Elastic Strips with Spacelike Directrix


Tukel G. O. , YÜCESAN A.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.42, no.5, pp.2623-2638, 2019 (SCI-Expanded) identifier identifier

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.