Generalized elastica in so(3)

ÖZKAN TÜKEL G., TURHAN T., YÜCESAN A.

Miskolc Mathematical Notes, cilt.20, sa.2, ss.1273-1283, 2019 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.18514/mmn.2019.2900
  • Dergi Adı: Miskolc Mathematical Notes
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1273-1283
  • Anahtar Kelimeler: Euler-Lagrange equation, Generalized elastic lie quadratic, generalized elastica
  • Isparta Uygulamalı Bilimler Üniversitesi Adresli: Evet

Özet

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).