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Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?

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journal contribution
posted on 2015-06-16, 13:39 authored by Alexey BolsinovAlexey Bolsinov, A.A. Kilin, A.O. Kazakov
The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy is given for the rolling ellipsoid of revolution problem in two cases, namely, on a smooth and on a rough plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no difference between the two systems, and thus disprove the conjecture by Cushman and Duistermaat stating that the topological monodromy gives a topological obstruction for Hamiltonization of the rolling ellipsoid of revolution on a rough plane.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

JOURNAL OF GEOMETRY AND PHYSICS

Volume

87

Pages

61 - 75 (15)

Citation

BOLSINOV, A.V., KILIN, A.A. and KAZAKOV, A.O., 2015. Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra? Journal of Geometry and Physics, 87, pp.61-75

Publisher

© Elsevier

Version

  • SMUR (Submitted Manuscript Under Review)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2015

ISSN

0393-0440

Language

  • en