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A STUDY ON A RULED SURFACE WITH LIGHTLIKE RULING FOR A NULL CURVE WITH CARTAN FRAME
Ayyildiz, Nihat,Turhan, Tunahan Korean Mathematical Society 2012 대한수학회보 Vol.49 No.3
In this study, we investigate the curvature functions of ruled surface with lightlike ruling for a null curve with Cartan frame in Minkowski 3-space. Also, we give relations between the curvature functions of this ruled surface and curvature functions of central normal surface. Finally, we use the curvature theory of the ruled surface for determine differential properties of a robot end-effector motion.
Ayyildiz, Nihat,Yucesan, Ahmet Korean Mathematical Society 2006 대한수학회지 Vol.43 No.6
This paper develops in detail the differential geometry of ruled surfaces from two perspectives, and presents the underlying relations which unite them. Both scalar and dual curvature functions which define the shape of a ruled surface are derived. Explicit formulas are presented for the computation of these functions in both formulations of the differential geometry of ruled surfaces. Also presented is a detailed analysis of the ruled surface which characterizes the shape of a general ruled surface in the same way that osculating circle characterizes locally the shape of a non-null Lorentzian curve.
A STUDY ON A RULED SURFACE WITH LIGHTLIKE RULING FOR A NULL CURVE WITH CARTAN FRAME
Nihat Ayyildiz,Tunahan Turhan 대한수학회 2012 대한수학회보 Vol.49 No.3
In this study, we investigate the curvature functions of ruled surface with lightlike ruling for a null curve with Cartan frame in Minkow\-ski 3-space. Also, we give relations between the curvature functions of this ruled surface and curvature functions of central normal surface. Finally, we use the curvature theory of the ruled surface for determine differential properties of a robot end-effector motion.