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Title: Topology and bifurcations in nonholonomic mechanics
Authors: Bizyaev, Ivan A.
Bolsinov, Alexey V.
Borisov, Alexey V.
Mamaev, Ivan S.
Keywords: Nonholonomic hinge
Topology
Bifurcation diagram
Tensor invariants
Poisson bracket
Stability
Issue Date: 2015
Publisher: © World Scientific Publishing Company
Citation: BIZYAEV, I.A. ... et al, 2015. Topology and bifurcations in nonholonomic mechanics. International Journal of Bifurcation and Chaos, 25 (10), 1530028.
Abstract: 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.
Description: 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
Version: Submitted for publication
DOI: 10.1142/S0218127415300281
URI: https://dspace.lboro.ac.uk/2134/19383
Publisher Link: http://dx.doi.org/10.1142/S0218127415300281
ISSN: 0218-1274
Appears in Collections:Published Articles (Maths)

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