Kirchhoff elastic rods in higher-dimensional space forms

Kawakubo, Satoshi

doi:10.3792/pjaa.87.5

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Cited by 2 publications

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“…On the other hand, there are not so many studies on Kirchhoff rods in space forms of dimension n ≥ 4. In [23], the present author constructed examples of Kirchhoff rods whose centrelines are fully immersed in R n , S n , H n (n ≥ 4). In the case of n ≥ 4, however, explicit formulas of the higher-order Frenet curvatures, or other kinds of curvatures of all Kirchhoff rods are not known.…”

Section: Introductionmentioning

confidence: 99%

Global Solutions of the Equation of the Kirchhoff Elastic Rod in Space Forms

Kawakubo

2012

Bull. Aust. Math. Soc.

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The Kirchhoff elastic rod is one of the mathematical models of equilibrium configurations of thin elastic rods, and is defined to be a solution of the Euler–Lagrange equations associated to the energy with the effect of bending and twisting. In this paper, we consider Kirchhoff elastic rods in a space form. In particular, we give the existence and uniqueness of global solutions of the initial-value problem for the Euler–Lagrange equations. This implies that an arbitrary Kirchhoff elastic rod of finite length extends to that of infinite length.

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Section: Introductionmentioning

confidence: 99%