Lie symmetry analysis for Cosserat rods

Dominik L. Michels, Dmitry A. Lyakhov, Vladimir P. Gerdt, Gerrit A. Sobottka, Andreas G. Weber

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

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 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.

Original languageEnglish (US)
Title of host publicationComputer Algebra in Scientific Computing - 16th International Workshop, CASC 2014, Proceedings
PublisherSpringer Verlag
Pages324-334
Number of pages11
ISBN (Print)9783319105147
DOIs
StatePublished - Jan 1 2014
Event16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014 - Warsaw, Poland
Duration: Sep 8 2014Sep 12 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8660 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014
CountryPoland
CityWarsaw
Period09/8/1409/12/14

Keywords

  • Cosserat Rods
  • General Solution
  • Janet Basis
  • Kirchhoff Rods
  • Lie Symmetry Method

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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