摘要
根据微分几何基本理论,对圆柱螺线的性质进行探讨,证明了圆柱螺线的切线与Z轴相交于定角,圆柱螺线的曲率与挠率都是常数,且曲率与挠率都是常数的曲线必是圆柱螺线,圆柱螺线必是Bertrand曲线,圆柱螺线是其所在圆柱面的测地线等性质。
According to the basic principles of differential geometry, this article discusses the properties of cylindrical spirals, and it is proved that the tangents of cylindrical spirals cross axis Z at the fixed-angle; the curvature and torsion of cylindrical spirals are all constants, and the curves whose curvature and torsion are constants must be the cylindrical spirals; the cylindrical spirals must be Bertrand curves; cylindrical spirals are the geodesic curves of local cylindrical surface, and so on.
出处
《温州职业技术学院学报》
2008年第2期47-49,共3页
Journal of Wenzhou Polytechnic
关键词
圆柱螺线
曲率
挠率
测地线
测地曲率
Cylindrical spiral
Curvature
Torsion
Geodesic curve
Geodesic curvature
