theory; integrability; first integral; planetary problem; Poincaré coordinates; two-body problem; Kepler problem; adiabatic invariants; Liouville-Arnold theorem; action-angle coordinates; Lagrangian fibration; Hamiltonian system
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Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem Féjoz, Jacques; Guardia, Marcel; Kaloshin, Vadim; Roldán, Pablo (2016) Article accepté pour publication ou publié