| 关于圆柱螺线性质的一些探讨 |
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| 引用本文： | 闫焱.关于圆柱螺线性质的一些探讨[J].西安文理学院学报,2006,9(4):45-47. |
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| 作者姓名： | 闫焱 |
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| 作者单位： | 西安文理学院数学系 陕西西安710065 |
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| 基金项目： | 西安文理学院校科研和教改项目 |
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| 摘 要： | 通过对一般曲线的切向量的球面像的曲率和挠率的计算,得出了圆柱螺线的三个基本向量的球面像都是球面上的平面曲线,并且是圆弧的结论.用不同的方法证明了圆柱螺线是它所在圆柱面上的测地线.说明了圆柱螺线是Bertrand曲线,同时曲率和挠率都是常数的空间曲线一定是圆柱螺线.
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| 关 键 词： | 圆柱螺线 球面像 曲率 挠率 |
| 文章编号： | 1008-5564(2006)04-0045-03 |
| 收稿时间： | 06 7 2006 12:00AM |
| 修稿时间： | 2006年6月7日 |
Properties of Cylindrical Spirals |
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| YAN Yan.Properties of Cylindrical Spirals[J].Journal of Xi‘an University of Arts & Science:Natural Science Edition,2006,9(4):45-47. |
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| Authors: | YAN Yan |
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| Abstract: | The properties of cylindrical spirals were discussed.Through the calculation of curvature and torsion of a common curve of tangential vector of sphere mapping,it was concluded that the sphere mappings of three basic vectors of a cylindrical spiral: tangential vector,major normal vector and secondary normal vector,were all both planar spherical curves and arcs.In addition,it was proved that the cylindrical spiral was a geodesic in the cylindrical surface.It shows that cylindrical spirals are Bertrand curves and a space curve with constant curvature and torsion is a cylindrical spiral. |
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| Keywords: | cylindrical spiral sphere mapping curvature torsion |
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