Elastic Strips with Spacelike Directrix

ÖZKAN TÜKEL G., YÜCESAN A.

Bulletin of the Malaysian Mathematical Sciences Society, vol.42, no.5, pp.2623-2638, 2019 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 5
  • Publication Date: 2019
  • Doi Number: 10.1007/s40840-018-0622-0
  • Journal Name: Bulletin of the Malaysian Mathematical Sciences Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2623-2638
  • Keywords: Conservation laws, Elastic strips, Variational calculus
  • Isparta University of Applied Sciences Affiliated: Yes

Abstract

The elasticity of a rectifying strip with a spacelike directrix (base curve) is studied using the differential geometry of developable surfaces and variational techniques. Two conservation laws are derived in Minkowski 3-space R13 by constructing two different variations including only Lorentz translations or rotations. By means of these laws two new types of elastic strips are defined: momentum strips and force-free strips. There exists a connection between elastic curves on de Sitter 2-space and pseudohyperbolic space and elastic strips with spacelike directrix.