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arXiv · 1705.01866

Integrable discretization and deformation of the nonholonomic Chaplygin ball

A. V. Tsiganov
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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.

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A. V. Tsiganov. 2017-05-04. Integrable discretization and deformation of the nonholonomic Chaplygin ball. https://doi.org/10.1134/s1560354717040025

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