Queries, comments, suggestions? Please contact us.



Area Mathematics - General concepts and linear algebra / Scalar and vector fields

IEV ref102-05-07

en
vector surface element
in the three-dimensional Euclidean space, vector normal to a given surface at a given point, the magnitude of which is the scalar surface element at the given point

Note 1 to entry: When the space orientation is defined by a right-handed trihedron, the direction of the vector surface element defines the orientation of the surface at that point as being in the anti-clockwise direction for an observer looking in the direction opposite to that of the vector.

Note 2 to entry: For a surface defined by r = f(u, v) where (u,v)U R 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaacIcacaWG1bGaai ilaiaadAhacaGGPaGaeyicI4CcLbuacaqGvbGccqGHgksZieqacaWF sbWaaWbaaSqabeaajugabiaabkdaaaaaaa@440F@ , the vector surface element is given by

f u × f v dudv MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaeyOaIy RaaCOzaaqaaiabgkGi2kaadwhaaaGaey41aq7aaSaaaeaacqGHciIT caWHMbaabaGaeyOaIyRaamODaaaacqGHflY1ciGGKbGaamyDaiGacs gacaWG2baaaa@4705@ .

Note 3 to entry: A vector surface element is preferably designated by e n dA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwgadaWgaaWcba GaaeOBaaqabaGccaGGKbGaamyqaaaa@3C90@ or sometimes by ndA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaah6gacaGGKbGaam yqaaaa@3B72@ , where e n =n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwgadaWgaaWcba GaaeOBaaqabaGccqGH9aqpcaWHUbaaaa@3CDF@ is a unit vector normal to the surface and dA is a scalar surface element.


fr
élément vectoriel de surface, m
dans l'espace euclidien à trois dimensions, vecteur normal à une surface donnée en un point donné, dont la norme est l'élément scalaire de surface au point donné

Note 1 à l'article: Lorsque l'orientation de l'espace est définie par un trièdre direct, la direction de l'élément vectoriel de surface définit l'orientation de la surface en ce point comme étant dans le sens inverse des aiguilles d'une montre pour un observateur regardant dans la direction opposée de celle du vecteur.

Note 2 à l'article: Pour une surface définie par r = f(u, v), où (u,v)U R 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaacIcacaWG1bGaai ilaiaadAhacaGGPaGaeyicI4CcLbuacaqGvbGccqGHgksZieqacaWF sbWaaWbaaSqabeaajugabiaabkdaaaaaaa@440F@ , l'élément vectoriel de surface est

f u × f v dudv MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaeyOaIy RaaCOzaaqaaiabgkGi2kaadwhaaaGaey41aq7aaSaaaeaacqGHciIT caWHMbaabaGaeyOaIyRaamODaaaacqGHflY1ciGGKbGaamyDaiGacs gacaWG2baaaa@4705@ .

Note 3 à l'article: Un élément vectoriel de surface est désigné de préférence par e n dA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwgadaWgaaWcba GaaeOBaaqabaGccaGGKbGaamyqaaaa@3C90@ ou parfois par ndA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaah6gacaGGKbGaam yqaaaa@3B72@ , où e n =n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwgadaWgaaWcba GaaeOBaaqabaGccqGH9aqpcaWHUbaaaa@3CDF@ est un vecteur unité normal à la surface et où dA est un élément scalaire de surface.


de
vektorielles Flächenelement, n

es
elemento vectorial de superficie

ja
ベクトル面積素

pl
element różniczkowy wektorowy powierzchni

pt
elemento vectorial de superfície

sr
векторски елемент површи, м јд

sv
vektoriellt ytelement

zh
向量曲面元素

Publication date: 2008-08
Copyright © IEC 2017. All Rights Reserved.