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Article

On the Torsional Energy of Deformed Curves and Knots

by
Svetozar R. Rančić
1,†,
Ljubica S. Velimirović
1,† and
Marija S. Najdanović
2,*,†
1
Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
2
Faculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Axioms 2024, 13(10), 661; https://doi.org/10.3390/axioms13100661
Submission received: 28 August 2024 / Revised: 21 September 2024 / Accepted: 23 September 2024 / Published: 25 September 2024
(This article belongs to the Special Issue Theory of Curves and Knots with Applications)

Abstract

This paper deals with the study of torsional energy (total squared torsion) at infinitesimal bending of curves and knots in three dimensional Euclidean space. During bending, the curve is subject to change, and its properties are changed. The effect that deformation has on the curve is measured by variations. Here, we observe the infinitesimal bending of the second order and variations of the first and the second order that occur in this occasion. The subjects of study are curves and knots, in particular torus knots. We analyze various examples both analytically and graphically, using our own calculation and visualization software tool.
Keywords: second-order infinitesimal bending; first variation; second variation; torsional energy; curve; knot; torus knot second-order infinitesimal bending; first variation; second variation; torsional energy; curve; knot; torus knot

Share and Cite

MDPI and ACS Style

Rančić, S.R.; Velimirović, L.S.; Najdanović, M.S. On the Torsional Energy of Deformed Curves and Knots. Axioms 2024, 13, 661. https://doi.org/10.3390/axioms13100661

AMA Style

Rančić SR, Velimirović LS, Najdanović MS. On the Torsional Energy of Deformed Curves and Knots. Axioms. 2024; 13(10):661. https://doi.org/10.3390/axioms13100661

Chicago/Turabian Style

Rančić, Svetozar R., Ljubica S. Velimirović, and Marija S. Najdanović. 2024. "On the Torsional Energy of Deformed Curves and Knots" Axioms 13, no. 10: 661. https://doi.org/10.3390/axioms13100661

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