On action-angle coordinates and the Poincaré coordinates (Q2449297)
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| Language | Label | Description | Also known as |
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| English | On action-angle coordinates and the Poincaré coordinates |
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On action-angle coordinates and the Poincaré coordinates (English)
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7 May 2014
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The first part of this article briefly sketches the work done so far on action-angle coordinates, and then proves their existence along the lines of [\textit{J. J. Duistermaat}, Commun. Pure Appl. Math. 33, 687--706 (1980; Zbl 0439.58014); \textit{V. Guillemin} and \textit{S. Sternberg}, Symplectic techniques in physics. Reprinted with corrections. Cambridge etc.: Cambridge University Press (1990; Zbl 0734.58005)]. In the second part, the author constructs Poincaré coordinates in the Kepler problem using similar principles.
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Hamiltonian system
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Lagrangian fibration
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action-angle coordinates
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Liouville-Arnold theorem
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adiabatic invariants
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Kepler problem
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two-body problem
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Poincaré coordinates
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planetary problem
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first integral
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integrability
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perturbation theory
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