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.
Original language | English (US) |
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Pages (from-to) | 357-514 |
Number of pages | 158 |
Journal | Acta Numerica |
Volume | 10 |
DOIs | |
State | Published - May 1 2001 |
Externally published | Yes |
ASJC Scopus subject areas
- Numerical Analysis
- General Mathematics