An overview of variational integrators
A. Lew, J. E. Marsden, M. Ortiz, and M. West
in Finite Element Methods: 1970's and Beyond, 98-115, CIMNE, ISBN: 84-95999-49-8, 2004.
The purpose of this paper is to survey some recent advances in variational integrators for both finite dimensional mechanical systems as well as continuum mechanics. These advances include the general development of discrete mechanics, applications to dissipative systems, collisions, spacetime integration algorithms, AVI's (Asynchronous Variational Integrators), as well as reduction for discrete mechanical systems. To keep the article within the set limits, we will only treat each topic briefly and will not attempt to develop any particular topic in any depth. We hope, nonetheless, that this paper serves as a useful guide to the literature as well as to future directions and open problems in the subject.
Full text: LeMaOrWe2004.pdf