Variational integrators, the Newmark scheme, and dissipative systems

M. West, C. Kane, J. E. Marsden and M. Ortiz

in EQUADIFF 99 (Vol. 2): Proceedings of the International Conference on Differential Equations, B. Fiedler, K. Gröger and J. Sprekels, editors, pages 1009-1011, 2000, World Scientific, ISBN 981-02-4359-6 (set), ISBN 981-02-4989-6 (Vol. 2)

Variational methods are a class of symplectic-momentum integrators for ODEs. Using these schemes, it is shown that the classical Newmark algorithm is structure preserving in a non-obvious way, thus explaining the observed numerical behavior. Modifications to variational methods to include forcing and dissipation are also proposed, extending the advantages of structure preserving integrators to non-conservative systems.

Full text: WeKaMaOr2000.pdf