请输入您要查询的字词:

 

单词 FrenetFrame
释义

Frenet frame


Let I be an intervalMathworldPlanetmathPlanetmath and let γ:I3 be aparameterized space curve, assumed to beregularPlanetmathPlanetmathPlanetmath (http://planetmath.org/SpaceCurve) and free of points of inflection. Weinterpret γ(t) as the trajectory of a particle moving through3-dimensional space. The moving trihedron (also known as the Frenetframe, the Frenet trihedron, the repère mobile, and the movingframe) is an orthonormal basis of 3-vectors T(t),N(t),B(t), definedand named as follows:

T(t)=γ(t)γ(t),the unit tangent;
N(t)=T(t)T(t),the unit normal;
B(t)=T(t)×N(t),the unit binormal.

A straightforward application of the chain ruleMathworldPlanetmath shows that thesedefinitions are covariant with respect to reparameterizations. Hence,the above three vectors should be conceived as being attached to thepoint γ(t) of the oriented space curve, rather than beingfunctions of the parameter t.

Corresponding to the above vectors are 3 planes, passing through eachpoint γ(t) of the space curve. The osculating plane atthe point γ(t) is the plane spanned by T(t) and N(t); thenormal planeMathworldPlanetmath at γ(t) is the plane spanned by N(t) andB(t); the rectifying plane at γ(t) is the plane spanned byT(t) and B(t).

TitleFrenet frame
Canonical nameFrenetFrame
Date of creation2013-03-22 12:15:44
Last modified on2013-03-22 12:15:44
Ownerrmilson (146)
Last modified byrmilson (146)
Numerical id16
Authorrmilson (146)
Entry typeDefinition
Classificationmsc 53A04
Synonymmoving trihedron
Synonymmoving frame
Synonymrepère mobile
SynonymFrenet trihedron
Related topicSpaceCurve
Definesosculating plane
Definesnormal plane
Definesrectifying plane
Definesunit normal
Definesunit tangent
Definesbinormal
随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 17:40:31