LAGRANGIAN ASPECTS OF THE KIRCHHOFF ELASTIC ROD

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