Lie Symmetry Analysis for Cosserat Rods
Dmitry A. Lyakhov,National Academy of Sciences of Belarus,
Vladimir P. Gerdt,Joint Institute for Nuclear Research,
Gerrit A. Sobottka,University of Bonn,
Andreas G. Weber,University of Bonn.
In Proceedings of Computer Algebra in Scientific Computing, CASC 2014, Pages 326-336,
Lecture Notes in Computer Science, Springer, Sept. 2014.
BibTeX Springer
@incollection
author = {Dominik L.~Michels and Dmitry A.~Lyakhov and Vladimir P.~Gerdt and Gerrit A.~Sobottka and Andreas G.~Weber},
title = {Lie Symmetry Analysis for Cosserat Rods},
pages = {326--336},
booktitle = {Computer Algebra in Scientific Computing – CASC 2014},
series = {Lecture Notes in Computer Science},
volume = {8660},
year= {2014},
publisher= {Springer},
address = {Berlin, Heidelberg},
isbn = {978-3-319-10514-7}
}
BibTeX arXiv
@misc
author = {Dominik L.~Michels and Dmitry A.~Lyakhov and Vladimir P.~Gerdt and Gerrit A.~Sobottka and Andreas G.~Weber},
title = {Lie Symmetry Analysis for Cosserat Rods},
year= {2014},
eprint= {arXiv:1411.1735},
howpublished = {Computer Algebra in Scientific Computing – CASC 2014, Pages 326--336, Lecture Notes in Computer Science, Springer, Sept. 2014}
}
Abstract
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 functions 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.
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