KIRCHHOFF ELASTIC RODS IN THE THREE-SPHERE

Abstract

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.