Abstract:

It is natural to look forward to those discrete systems which

preserve as much as possible the intrinsic properties of the

continuous system" (Feng Kang 1985).

Discrete mechanics permits the construction of geometric integrators

for Lagrangian mechanical systems. Moreover, it is possible to extend

this construction to reduced Lagrangian systems using the Lie

groupoid theory. Therefore, we will obtain geometric integrators for

Euler-Poincare equations, Lagrange-Poincare equations...with

remarkable geometric properties.

Finally, we will extend these constructions to the case of

nonholonomic constraints.