*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.

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.

##### Documents and Links

WWW,Springer Version,WWW,arXiv Version,

WWW,CASC 2014.