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Discrete mechanics and variational integrators

Marsden, J. E. and West, M. (2001) Discrete mechanics and variational integrators. Act Numerica, 10 (5). pp. 357-514. doi:10.1017/S096249290100006X.

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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.

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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.
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Issue or Number:5
Record Number:CaltechAUTHORS:20100910-151730942
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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:08 Nov 2021 23:55

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