## Discrete Lagrangian mechanics and geometrically exact Cosserat rods

• Inspired by Kirchhoff’s kinetic analogy, the special Cosserat theory of rods is formulatedin 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.

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Verfasserangaben: P. Jung, S. Leyendecker, J. Linn, M. Ortiz urn:nbn:de:hbz:386-kluedo-16019 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (160) Bericht Englisch 2009 2009 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik Fraunhofer ITWM 20.05.2009 Lagrangian mechanics ; Noether’s theorem ; Special Cosserat rods ; discrete mechanics Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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