## On end rotation for open rods undergoing large
deformations

G.H.M. van der Heijden, M.A. Peletier &
R. Planqué

We give a careful discussion of end rotation in elastic rods, focusing on
ambiguities that arise if arbitrarily large deformations are allowed. By
introducing a closure and restricting to a class of deformations we show
that a rigorous treatment of end rotation can be obtained. The results
underpin various non-rigorous discussions in the literature and serve to
promote the variational analysis of boundary-value problems for rods
undergoing large deformations. As an example we discuss the application to
the model of a rod lying on the surface of a cylinder.
keywords: rod theory, end rotation, twist, writhe, large deformations

*Quarterly of Applied Mathematics* **65**, 385-402 (2007)