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Discrete mechanics and variational integrators

Published online by Cambridge University Press:  09 January 2003

J. E. Marsden  and
M. West
J. E. Marsden
Affiliation:
Control and Dynamical Systems 107-81, Caltech, Pasadena, CA 91125-8100, USA E-mail: marsden@cds.caltech.edu, mwest@cds.caltech.edu
M. West
Affiliation:
Control and Dynamical Systems 107-81, Caltech, Pasadena, CA 91125-8100, USA E-mail: marsden@cds.caltech.edu, mwest@cds.caltech.edu
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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.

Type
Research Article
Information
Acta Numerica , Volume 10 , May 2001 , pp. 357 - 514
Copyright
© Cambridge University Press 2001

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