On the writhe of non-closed curves
Biological Physics
2008-04-01 v1
Abstract
The writhe of a space curve fragment is considered for various boundary conditions. An expression for the writhe as a function of arclength for an arbitrary space curve is obtained. The formula is built on the base of closing the tangent indicatrix with a geodesic. The corresponding closure of a curve in 3-space is explicitly constructed. The addition rule for writhe is formulated. A relationship connecting the writhe with the Gauss integral over the open curve is presented. The single and double regular helical shapes are examined as examples.
Cite
@article{arxiv.physics/0212095,
title = {On the writhe of non-closed curves},
author = {E. L. Starostin},
journal= {arXiv preprint arXiv:physics/0212095},
year = {2008}
}
Comments
56 pages, 9 figures