Van Der Heijden, G;
Starostin, E;
(2018)
Equilibria of elastic cable knots and links.
In: Blatt, S and Reiter, P and Schikorra, A, (eds.)
New Directions in Geometric and Applied Knot Theory.
(pp. 258-275).
De Gruyter: Warsaw, Poland.
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Abstract
We present a theory for equilibria of geometrically exact braids made of two thin, uniform, homogeneous, isotropic, initially-straight, inextensible and unshearable elastic rods of circular cross-section. We formulate a second-order variational problem for an action functional whose Euler–Lagrange equations, partly in Euler– Poincaré form, yield a compact system of ODEs for which we define boundary-value problems for braids closed into knots or links. The purpose of the chapter is to present a pathway of deformations leading to braids with a knotted axis, thereby offering a way to systematically compute elastic cable knots and links. A representative bifurcation diagram and selected numerical solutions illustrate our approach.
| Type: | Book chapter |
|---|---|
| Title: | Equilibria of elastic cable knots and links |
| ISBN-13: | 978-3-11-057149-3 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1515/9783110571493 |
| Publisher version: | https://www.degruyter.com/view/product/497162 |
| Language: | English |
| Additional information: | © 2018 Eugene L. Starostin and Gert H.M. van der Heijden, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 License. https://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Keywords: | elastic knots and links, cable knots, equilibria, variational problem, bifurcation |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Civil, Environ and Geomatic Eng |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10067413 |
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