14 citations · 25 across the 3 of their papers we have counts for
3 papers
math-ph2013★ 14 cited
Euler elasticae in the plane and the Whitney--Graustein theorem
Sergey Avvakumov, Oleg Karpenkov, Alexey Sossinsky
In this paper, we apply classical energy principles to Euler elasticae, i.e., closed C^2 curves in the plane supplied with the Euler functional U (the integral of the square of the…
math-ph2011★ 6 cited
Energies of knot diagrams
Oleg Karpenkov, Alexey Sossinsky
We introduce and begin the study of new knot energies defined on knot diagrams. Physically, they model the internal energy of thin metallic solid tori squeezed between two parallel…
math.GT2010★ 5 cited
Mechanical Normal Forms of Knots and Flat Knots
A. B. Sossinsky
A new type of knot energy is presented via real life experiments involving a thin resilient metallic tube. Knotted in different ways, the device mechanically acquires a uniquely de…