Tohoku Mathematical Journal

Kirchhoff elastic rods in a Riemannian manifold

Satoshi Kawakubo

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Imagine a thin elastic rod like a piano wire. We consider the situation that the elastic rod is bent and twisted and both ends are welded together to form a smooth loop. Then, does there exist a stable equilibrium? In this paper, we generalize the energy of uniform symmetric Kirchhoff elastic rods in the $3$-dimensional Euclidean space to consider such a variational problem in a Riemannian manifold. We give the existence and regularity of minimizers of the energy in a compact or homogeneous Riemannian manifold.

Article information

Tohoku Math. J. (2), Volume 54, Number 2 (2002), 179-193.

First available in Project Euclid: 11 April 2005

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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: 74G60: Bifurcation and buckling 74K10: Rods (beams, columns, shafts, arches, rings, etc.)


Kawakubo, Satoshi. Kirchhoff elastic rods in a Riemannian manifold. Tohoku Math. J. (2) 54 (2002), no. 2, 179--193. doi:10.2748/tmj/1113247562.

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