Discrete mechanics and variational integrators

J. E. Marsden, M. West

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)357-514
Number of pages158
JournalActa Numerica
StatePublished - May 1 2001
Externally publishedYes

ASJC Scopus subject areas

  • Numerical Analysis
  • General Mathematics


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