Kirchhoff’s theory of an elastic rod

Abstract

By way of background, a rapid review of Kirchhoff’s theory of an inextensible, unshearable elastic rod is discussed in this chapter. The formulation of the theory incorporates a pair of deformable vectors (or directors) associated with each point of a flexible material curve. In addition, the Frenet and Bishop framings of the material curve are introduced. The latter framing does not feature in classic textbooks on rod theories and is central to understanding the discrete elastic rod formulation.