Topology and bifurcations in nonholonomic mechanics
journal contributionposted on 11.11.2015, 13:22 by Ivan A. Bizyaev, Alexey Bolsinov, Alexey V. Borisov, Ivan S. Mamaev
Any type of content formally published in an academic journal, usually following a peer-review process.
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.
- Mathematical Sciences