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The total torsion of knots under second order infinitesimal bending

Najdanović Marija S. (University of Priština-Kosovska Mitrovica, Faculty of Sciences, Department of Mathematics, Kosovska Mitrovica, Serbia), marija.najdanovic@pr.ac.rs
Velimirović Ljubica S. (Faculty of Sciences and Mathematics, University of Niš, Serbia), vljubica@pmf.ni.ac.rs
Rančić Svetozar R. (Faculty of Sciences and Mathematics, University of Niš, Serbia), rancicsv@yahoo.com

In this paper we consider infinitesimal bending of the second order of curves and knots. The total torsion of the knot during the second order infinitesimal bending is discussed and expressions for the first and the second variation of the total torsion are given. Some examples aimed to illustrate infinitesimal bending of knots are shown using figures. Colors are used to illustrate torsion values at different points of bent knots and the total torsion is numerically calculated.

Keywords: second order infinitesimal bending, first variation, second variation, total torsion, knot

Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174012