GENERALIZED ELASTICA IN SO(3)


Tukel G. O. , Turhan T., YÜCESAN A.

MISKOLC MATHEMATICAL NOTES, vol.20, no.2, pp.1273-1283, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.18514/mmn.2019.2900
  • Title of Journal : MISKOLC MATHEMATICAL NOTES
  • Page Numbers: pp.1273-1283

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 gamma 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 parallel to V(t) parallel to = constant when G Lie group is SO(3).