Distributional radius of curvature

Document Type

Article

Publication Date

3-10-2006

Abstract

We show that any continuous plane path that turns to the left has a well-defined distribution that corresponds to the radius of curvature of smooth paths. We show that the distributional radius of curvature determines the path uniquely except for a translation. We show that Dirac delta contributions in the radius of curvature correspond to facets, that is, flat sections of the path, and show how a path can be deformed into a facet by letting the radius of curvature approach a delta function. Copyright © 2005 John Wiley & Sons, Ltd.

Publication Source (Journal or Book title)

Mathematical Methods in the Applied Sciences

First Page

427

Last Page

444

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