A consistent treatment of link and writhe for open rods, and their relation to end rotation

Details A consistent treatment of link and writhe for open rods, and their relation to end rotation A consistent treatment of link and writhe for open rods, and their relation to end rotation

2003-10-27

arxiv.org/abs/math-ph/0310057v1

Physics

Mathematical Physics

17 pages, 4 figures

Scientific paper

We combine and extend the work of Alexander & Antman \cite{alexander.82} and Fuller \cite{fuller.71,fuller.78} to give a framework within which precise definitions can be given of topological and geometrical quantities characterising the contortion of open rods undergoing large deformations under end loading. We use these definitions to examine the extension of known results for closed rods to open rods. In particular, we formulate the analogue of the celebrated formula $Lk=Tw+Wr$ (link equals twist plus writhe) for open rods and propose an end rotation, through which the applied end moment does work, in the form of an integral over the length of the rod. The results serve to promote the variational analysis of boundary-value problems for rods undergoing large deformations.

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