On Solutions to Euler-Lagrange Equations Governing Isotropic, Homogeneous, Naturally Curved Kirchhoff’s Elastic Rods

Abstract

Motivated by the elastic rod model for DNA with intrinsic curvature, we study the solution space of the Euler-Lagrange equations governing isotropic, homogeneous, naturally curved Kirchhoff's elastic thin rods. Our studies show that for each given total energy and twisting density, there are at most three solutions, aside from the case where the twisting density is some particular constant. We also propose in this paper a reasonable condition under which an improvement on the number of the solutions may be possible. Finally, numerical calculations are presented to support our conclusions.