Geodesic
Topology and bifurcations in nonholonomic mechanics
Russian journal of nonlinear dynamics, Tome 11 (2015) no. 4, pp. 735-762

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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 2. 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.
Keywords: nonholonomic hinge, topology, bifurcation diagram, tensor invariants, stability.
Mots-clés : Poisson bracket 
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     title = {Topology and bifurcations in nonholonomic mechanics},
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I. A. Bizyaev; A. V. Bolsinov; A. V. Borisov; I. S. Mamaev. Topology and bifurcations in nonholonomic mechanics. Russian journal of nonlinear dynamics, Tome 11 (2015) no. 4, pp. 735-762. http://geodesic.mathdoc.fr/item/ND_2015_11_4_a7/