Open AccessInfinitesimal bending influence on the Willmore energy of curves
Author(s) -
Marija S. Najdanović
Publication year - 2015
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1510411n
Subject(s) - infinitesimal , willmore energy , mathematics , curvature , tangent , mathematical analysis , infinitesimal transformation , torsion (gastropod) , frenet–serret formulas , geometry , arc length , first variation , mean curvature , principal curvature , arc (geometry) , medicine , surgery
In this paper we study the change of the Willmore energy of curves, as a special case of so-called Helfrich energy, under infinitesimal bending determined by the stationarity of arc length. We examine the variation of the unit tangent, principal normal and binormal vector fields, the curvature and the torsion of the curve. We obtain an explicit formula for calculating the variation of the Willmore energy, as well as the Euler-Lagrange equations describing equilibrium. We find an infinitesimal bending field for a helix and compute the variation of its Willmore energy under such infinitesimal bending.