Generalized elastica in so(3)

ÖZKAN TÜKEL G., TURHAN T., YÜCESAN A.

Miskolc Mathematical Notes, vol.20, no.2, pp.1273-1283, 2019 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.18514/mmn.2019.2900
  • Journal Name: Miskolc Mathematical Notes
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1273-1283
  • Keywords: Euler-Lagrange equation, Generalized elastic lie quadratic, generalized elastica
  • Isparta University of Applied Sciences Affiliated: Yes

Abstract

In a Lie group G equipped with bi-invariant Riemannian metric, we characterize the generalized elastica by an Euler-Lagrange equation in terms of the Lie reduction V of a curve γ in G. We define a generalized elastic Lie quadratic in the Lie algebra of G: For a generalized elastic Lie quadratic, we construct the Lax equation that is crucial to the solution of a generalized elastica with regard to its generalized elastic Lie quadratic. Then we solve this equation for a null generalized elastic Lie quadratic with[norm of matrix]V.(t)[norm of matrix] =constant when G Lie group is SO(3).