2010/11/16 by David Iglesias, D. Iglesias, Iglesias, D. +9
Engineering · Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations #math-ph #math.DG #math.MP
paper · pdf · doi:10.48550/arxiv.1011.3724
22 pages, several examples have been included, abstract and introduction have been modified, added references
openalex publication_date 2010/11/16 · arxiv created 2011/03/31 · arxiv updated 2011/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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^*G. Other situations include finite difference methods for time-dependent linear differential-algebraic equations and discrete nonholonomic Lagrangian systems, as particular examples.