ON SPHERICAL ELASTIC CURVES: SPHERICAL INDICATRIX ELASTIC CURVES


Tukel G. O. , Turhan T. , YÜCESAN A.

JOURNAL OF SCIENCE AND ARTS, ss.699-706, 2017 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: Konu: 4
  • Basım Tarihi: 2017
  • Dergi Adı: JOURNAL OF SCIENCE AND ARTS
  • Sayfa Sayıları: ss.699-706

Özet

In this paper, we study spherical elastic curves corresponding spherical indicatrix of regular curves with non-vanishing curvature in Euclidean 3-space. From classical variational problem of elastic curves, we derive two Euler-Lagrange equations associated to actions of bending energy functional defined on tangent spherical indicatrix of curves in Euclidean 3-space. We show that the solution of the equation system obtaining with respect to curvature and torsion of the curve corresponds to general helix which is often studied in geometry and we arrange a classification expressing curves whose tangent spherical indicatrix are elastic curve. Finally, we make similar calculations for curves whose principal normal and binormal spherical indicatrix are elastic and we give an example for tangent spherical indicatrix elastic curves.