The curvature of plane elastic curves
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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.
RightsThis 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.
NPS Report NumberNPS-MA-93-013
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