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