Kirchhoff elastic rods in the three-sphere

被引：13

作者：

Kawakubo, S ^{[1
]}

机构：

[1] Fukuoka Univ, Dept Appl Math, Fukuoka 8140180, Japan

来源：

TOHOKU MATHEMATICAL JOURNAL | 2004年 / 56卷 / 02期

关键词：

elastic rods; calculus of variations;

D O I：

10.2748/tmj/1113246551

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Kirchhoff elastic rod is one of the mathematical models of thin elastic rods, and is a critical point of the energy functional with the effect of bending and twisting. In this paper, we study Kirchhoff elastic rods in the three-sphere of constant curvature. In particular, we give explicit expressions of Kirchhoff elastic rods in terms of elliptic functions and integrals. In addition, we obtain equivalent conditions for Kirchhoff elastic rods to be closed, and give an example of closed Kirchhoff elastic rods.

引用

页码：205 / 235

页数：31

共 23 条

[1]

[Anonymous], 1983, Exterior Differential Systems and the Calculus of Variations

[2] Elasticae with constant slant in the complex projective plane and new examples of Willmore tori in five spheres [J].