A Caltech Library Service

Discrete mechanics and variational integrators

Marsden, J. E. and West, M. (2001) Discrete mechanics and variational integrators. Act Numerica, 10 (5). pp. 357-514.

PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


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.

Item Type:Article
Related URLs:
URLURL TypeDescription
Additional Information:© Cambridge University Press 2001. We thank many colleagues for their explicit and implicit help in putting this article together, including Razvan Fetecau, Arieh Iserles, Sameer Jalnapurkar, Couro Kane, Melvin Leok, Adrian Lew, Ben Leimkuhler, Michael Ortiz, George Patrick, Sergey Pekarsky, Reinout Quispel, Sebastian Reich, Steve Shkoller, and Robert Skeel. This work was supported by the California Institute of Technology and NSF/KDI grant ATM-9873133, as well as NSF grant DMS-9874082.
Funding AgencyGrant Number
Record Number:CaltechAUTHORS:20100910-151730942
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19876
Deposited By: Ruth Sustaita
Deposited On:16 Sep 2010 20:59
Last Modified:26 Dec 2012 12:24

Repository Staff Only: item control page