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Zbl 1123.37327
Marsden, Jerrold E.; West, M.
Discrete mechanics and variational integrators. (English)
[J] Acta Numerica 10, 357-514 (2001). ISSN 0962-4929; ISSN 1474-0508/e

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 2000:: *37M15 Symplectic integrators
37J05 Relations with symplectic geometry and topology
65P10 Hamiltonian systems including symplectic integrators
70-08 Computational methods (mechanics of particles and systems)
70H05 Hamilton's equations

Cited in: Zbl 1260.70011 Zbl 1231.65007

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