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 a new geodesic flow on the unit two-dimensional sphere whose additional integrals of motion are polynomials in the momenta of fourth order.
Keywords:
nonholonomic systems, Abel quadratures, arithmetic of divisors
Citation:
Tsiganov A. V., Integrable Discretization and Deformation of the Nonholonomic Chaplygin Ball, Regular and Chaotic Dynamics,
2017, Volume 22, Number 4,
pp. 353-367