Elastica in Galilean 3-Space

ÖZKAN TÜKEL G., TURHAN T.

Konuralp Journal of Mathematics, vol.8, no.2, pp.419-422, 2020 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 2
  • Publication Date: 2020
  • Journal Name: Konuralp Journal of Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.419-422
  • Keywords: Elastic curves, Euler-Lagrange equations, Galilean 3-space
  • Isparta University of Applied Sciences Affiliated: Yes

Abstract

In this work, we aim to develop classical Euler-Bernoulli elastic curves in a non-Euclidean space. So, we study the curvature energy action under some boundary conditions in the Galilean 3−space G3. Then, we derive the Euler-Lagrange equation for bending energy functional acting on suitable curves in G3. We solve this differential equation by using some solving methods in applied mathematics. Finally, we give an example for elastic curves in Galilean 3−space G3.