Kirchhoff elastic rods in three-dimensional space forms
Satoshi KAWAKUBO
Source: J. Math. Soc. Japan Volume 60, Number 2
(2008), 551-582.
Abstract
The Kirchhoff elastic rod is one of the mathematical models of thin elastic rods, and is characterized as a critical point of the energy functional obtained by adding the effect of twisting to the bending energy. In this paper, we investigate Kirchhoff elastic rods in three-dimensional space forms. In particular, we give explicit formulas of Kirchhoff elastic rods in the three-sphere and in the three-dimensional hyperbolic space in terms of Jacobi sn function and the elliptic integrals.
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1212156662
Digital Object Identifier: doi:10.2969/jmsj/06020551
Mathematical Reviews number (MathSciNet): MR2421988
Zentralblatt MATH identifier: 1142.58012
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