Journal of the Mathematical Society of Japan

Kirchhoff elastic rods in three-dimensional space forms


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

First available in Project Euclid: 30 May 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

elastic rod elastica calculus of variations


KAWAKUBO, Satoshi. Kirchhoff elastic rods in three-dimensional space forms. J. Math. Soc. Japan 60 (2008), no. 2, 551--582. doi:10.2969/jmsj/06020551.

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