HYPERELASTIC LIE QUADRATICS


Tukel G. O. , Turhan T., YÜCESAN A.

HONAM MATHEMATICAL JOURNAL, cilt.41, ss.369-380, 2019 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 41 Konu: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.5831/hmj.2019.41.2.369
  • Dergi Adı: HONAM MATHEMATICAL JOURNAL
  • Sayfa Sayıları: ss.369-380

Özet

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).