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On the writhe of non-closed curves

Starostin, EL; (2002) On the writhe of non-closed curves. Ch. 26 in: Vol. 36: Physical and Numerical Models in Knot Theory Including Applications to the Life Sciences, ISBN 978-981-256-187-9, World Scientific (2005) 525-545.

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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.

Type:Article
Title:On the writhe of non-closed curves
Additional information:56 pages, 9 figures
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Civil, Environmental and Geomatic Engineering

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