Relaxed elastic line on a curved pseudo-hypersurface in pseudo-Euclidean spaces

Coken, ABDİLKADİR; Yucesan, A; Ayyildiz, N; Manning, GS

doi:10.1016/j.jmaa.2005.05.051

Relaxed elastic line on a curved pseudo-hypersurface in pseudo-Euclidean spaces

Coken A. C., Yucesan A., Ayyildiz N., Manning G.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.315, no.1, pp.367-378, 2006 (SCI-Expanded)

Publication Type: Article / Article
Volume: 315 Issue: 1
Publication Date: 2006
Doi Number: 10.1016/j.jmaa.2005.05.051
Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Page Numbers: pp.367-378
Keywords: relaxed elastic line, elasticity problem, pseudo-Euclidean spaces, pseudo-hypersurfaces, geodesics, Euler-Lagrange equations
Akdeniz University Affiliated: No

Abstract

In this work, we derive the Euler-Lagrange equation for an elastic line which is lying on a pseudo-hypersurface in pseudo-Euclidean spaces E-v(n). Following this, we check the solutions which depend on the boundary conditions whether they are geodesic on a pseudo-hypersurface or not. The relaxed elastic line on a pseudo-hyperplane, a pseudo-hypersphere, and pseudo-hyperbolic space is a geodesic. However, the relaxed elastic line on a pseudo-hypercylinder, is a space-like geodesic. (c) 2005 Elsevier Inc. All rights reserved.