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arXiv · 1306.4431

Intrinsic Equations For a Relaxed Elastic Line of Second Kind on an Oriented Surface

Ergin Bayram·Emin Kasap
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Abstract

Let α(s) be an arc on a connected oriented surface S in E3, parameterized by arc length s, with torsion τ and length l. The total square torsion F of α is defined by T=\int_{0}^{l}τ^{2}ds\ $. . The arc α is called a relaxed elastic line of second kind if it is an extremal for the variational problem of minimizing the value of F within the family of all arcs of length l on S having the same initial point and initial direction as α. In this study, we obtain differential equation and boundary conditions for a relaxed elastic line of second kind on an oriented surface.

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Ergin Bayram, Emin Kasap. 2014-01-07. Intrinsic Equations For a Relaxed Elastic Line of Second Kind on an Oriented Surface. https://doi.org/10.1142/s0219887816500109

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