Discrete variational Lie group formulation of geometrically exact beam dynamics

F. Demoures (1) , F. Gay-Balmaz (2) , S. Leyendecker (3) , S. Ober-Blöbaum (4) , T. S. Ratiu (1) , Y. Weinand (1)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 LMD - Laboratoire de Météorologie Dynamique (UMR 8539)
3 FAU - Friedrich-Alexander Universität Erlangen-Nürnberg = University of Erlangen-Nuremberg
4 University of Paderborn

The goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics, by using a Lie group variational integrator. Both spatial and temporal discretization are implemented in a geometry preserving manner. The resulting scheme preserves both the discrete momentum maps and symplectic structures, and exhibits almost-perfect energy conservation. Comparisons with existing numerical schemes are provided and the convergence behavior is analyzed numerically.

Domaines: Mathématiques [math]

F. Demoures, F. Gay-Balmaz, S. Leyendecker, S. Ober-Blöbaum, T. S. Ratiu, et al.. Discrete variational Lie group formulation of geometrically exact beam dynamics. Numerische Mathematik, 2015, 130 (1), pp.73-123. ⟨10.1007/s00211-014-0659-4⟩. ⟨hal-01396186⟩