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Discrete mechanics and variational integrators

  • J. E. Marsden (a1) and M. West (a1)

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.

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Discrete mechanics and variational integrators

  • J. E. Marsden (a1) and M. West (a1)

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