从另一个角度看E^3的相关曲线

IF 0.7 Q2 MATHEMATICS
S. Şenyurt, Davut Canlı, K. H. Ayvaci
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引用次数: 0

摘要

本文定义了切线、主法线和副法线方向的关联曲线,使得任何给定曲线的每个向量分别位于其伴侣的密切平面、法线平面和整流平面上。对于每个关联的曲线,根据Frenet帧向量来公式化新的移动帧和相应的曲率。除此之外,还讨论了曲线及其相关配偶之间距离函数的可能解。特别地,可以看出,渐开线曲线一般属于切线相关曲线族,Bertrand和Mannheim曲线属于主法线相关曲线。最后,作为一个应用,我们给出了一些例子,并将给定的曲线与其伙伴及其相应的运动框架映射在一起。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Associated curves from a different point of view in $E^3$
In this paper, tangent, principal normal and binormal wise associated curves are defined such that each of these vectors of any given curve lies on the osculating, normal and rectifying plane of its partner, respectively. For each associated curve, a new moving frame and the corresponding curvatures are formulated in terms of Frenet frame vectors. In addition to this, the possible solutions for distance functions between the curve and its associated mate are discussed. In particular, it is seen that the involute curves belong to the family of tangent associated curves in general and the Bertrand and the Mannheim curves belong to the principal normal associated curves. Finally, as an application, we present some examples and map a given curve together with its partner and its corresponding moving frame.
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