Discrete Nonholonomic LL Systems on Lie Groups

Abstract

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.

32 pages, 13 figures

References in corpus (3)

• Discrete Euler-Poincaré and Lie-Poisson Equations
• Explicit Lie-Poisson integration and the Euler equations
• Geometry and integrability of Euler-Poincare-Suslov equations

Cited by in corpus (12)

• Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
• Momentum and energy preserving integrators for nonholonomic dynamics
• Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations
• Geometric discrete analogues of tangent bundles and constrained Lagrangian systems
• Feedback Integrators for Nonholonomic Mechanical Systems
• Accelerated Optimization on Riemannian Manifolds via Discrete Constrained Variational Integrators
• Variational integrators for interconnected Lagrange-Dirac systems
• Nonassociative analogs of Lie groupoids
• Discrete mechanics on unitary octonions
• The geometric discretisation of the Suslov problem: a case study of consistency for nonholonomic integrators
• On the Cartan Model of the Canonical Vector Bundles over Grassmannians
• Hirota-Kimura Type Discretization of the Classical Nonholonomic Suslov Problem