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Intrinsic Equations for a Relaxed Elastic Line of Second Kind in Minkowski 3-Space

Date

2015

Author

Bayram, Ergin
Kasap, Emin

Metadata

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Abstract

Let alpha be an arc on a connected oriented surface S in Minkowski 3-space, parameterized by arc length s, with torsion tau and length l. The total square torsion H of alpha is defined by H = integral(1)(0)tau(2)ds. The arc alpha is called a relaxed elastic line of second kind if it is an extremal for the variational problem of minimizing the value of H within the family of all arcs of length l on S having the same initial point and initial direction as alpha. In this study, we obtain the differential equation and boundary conditions for a relaxed elastic line of second kind on an oriented surface in Minkowski 3-space. This formulation should give a more direct and more geometric approach to questions concerning relaxed elastic lines of second kind on a surface.

Source

Filomat

Volume

29

Issue

3

URI

https://doi.org/10.2298/FIL1503493B
https://hdl.handle.net/20.500.12712/14703

Collections

  • Scopus İndeksli Yayınlar Koleksiyonu [14046]
  • WoS İndeksli Yayınlar Koleksiyonu [12971]



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