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    Topology and Bifurcations in Nonholonomic Mechanics

    2015, Vol. 11, No. 4, pp.  735–762

    Author(s): Bizyaev I. A., Bolsinov A. V., Borisov A. V., Mamaev I. S.

    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, Poisson bracket, stability
    Citation: Bizyaev I. A., Bolsinov A. V., Borisov A. V., Mamaev I. S., Topology and Bifurcations in Nonholonomic Mechanics, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 4, pp.  735–762
    DOI:10.20537/nd1504008


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