$\mathbb{E}^{3}$中的Salkowski曲线及其修正正交框架

Sümeyye GÜR MAZLUM, S. Şenyurt, M. Bektaş
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引用次数: 1

摘要

本文研究了$\mathbb{E}^{3}$中Salkowski曲线的一些性质。然后我们在Salkowski曲线的参数方程中解释了角度$(nt)$。我们给出了这个角与萨尔科夫斯基曲线的二法向量和达布向量之间的夹角之间的关系。通过这个角度,我们得到了曲线达布向量方向上的单位向量。最后,我们计算了曲率和扭转的修正正交框架,并给出了曲线的Frenet框架与修正正交框架之间的关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$
In this study, we examine some properties of Salkowski curves in $\mathbb{E}^{3}$. We then make sense of the angle $(nt)$ in the parametric equation of the Salkowski curves. We provide the relationship between this angle and the angle between the binormal vector and the Darboux vector of the Salkowski curves. Through this angle, we obtain the unit vector in the direction of the Darboux vector of the curve. Finally, we calculate the modified orthogonal frames with both the curvature and the torsion and give the relationships between the Frenet frame and the modified orthogonal frames of the curve.
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