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Lie Symmetry Analysis for Cosserat Rods

Michels, Dominik L. and Lyakhov, Dimitry A. and Gerdt, Vladimir P. and Sobottka, Gerrit A. and Weber, Andreas G. (2014) Lie Symmetry Analysis for Cosserat Rods. In: Computer Algebra in Scientific Computing (CASC), 2014. Lecture Notes in Computer Science. No.8660. Springer International Publishing , Switzerland, pp. 324-334. ISBN 978-3-319-10515-4. https://resolver.caltech.edu/CaltechAUTHORS:20150116-102717658

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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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/978-3-319-10515-4_23DOIArticle
http://arxiv.org/abs/1411.1735arXivDiscussion Paper
http://rdcu.be/tCriPublisherFree ReadCube access
Additional Information:© 2014 Springer International Publishing Switzerland. The contribution of the third author (V.P.G.) was partially supported by the grant 13-01-00668 from the Russian Foundation for Basic Research. We thank Markus Lange-Hegermann and Paul Mueller for useful remarks. The authors are grateful to the reviewers' valuable comments that improved the manuscript.
Funders:
Funding AgencyGrant Number
Russian Foundation for Basic Research13-01-00668
Subject Keywords:Cosserat Rods, General Solution, Janet Basis, Kirchhoff Rods, Lie Symmetry Method
Series Name:Lecture Notes in Computer Science
Issue or Number:8660
Record Number:CaltechAUTHORS:20150116-102717658
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150116-102717658
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53821
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:16 Jan 2015 19:04
Last Modified:29 Apr 2020 22:03

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