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The extended polar writhe : a tool for open curves mechanics.

Prior, C. B. and Neukirch, S. (2016) 'The extended polar writhe : a tool for open curves mechanics.', Journal of physics A : mathematical and theoretical., 49 (21). p. 215201.


A measure of the writhing of a curve is introduced and is used to extend the C?lug?reanu? decomposition for closed curves, as well as the polar decomposition for curves bound between planes. The new writhe measure is also shown to be able to assess changes in linking due to belt-trick and knotting type deformations, and further its utility is illustrated on examples taken from elastic rod parameter-continuation studies. Finally C++ and mathematica codes are made available and shown to be faster than existing algorithms for the numerical computation of the writhe.

Item Type:Article
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Publisher statement:This is an author-created, un-copyedited version of an article published in Journal of physics A : mathematical and theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Date accepted:22 February 2016
Date deposited:21 April 2016
Date of first online publication:20 April 2016
Date first made open access:20 April 2017

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