On the General Analytical Solution of the Kinematic Cosserat Equations

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9890)


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.


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



This work has been partially supported by the Max Planck Society (FKZ-01IMC01/FKZ-01IM10001), the Russian Foundation for Basic Research (16-01-00080), and a BioX Stanford Interdisciplinary Graduate Fellowship. The reviewers’ valuable comments are gratefully acknowledged.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA
  2. 2.Visual Computing CenterKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  3. 3.Group of Algebraic and Quantum ComputationsJoint Institute for Nuclear ResearchDubnaRussia
  4. 4.Department of BioengineeringStanford UniversityStanfordUSA
  5. 5.Institute of Computer Science IIUniversity of BonnBonnGermany

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