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Discrete mechanics and variational integrators. (English) Zbl 1123.37327
Summary: 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.

MSC:
37M15Symplectic integrators (dynamical systems)
37J05Relations of dynamical systems with symplectic geometry and topology
65P10Numerical methods for Hamiltonian systems including symplectic integrators
70-08Computational methods (mechanics of particles and systems)
70H05Hamilton’s equations