Lie Symmetry Analysis for Cosserat Rods

  • Dominik L. Michels
  • Dmitry A. Lyakhov
  • Vladimir P. Gerdt
  • Gerrit A. Sobottka
  • Andreas G. Weber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8660)

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.

Keywords

Cosserat Rods General Solution Janet Basis Kirchhoff Rods Lie Symmetry Method 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dominik L. Michels
    • 1
  • Dmitry A. Lyakhov
    • 2
  • Vladimir P. Gerdt
    • 3
  • Gerrit A. Sobottka
    • 4
  • Andreas G. Weber
    • 4
  1. 1.Department of Computing and Mathematical SciencesCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Radiation Gaseous Dynamics LabA. V. Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of BelarusMinskBelarus
  3. 3.Group of Algebraic and Quantum ComputationsJoint Institute for Nuclear ResearchDubna, Moscow RegionRussia
  4. 4.Multimedia, Simulation and Virtual Reality Group, Institute of Computer Science IIUniversity of BonnBonnGermany

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