圆柱面上具非零曲率和挠率的曲线特征  

The Feature of the Curves with Nonzero Curvature and Torsion on Cylindrical Surfaces

作　　者：刘倩[1] Liu Qian(Henan Information and Engineering University)

机构地区：[1]河南信息工程大学

出　　处：《哈尔滨师范大学自然科学学报》2019年第4期50-53,共4页Natural Science Journal of Harbin Normal University

摘　　要：三维欧氏空间中的曲线的Frenet标架的运动方程满足Frenet公式,并且在相差一个旋转变换和平移变换的意义下由其曲率和挠率唯一确定.在曲线所在曲面有特殊结构的情况下,可以得出曲面上曲线的曲率和挠率满足的关系.文中只利用了圆柱面上曲线在中心轴上的投影函数给出了圆柱面上具非零曲率和挠率的光滑曲线其曲率和挠率必须满足的方程.The moving equations of the Frenet frame of curves in the Euclid Space of three dimension is satisfied the Frenet formula,which are only determined by its curvature and torsion up to a rotational transformation or a translation transformation.The relation between curvature and torsion of the curves which on the surface that have special structure is derived in the paper.The projection function of curves on cylindrical surfaces to the center axis is used,then the equation of the curvature and torsion of the curves on cylindrical surfaces is got.

关 键 词：曲线理论 FRENET公式 曲率 挠率 结构方程 

分 类 号：O186.11[理学—数学]