The total curvature of knots under second-order infinitesimal bending

Abstract

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