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

We review the geometric rod theory for the case of a naturally straight, li nearly elastic, inextensible, circular rod suffering bending and torsion bu t no shear. Our primary focus is on the post-buckling behaviour of such rod s when subjected to end moment and tension. Although this is a classic prob lem with an extensive literature, dating back to Kirchhoff, the usual appro ach tends to neglect the physical interpretation of solutions (i.e., rod co nfigurations) to the models proposed. Here, we explicitly compute geometric al properties of buckled rods. In a unified approach, making use of Kirchho ff's dynamic analogy, both the classical helical and the more recently inve stigated localised buckling are considered. Special attention is given to a consistent treatment of concepts of link, twist and writhe.