English

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