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November 2009 Bifurcation diagrams and critical subsystems of the Kowalevski gyrostat in two constant fields
Mikhail P. Kharlamov
Hiroshima Math. J. 39(3): 327-350 (November 2009). DOI: 10.32917/hmj/1257544212

Abstract

The Kowalevski gyrostat in two constant fields is known as the unique example of an integrable rigid body problem described by the Hamiltonian system with three degrees of freedom not reducible to a family of systems in fewer dimensions. The practical explicit integration of this system can hardly be obtained by the existing techniques. Then the challenging problem becomes to fulfill the qualitative investigation based on the study of the Liouville foliation of the phase space. As the first approach to topological analysis of this system we find the stratified critical set of the momentum map; this set is represented as the union of manifolds with induced almost Hamiltonian systems having less than three degrees of freedom. We obtain the equations of the bifurcation diagram in three-dimensional space. These equations have the form convenient for the classification of the bifurcation sets arising on 5-dimensional iso-energetic levels.

Citation

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Mikhail P. Kharlamov. "Bifurcation diagrams and critical subsystems of the Kowalevski gyrostat in two constant fields." Hiroshima Math. J. 39 (3) 327 - 350, November 2009. https://doi.org/10.32917/hmj/1257544212

Information

Published: November 2009
First available in Project Euclid: 6 November 2009

zbMATH: 1355.70009
MathSciNet: MR2569008
Digital Object Identifier: 10.32917/hmj/1257544212

Subjects:
Primary: 70E17
Secondary: 70G40, 70H06

Rights: Copyright © 2009 Hiroshima University, Mathematics Program

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Vol.39 • No. 3 • November 2009
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