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GLOBAL SOLUTIONS OF THE EQUATION OF THE KIRCHHOFF ELASTIC ROD IN SPACE FORMS

Part of: Thin bodies, structures Optimality conditions Variational problems in infinite-dimensional spaces

Published online by Cambridge University Press:  27 September 2012

SATOSHI KAWAKUBO
SATOSHI KAWAKUBO*
Affiliation:
Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180, Japan (email: kawakubo@math.sci.fukuoka-u.ac.jp)
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Abstract

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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.

Keywords

Kirchhoff elastic rodscalculus of variationsordinary differential equationsinitial-value problemsglobal solutions

MSC classification

Secondary: 49K15: Problems involving ordinary differential equations 58E10: Applications to the theory of geodesics (problems in one independent variable) 74K10: Rods (beams, columns, shafts, arches, rings, etc.)

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 1 , August 2013 , pp. 70 - 80
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

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