Accession Number:

ADA263198

Title:

The Curvature of Plane Elastic Curves

Descriptive Note:

Tech Rept. Jan 1993-Mar 1993

Corporate Author:

NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1993-03-17

Pagination or Media Count:

19.0

Abstract:

In this paper plane elastic curves are revisited from a viewpoint that emphasizes curvature properties of these curves. The family of elastic curves is considered in dependence of a tension parameter Sigma and the squared global curvature maximum K2m. It is shown that for any elastic curve K2m is bigger than the tension parameter Sigma. A curvature analysis of the fundamental forms of the elastic curves is presented. A formula is established that gives the maximum turning angle of an elastica as a function depending on K2m and Sigma. Finally, it is shown that an elastic curve can be represented as a linear combination of its curvature, arc length and energy function and that any curve with this property is an elastic.... Elastic curves, Curvature analysis.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE