On the general analytical solution of the kinematic cosserat equations

Dominik L. Michels, Dmitry A. Lyakhov, Vladimir P. Gerdt, Zahid Hossain, Ingmar H. Riedel-Kruse, Andreas G. Weber

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.

Original languageEnglish (US)
Title of host publicationComputer Algebra in Scientific Computing - 18th International Workshop, CASC 2016, Proceedings
EditorsEvgenii V. Vorozhtsov, Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler
Number of pages14
ISBN (Print)9783319456409
StatePublished - 2016
Externally publishedYes
Event18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016 - Bucharest, Romania
Duration: Sep 19 2016Sep 23 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9890 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016


  • Cosserat rods
  • Differential thomas decomposition
  • Flagellated microswimmers
  • General analytical solution
  • Kinematic equations
  • Lie symmetry analysis
  • Stokes flow
  • Symbolic computation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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