Integrable discretization and deformation of the nonholonomic Chaplygin ball

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.

14 pages, LaTeX with AMS fonts

References in corpus (6)

• Simultaneous separation for the Neumann and Chaplygin systems
• New bi-Hamiltonian systems on the plane
• Backlund transformations and divisor doubling
• Bäcklund transformations for the nonholonomic Veselova system
• A Discretization of the Nonholonomic Chaplygin Sphere Problem
• Integrable geodesic flows on Riemannian manifolds: Construction and Obstructions

Cited by in corpus (8)

• Backlund transformations and divisor doubling
• Hamiltonization and separation of variables for Chaplygin ball on a rotating plane
• Elliptic curve arithmetic and superintegrable systems
• On exact discretization of the cubic-quintic Duffing oscillator
• Discretization and superintegrability all rolled into one
• Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere
• On discretization of the Euler top
• Duffing oscillator and elliptic curve cryptography