Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-23T19:07:10.197Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected], [email protected]
M. West
Affiliation:
Control and Dynamical Systems 107-81, Caltech, Pasadena, CA 91125-8100, USA E-mail: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)