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Discrete geometric mechanics for variational time integrators

Stern, Ari and Desbrun, Mathieu (2006) Discrete geometric mechanics for variational time integrators. In: SIGGRAPH '06 ACM SIGGRAPH 2006 Courses. ACM , New York, NY, pp. 75-80. ISBN 1-59593-364-6. https://resolver.caltech.edu/CaltechAUTHORS:20161220-144529319

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Abstract

In this chapter, we present a geometric--instead of a traditional numerical-analytic--approach to the problem of time integration. Geometry at its most abstract is the study of symmetries and their associated invariants. Variational approaches based on such notions are commonly used in geometric modeling and discrete differential geometry. Here we will treat mechanics in a similar way. Indeed, the very essence of a mechanical system is characterized by its symmetries and invariants. Thus preserving these symmetries and invariants (e.g., certain momenta) into the discrete computational setting is of paramount importance if one wants discrete time integration to properly capture the underlying continuous motion. Motivated by the well-known variational and geometric nature of most dynamical systems, we review the use of discrete variational principles as a way to derive robust, and accurate time integrators.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/1185657.1185669DOIArticle
http://dl.acm.org/citation.cfm?doid=1185657.1185669PublisherArticle
ORCID:
AuthorORCID
Stern, Ari0000-0002-9493-268X
Desbrun, Mathieu0000-0003-3424-6079
Additional Information:© 2006 ACM.
Record Number:CaltechAUTHORS:20161220-144529319
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161220-144529319
Official Citation:Ari Stern and Mathieu Desbrun. 2006. Discrete geometric mechanics for variational time integrators. In ACM SIGGRAPH 2006 Courses (SIGGRAPH '06). ACM, New York, NY, USA, 75-80. DOI=http://dx.doi.org/10.1145/1185657.1185669
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73004
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:20 Dec 2016 23:23
Last Modified:09 Mar 2020 13:19

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