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A Symbolic-Numeric Method for Solving Boundary Value Problems of Kirchhoff Rods

  • Liu Shu
  • Andreas Weber
Conference paper
  • 660 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3718)

Abstract

We study solution methods for boundary value problems associated with the static Kirchhoff rod equations. Using the well known Kirchhoff kinetic analogy between the equations describing the spinning top in a gravity field and spatial rods, the static Kirchhoff rod equations can be fully integrated. We first give an explicit form of a general solution of the static Kirchhoff equations in parametric form that is easy to use. Then by combining the explicit solution with a minimization scheme, we develop a unified method to match the parameters and integration constants needed by the explicit solutions and given boundary conditions. The method presented in the paper can be adapted to a variety of boundary conditions. We detail our method on two commonly used boundary conditions.

Keywords

Euler Angle Minimization Scheme Local Reference Frame Elastic Strip Give Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Liu Shu
    • 1
  • Andreas Weber
    • 1
  1. 1.Institut für Informatik IIUniversität BonnBonnGermany

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