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

Research output: Contribution to journal › Article › peer-review

55 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	73-123
Number of pages	51
Journal	Numerische Mathematik
Volume	130
Issue number	1
DOIs	https://doi.org/10.1007/s00211-014-0659-4
Publication status	Published - 1 May 2015

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 7 Affordable and Clean Energy

Keywords

53D05
65P10
74B20
74H15

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10.1007/s00211-014-0659-4

Cite this

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abstract = "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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AU - Gay-Balmaz, F.

AU - Leyendecker, S.

AU - Ober-Blöbaum, S.

AU - Ratiu, T. S.

AU - Weinand, Y.

PY - 2015/5/1

Y1 - 2015/5/1

N2 - 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.

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.

KW - 53D05

KW - 65P10

KW - 74B20

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Discrete variational Lie group formulation of geometrically exact beam dynamics

Abstract

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Keywords

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