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Equilibria of elastic cable knots and links

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. Green open access

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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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