## Helical and localised buckling in twisted rods: a unified analysis of the symmetric case

G.H.M. van der Heijden & J.M.T. Thompson

We review the geometric rod theory for the case of a naturally straight,
linearly elastic, inextensible, circular rod suffering bending and torsion
but no shear. Our primary focus is on the post-buckling behaviour of such
rods when subjected to end moment and tension. Although this is a classic
problem with an extensive literature, dating back to Kirchhoff, the usual
approach tends to neglect the physical interpretation of solutions (i.e.,
rod configurations) to the models proposed. Here, we explicitly compute
geometrical properties of buckled rods. In a unified approach, making use
of Kirchhoff's dynamic analogy, both the classical helical and the more
recently investigated localised buckling are considered. Special attention
is given to a consistent treatment of concepts of link, twist and writhe.
keywords: rod theory, buckling, helix, localisation, homoclinic orbit,
link, twist, writhe

*Nonlinear Dynamics* **21**, 71-99 (2000)