Notes on Curves at a Constant Distance from the Edge of Regression on a Curve in Galilean 3-Space G_(3)  

作　　者：Ali Cakmak Sezai Kızıltug Gokhan Mumcu 

机构地区：[1]Department of Mathematics,Faculty of Arts and Sciences,Bitlis Eren University,Bitlis,13000,Turkey [2]Graduate School of Natural and Applied Sciences,Erzincan Binali Yıldırım University,Erzincan,24002,Turkey [3]Department of Mathematics,Faculty of Arts and Science,Erzincan Binali Yıldırım University,Erzincan,24002,Turkey

出　　处：《Computer Modeling in Engineering & Sciences》2023年第6期2731-2742,共12页工程与科学中的计算机建模（英文）

摘　　要：In this paper,we define the curve rλ=r+λd at a constant distance from the edge of regression on a curve r(s)with arc length parameter s in Galilean 3-space.Here,d is a non-isotropic or isotropic vector defined as a vector tightly fastened to Frenet trihedron of the curve r(s)in 3-dimensional Galilean space.We build the Frenet frame{Tλ,Nλ,Bλ}of the constructed curve rλwith respect to two types of the vector d and we indicate the properties related to the curvatures of the curve rλ.Also,for the curve rλ,we give the conditions to be a circular helix.Furthermore,we discuss ruled surfaces of type A generated via the curve rλand the vector D which is defined as tangent of the curve rλin 3-dimensional Galilean space.The constructed ruled surfaces also appear in two ways.The first is constructed with the curve rλ(s)=r(s)+λT(s)and the non-isotropic vector D.The second is formed by the curve rλ=r(s)+λ2N+λ3B and the non-isotropic vector D.We calculate the distribution parameters of the constructed ruled surfaces and we show that the ruled surfaces are developable.Finally,we provide examples and visuals to back up our research.

关 键 词：Edge of regression Galilean space CURVATURE HELIX ruled surface 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]