This article is cited in 13 papers

On Action-angle Coordinates and the Poincaré Coordinates

Jacques Féjoz<sup>ab

a</sup> Université Paris-Dauphine – CEREMADE (UMR 7534), Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
^b Observatoire de Paris – IMCCE (UMR 8028), 77 avenue Denfert-Rochereau, 75014 Paris, France

Abstract: 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.

Keywords: Hamiltonian system, Lagrangian fibration, action-angle coordinates, Liouville–Arnold theorem, adiabatic invariants, Kepler problem, two-body problem, Poincaré coordinates, planetary problem, first integral, integrability, perturbation theory.

MSC: 01-01, 37-03, 37C80, 37J35, 70-03, 70H06, 70H15

Received: 30.10.2013
Accepted: 11.11.2013

Language: English

DOI: 10.1134/S1560354713060105

Bibliographic databases:

• 
• 
•