Motion of elastic wire with thickness

Abstract

There are several types of equation of motion of elastic wires. In this paper, we treat an equation taking account of the thickness of wire. The equation was introduced by Caflisch and Maddocks on plane curves, and they proved the existence of solutions. We will prove the existence of solutions for any dimensional Euclidean space. Note that, in the case of plane, the equation can be explicitly written in terms of polar coordinates. For higher dimensional case, we use covariant differentiation on the unit sphere.