Discrete mechanics and variational integrators
J. E. Marsden and M. West
Acta Numerica 10, 357-514, 2001.
This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem. The approach also allows us to include forces, dissipation and constraints in a natural way. Amongst the many specific schemes treated as examples, the Verlet, SHAKE, RATTLE, Newmark, and the symplectic partitioned Runge-Kutta schemes are presented.
Full text: MaWe2001.pdf