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Published in:
2014 | OriginalPaper | Chapter
Lie Symmetry Analysis for Cosserat Rods
Authors : Dominik L. Michels, Dmitry A. Lyakhov, Vladimir P. Gerdt, Gerrit A. Sobottka, Andreas G. Weber
Published in: Computer Algebra in Scientific Computing
Publisher: Springer International Publishing
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We consider a subsystem of the Special Cosserat Theory of Rods and construct an explicit form of its solution that depends on three arbitrary functions in (
s
,
t
) and three arbitrary function in
t
. Assuming analyticity of the arbitrary functions in a domain under consideration, we prove that the obtained solution is analytic and general. The Special Cosserat Theory of Rods describes the dynamic equilibrium of 1-dimensional continua, i.e. slender structures like fibers, by means of a system of partial differential equations.