Equilibria of elastic cable knots and links

Book chapter


Starostin, E. and van der Heijden, G. (2018). Equilibria of elastic cable knots and links. in: Reiter, Ph., Blatt, S. and Schikorra, A. (ed.) New Directions in Geometric and Applied Knot Theory De Gruyter. pp. 258-275
AuthorsStarostin, E. and van der Heijden, G.
EditorsReiter, Ph., Blatt, S. and Schikorra, A.
Abstract

We present a theory for equilibria of geometrically exact braids made of two thin, uniform, homogeneous, isotropic, initially-straight, inextensible and unshear- able 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 bifurca- tion diagram and selected numerical solutions illustrate our approach.

Keywordselastic knots and links, cable knots, equilibria, variational problem, bifurcation
Page range258-275
Year2018
Book titleNew Directions in Geometric and Applied Knot Theory
PublisherDe Gruyter
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ISBN9783110571486
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Print2018
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Deposited09 Nov 2022
Digital Object Identifier (DOI)https://doi.org/10.1515/9783110571493
Web address (URL)https://www.degruyter.com/document/doi/10.1515/9783110571493/html
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