On action-angle coordinates and the Poincaré coordinates

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 “∮ γ p dq ”. The second section...

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Bibliographic Details
Published in:Regular & chaotic dynamics 2013, Vol.18 (6), p.703-718
Main Author: Fejoz, Jacques
Format: Article
Language:English
Subjects:
Dynamical Systems
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Symplectic Geometry
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Summary: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 “∮ γ 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.
ISSN:1560-3547
1560-3547
1468-4845
DOI:10.1134/S1560354713060105