椭圆抛物面上的渐伸线  

Involute on the Elliptic Paraboloid

作　　者：毛婷[1] 项海燕[1] 方梦丹 牟金平[1] MAO Ting XIANG Haiyan FANG Mengdan MOU Jinping(School of Mathematics and Information Engineering, Taizhou University, Linhai 317000, Zhejiang, China)

机构地区：[1]台州学院数学与信息工程学院,浙江临海317000

出　　处：《台州学院学报》2017年第3期4-7,12,共5页Journal of Taizhou University

基　　金：浙江省教育厅基金资助项目(Y201533479);台州学院培育基金资助项目(2016PY017);台州学院学生校立项目(17XS14)

摘　　要：将平面渐伸线映射到椭圆抛物面上,得到椭圆抛物面上的渐伸线。对圆抛物面上的渐伸线进行研究,得到了这种渐伸线的切线、法平面、密切平面、曲率、挠率以及其正交轨线方程,并且研究了它的曲率与挠率之间的关系。Based on a mapping from a plane involute to an elliptic paraboloid, it gets an involute of the elliptic paraboloid（IEP）. According to the investigation on IEP, we get respectively its tangent, normal plane, osculating plane, curvature, torsion and orthogonal trajectory. In the meanwhile, the relation between the curvature and the torsion is discussed.

关 键 词：椭圆抛物面 渐伸线 曲率 挠率 法曲率 

分 类 号：O186.1[理学—数学]