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Topology and bifurcations in nonholonomic mechanics

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journal contribution
posted on 11.11.2015, 13:22 by Ivan A. Bizyaev, Alexey Bolsinov, Alexey V. Borisov, Ivan S. Mamaev
This paper develops topological methods for qualitative analysis of the behavior of nonholonomic dynamical systems. Their application is illustrated by considering a new integrable system of nonholonomic mechanics, called a nonholonomic hinge. Although this system is nonholonomic, it can be represented in Hamiltonian form with a Lie–Poisson bracket of rank two. This Lie–Poisson bracket is used to perform stability analysis of fixed points. In addition, all possible types of integral manifolds are found and a classification of trajectories on them is presented.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

Volume

25

Issue

10

Pages

? - ? (21)

Citation

BIZYAEV, I.A. ... et al, 2015. Topology and bifurcations in nonholonomic mechanics. International Journal of Bifurcation and Chaos, 25 (10), 1530028.

Publisher

© World Scientific Publishing Company

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

Notes

Preprint of an article published in International Journal of Bifurcation and Chaos, 25 (10), 1530028, DOI: 10.1142/S0218127415300281. © World Scientific Publishing Company. http://www.worldscientific.com/worldscinet/ijbc

ISSN

0218-1274

Language

en

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