TY - RPRT
A1 - Jung, P.
A1 - Leyendecker, S.
A1 - Linn, J.
A1 - Ortiz, M.
T1 - Discrete Lagrangian mechanics and geometrically exact Cosserat rods
N2 - 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.
T3 - Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) - 160
KW - Special Cosserat rods
KW - Lagrangian mechanics
KW - Noether’s theorem
KW - discrete mechanics
Y1 - 2009
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2093
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-16019
ER -