The curvature of plane elastic curves
Loading...
Authors
Brunnett, Guido
Subjects
Elastic curves
Curvature analysis
Curvature analysis
Advisors
Date of Issue
1993
Date
1993
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
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 K2/m. It is shown that for any elastic curve K2/m 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 K2/m 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.
Type
Technical Report
Description
Series/Report No
Department
Mathematics
Identifiers
NPS Report Number
NPS-MA-93-013
Sponsors
Funder
Format
15 p.: ill. ; 28 cm.
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.