Hamiltonization of Elementary Nonholonomic Systems
Exactly Solvable and Integrable Systems
2016-01-06 v1
Abstract
In this paper, we develop the Chaplygin reducing multiplier method; using this method, we obtain a conformally Hamiltonian representation for three nonholonomic systems, namely, for the nonholonomic oscillator, for the Heisenberg system, and for the Chaplygin sleigh. Furthermore, in the case of an oscillator and the nonholonomic Chaplygin sleigh, we show that the problem reduces to the study of motion of a mass point (in a potential field) on a plane and, in the case of the Heisenberg system, on the sphere. Moreover, we consider an example of a nonholonomic system (suggested by Blackall) to which one cannot apply the reducing multiplier method.
Cite
@article{arxiv.1601.00884,
title = {Hamiltonization of Elementary Nonholonomic Systems},
author = {Ivan A. Bizyaev and Alexey V. Borisov and Ivan S. Mamaev},
journal= {arXiv preprint arXiv:1601.00884},
year = {2016}
}