Discrete dynamics in implicit form

Abstract

A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie groupoid $G$ may be described in terms of Lagrangian implicit difference equations of the corresponding cotangent groupoid $T^{\ast }G$. Other situations include finite difference methods for time-dependent linear differential-algebraic equations and discrete nonholonomic Lagrangian systems, as particular examples.

arXiv comment22 pages, several examples have been included, abstract and introduction have been modified, added references

References in corpus (3)

• Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids
• Discrete Hamilton-Pontryagin mechanics and generating functions on Lie groupoids
• A Discretization of the Nonholonomic Chaplygin Sphere Problem

Cited by in corpus (1)

• Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings