Discrete mechanics and variational integrators

2001/05/01 by Jerrold E. Marsden, Matthew West · 15 citations
Mathematics · Engineering · Physics and Astronomy · #Numerical methods for differential equations #Advanced Numerical Methods in Computational Mathematics #Model Reduction and Neural Networks

paper · doi:10.1017/s096249290100006x

openalex publication_date 2001/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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.

Citations

• The chaotic rotation of Hyperion
• Construction of higher order symplectic integrators

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