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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.
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.
ON THE GEOMETRY OF RATIONAL BÉZIER CURVES
( Ayşe Yilmaz Ceylan ),( Tunahan Turhan ),( Gözde Özkan Tükel ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
The purpose of this paper is to assign a movable frame to an arbitrary point of a rational Bézier curve on the 2-sphere S<sup>2</sup> in Euclidean 3-space R<sup>3</sup> to provide a better understanding of the geometry of the curve. Especially, we obtain the formula of geodesic curvature for a quadratic rational Bézier curve that allows a curve to be characterized on the surface. Moreover, we give some important results and relations for the Darboux frame and geodesic curvature of a such curve. Then, in specific case, given characterizations for the quadratic rational Bézier curve are illustrated on a unit 2-sphere.
Ozkan Tukel, Gozde,Turhan, Tunahan,Yucesan, Ahmet The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.2
Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group G equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group G is SO(3).
Gozde Ozkan Tukel,Tunahan Turhan,Ahmet Yucesan 호남수학회 2019 호남수학학술지 Vol.41 No.2
Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group $G$ equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group $G$ is $SO(3).$