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Integrable discretization and deformation of the nonholonomic Chaplygin ball (1705.01866v1)
Published 4 May 2017 in nlin.SI, math-ph, math.DS, and 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.
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