Discrete variational Lie group formulation of geometrically exact beam dynamics

F. Demoures; F. Gay-Balmaz; S. Leyendecker; S. Ober-Blöbaum; T. S. Ratiu; Y. Weinand

doi:10.1007/s00211-014-0659-4

Discrete variational Lie group formulation of geometrically exact beam dynamics

F. Demoures
, F. Gay-Balmaz
, S. Leyendecker
, S. Ober-Blöbaum
, T. S. Ratiu
, Y. Weinand

Section de Mathématiques
ENAC-IIC-GEL
Institute of Applied Mechanics
Friedrich-Alexander University (FAU) Erlangen-Nürnberg and Universitätsklinikum Erlangen
Department of Mathematics
University Paderborn
Institute of Civil Engineering

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55 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	73-123
Nombre de pages	51
journal	Numerische Mathematik
Volume	130
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s00211-014-0659-4
état	Publié - 1 mai 2015

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10.1007/s00211-014-0659-4

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AU - Ratiu, T. S.

AU - Weinand, Y.

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AB - 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.

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Discrete variational Lie group formulation of geometrically exact beam dynamics

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