Lagrangian aspects of the Kirchhoff elastic rod

被引：160

作者：

Langer, J

Singer, DA

机构：

[1] Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106-7058

来源：

SIAM REVIEW | 1996年 / 38卷 / 04期

关键词：

elastic curve; elastic rod; vortex filament;

D O I：

10.1137/S0036144593253290

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The relation between Euler's planar elastic curves and vortex filaments evolving by the localized induction equation (LIE) of hydrodynamics was discovered by Hasimoto in 1971. Basic facts about (an integrable case of) Kirchhoff elastic rods are described here, which amplify the connection between the variational problem for rods and the soliton equation LIE. In particular, it is shown that the centerline of the Kirchhoff rod is an equilibrium for a linear combination of the first three conserved Hamiltonians in the LIE hierarchy.

引用

页码：605 / 618

页数：14

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