Intrinsic equations for a relaxed elastic line of second kind on an oriented surface

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BAYRAM E., Kasap E.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, cilt.13, sa.3, 2016 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 3
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1142/s0219887816500109
  • Dergi Adı: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Relaxed elastic line of second kind, oriented surface, calculus of variation, MINKOWSKI 3-SPACE, CURVES
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

Let alpha(s) be an arc on a connected oriented surface S in E-3, parameterized by arc length s, with torsion tau and length l. The total square torsion H of alpha is defined by H = integral(l)(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 differential equation and boundary conditions for a relaxed elastic line of second kind on an oriented surface.