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

BAYRAM E., Kasap E.

FILOMAT, vol.29, no.3, pp.493-505, 2015 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 3
  • Publication Date: 2015
  • Doi Number: 10.2298/fil1503493b
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.493-505
  • Keywords: Calculus of variations, Minkowski 3-space, Elastic line, ORIENTED SURFACE
  • Ondokuz Mayıs University Affiliated: Yes

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.