Discrete dynamics in implicit form

Details Discrete dynamics in implicit form Discrete dynamics in implicit form

2010-11-16

arxiv.org/abs/1011.3724v2

Mathematics

Differential Geometry

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

Scientific paper

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.

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