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Numerische Mathematik

, Volume 130, Issue 1, pp 73–123 | Cite as

Discrete variational Lie group formulation of geometrically exact beam dynamics

  • F. Demoures
  • F. Gay-Balmaz
  • S. Leyendecker
  • S. Ober-BlöbaumEmail author
  • T. S. Ratiu
  • Y. Weinand
Article

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.

Mathematics Subject Classification

53D05 65P10 74B20 74H15 

Notes

Acknowledgments

FD, TSR, and YW were partially supported by Swiss NSF Grant 200020-137704. TSR was partially supported by the government grant of the Russian Federation for support of research projects implemented by leading scientists, Lomonosov Moscow State University under the agreement No. 11.G34.31.0054. FGB was partially supported by a “Projet Incitatif de Recherche” contract from the Ecole Normale Supérieure de Paris and by the Swiss NSF Grant 200021-126802. SO was partially supported by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster “Intelligent Technical Systems OstWestfalenLippe” (it’s OWL) and managed by the Project Management Agency Karlsruhe (PTKA).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • F. Demoures
    • 1
  • F. Gay-Balmaz
    • 2
  • S. Leyendecker
    • 3
  • S. Ober-Blöbaum
    • 4
    Email author
  • T. S. Ratiu
    • 1
  • Y. Weinand
    • 5
  1. 1.Section de MathématiquesÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Laboratoire de Météorologie DynamiqueCNRS/École Normale Supérieure de ParisParisFrance
  3. 3.Department of Mechanical EngineeringUniversity of Erlangen-NurembergErlangenGermany
  4. 4.Department of MathematicsUniversity of Paderborn PaderbornGermany
  5. 5.Civil Engineering InstituteÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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