HYPERELASTIC LIE QUADRATICS


Tukel G. O. , Turhan T., YÜCESAN A.

HONAM MATHEMATICAL JOURNAL, vol.41, no.2, pp.369-380, 2019 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.5831/hmj.2019.41.2.369
  • Journal Name: HONAM MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.369-380
  • Süleyman Demirel University Affiliated: Yes

Abstract

Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group G equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group G is SO(3).