FoCM 2014 conference
Workshop B4 - Geometric Integration and Computational Mechanics
December 16, 15:00 ~ 15:25 - Room B11
Reduction by stages of discrete mechanical systems: a discrete Lagrange-Poincare approach
Javier Fernandez
Instituto Balseiro, Argentina - jfernand@ib.edu.ar
Discrete mechanical systems (DMS) are a type of dynamical system whose trajectories are the extrema of a discrete variational problem determined by a discrete Lagrangian function. Those trajectories provide interesting numerical integrators. Under fairly reasonable conditions symmetric DMSs can be reduced, that is, a new dynamical system can be constructed whose dynamics captures the essential features of the original one. In some cases, it is convenient to perform the reduction procedure in more than one step, what is generically known as reduction by stages. Unfortunately, the reduced systems are usually not DMSs so that a second reduction may not be possible within the standard DMS theory.
In this talk we expand the family of DMSs to a new family, the discrete Lagrange-Poincare systems, that is closed under reduction. As a consequence, the reduction by stages can be satisfactorily performed.