Willmore energy and total normalcy of knots

It is known that a knot is a closed, self-avoiding curve in 3-dimensional space. In the present article, we compute the total Normalcy and Willmore energy of knots under first order infinitesimal bending with modified orthogonal frame. Moreover, four illustrious examples with figures i.e. Trefoil knot, Figure eight knot, P3Q2 knot and P4Q3 knots, have been discussed and graphically presented to support the computations for bending parameter ? = 0 and ? > 0. Colors are used to illustrate normalcy values and Willmore energies at different points of these knots under infinitesimal bending.