Discrete Mechanics and Variational Integrators
Marsden, J. E. and M. West
Acta Numerica, 357-514.
Abstract:
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.