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词汇 Osculating plane
分类 英语词汇 英语翻译词典
释义

Osculating plane

中文百科

密切平面

密切平面：过空间曲线上P点的切线和P点的邻近一点Q可作一平面\sigma，当Q点沿着曲线趋近于P时，平面\sigma的极限位置\pi称为曲线在P点的密切平面。

一般参数的表示

(R-r(t_{0}),r'(t_{0}),r''(t_{0})) = 0

其中 R ＝ {X,Y,Z}表示P点的密切平面上任意一点的向径。

上式也可用行列式表示为 \begin{vmatrix} X-x(t_{0})&Y-y(t_{0})&Z-z(t_{0})\\x'(t_{0})&y'(t_{0})&z'(t_{0})\\x''(t_{0})&y''(t_{0})&z''(t_{0}) \end{vmatrix} = 0

自然参数的表示

(R-r(s_{0}),\dot{r}(s_{0}),\ddot{r}(s_{0})) = 0 其中r=r(s).

上式也可用行列式表示为 \begin{vmatrix} X-x(s_{0})&Y-y(s_{0})&Z-z(s_{0})\\ \dot{x}(s_{0})& \dot{y}(s_{0})& \dot{z}(s_{0})\\ \ddot{x}(s_{0})& \ddot{y}(s_{0})& \ddot{z}(s_{0}) \end{vmatrix} = 0

英语百科

Osculating plane 密切平面

A space curve, Frenet–Serret frame, and the osculating plane (spanned by T and N).

In mathematics, particularly in differential geometry, an osculating plane is a plane in a Euclidean space or affine space which meets a submanifold at a point in such a way as to have a second order of contact at the point. The word osculate is from the Latin osculatus which is a past participle of osculari, meaning to kiss. An osculating plane is thus a plane which "kisses" a submanifold.
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