Discrete Lagrangian mechanics and geometrically exact Cosserat rods
Jung P, Leyendecker S, Linn J, Ortiz M (2009)
Publication Language: English
Publication Type: Conference contribution, Conference Contribution
Publication year: 2009
Pages Range: dvd, 14 Seiten
Conference Proceedings Title: Proceedings of the ECCOMAS Thematic Conference on Mutlibody Dynamics
Event location: Warsaw
Abstract
Inspired by Kirchhoff ’s kinetic analogy, the special Cosserat theory of rods is formulated in the language of Lagrangian mechanics. A static rod corresponds to an abstract Lagrangian system where the energy density takes the role of the Lagrangian function. The equilibrium equations are derived from a variational principle. Noether’s theorem relates their first integrals to frame-indifference, isotropy and uniformity. These properties can be formulated in terms of Lie group symmetries. The rotational degrees of freedom, present in the geometrically exact beam theory, are represented in terms of orthonormal director triads. To reduce the number of unknowns, Lagrange multipliers associated with the orthonormality constraints are eliminated using null-space matrices. This is done both in the continuous and in the discrete setting. The discrete equilibrium equations are used to compute discrete rod configurations, where different types of boundary conditions can be handled.
Authors with CRIS profile
Additional Organisation(s)
Involved external institutions
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik (ITWM) / Fraunhofer Institute for Industrial Mathematics
Germany (DE)
Freie Universität Berlin
Germany (DE)
California Institute of Technology (Caltech)
United States (USA) (US)
Germany (DE)
Freie Universität Berlin
Germany (DE)
California Institute of Technology (Caltech)
United States (USA) (US)
How to cite
APA:
Jung, P., Leyendecker, S., Linn, J., & Ortiz, M. (2009). Discrete Lagrangian mechanics and geometrically exact Cosserat rods. In Proceedings of the ECCOMAS Thematic Conference on Mutlibody Dynamics (pp. dvd, 14 Seiten). Warsaw, PL.
MLA:
Jung, Pascal, et al. "Discrete Lagrangian mechanics and geometrically exact Cosserat rods." Proceedings of the ECCOMAS Thematic Conference on Mutlibody Dynamics, Warsaw 2009. dvd, 14 Seiten.
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