Journal of the Mathematical Society of Japan

Kirchhoff elastic rods in three-dimensional space forms

Satoshi KAWAKUBO

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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.

Article information

Source
J. Math. Soc. Japan Volume 60, Number 2 (2008), 551-582.

Dates
First available in Project Euclid: 30 May 2008

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

Subjects
Primary: 58E10: Applications to the theory of geodesics (problems in one independent variable)
Secondary: 74K10: Rods (beams, columns, shafts, arches, rings, etc.) 74G05: Explicit solutions

Keywords
elastic rod elastica calculus of variations

Citation

KAWAKUBO, Satoshi. Kirchhoff elastic rods in three-dimensional space forms. Journal of the Mathematical Society of Japan 60 (2008), no. 2, 551--582. doi:10.2969/jmsj/06020551. http://projecteuclid.org/euclid.jmsj/1212156662.


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