Integrable discretization and deformation of the nonholonomic Chaplygin ball
Exactly Solvable and Integrable Systems
2018-03-06 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
The rolling of a dynamically balanced ball on a horizontal rough table without slipping was described by Chaplygin using Abel quadratures. We discuss integrable discretizations and deformations of this nonholonomic system using the same Abel quadratures. As a by-product one gets new geodesic flow on the unit two-dimensional sphere whose additional integrals of motion are polynomials in the momenta of fourth order.
Keywords
Cite
@article{arxiv.1705.01866,
title = {Integrable discretization and deformation of the nonholonomic Chaplygin ball},
author = {A. V. Tsiganov},
journal= {arXiv preprint arXiv:1705.01866},
year = {2018}
}
Comments
14 pages, LaTeX with AMS fonts