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IEVref:102-05-22ID:
Language:enStatus: Standard
Term: rotation
Synonym1: curl
[Preferred]
Synonym2:
Synonym3:
Symbol:
Definition: vector rot U associated at each point of a given space region with a vector U, equal to the limit of the integral over a closed surface S of the vector product of the vector surface element and the vector U, divided by the volume of the interior of the surface, when the surface is contained in a sphere the radius of which tends to zero

rotU= lim V0 1 V S e n UdA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiGackhacaGGVbGaai iDaiaahwfacqGH9aqpdaWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGa amOvaiabgkziUkaaicdaaeqaaOWaaSaaaeaacaaIXaaabaGaamOvaa aadaWdwbqaaiaahwgadaWgaaWcbaGaamOBaaqabaGccqGHxdaTcaWH vbGaciizaiaadgeaaSqaaiaabofaaeqaniablkH7slabgUIiYlabgU IiYdaaaa@5061@

where endA is the vector surface element oriented outwards and V is the volume

Note 1 to entry: In orthonormal Cartesian coordinates, the three coordinates of the rotation are:

U z y U y z , U x z U z x , U y x U x y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaeyOaIy RaaGPaVlaadwfadaWgaaWcbaGaamOEaaqabaaakeaacqGHciITcGaA aIPaVlaadMhaaaGaeyOeI0YaaSaaaeaacqGHciITcaaMc8Uaamyvam aaBaaaleaacaWG5baabeaaaOqaaiabgkGi2kaaykW7caWG6baaaiaa ysW7caaMe8UaaGjbVlaacYcacaaMe8UaaGjbVlaaysW7caaMe8+aaS aaaeaacqGHciITcaaMc8UaamyvamaaBaaaleaacaWG4baabeaaaOqa aiabgkGi2kaaykW7caWG6baaaiabgkHiTmaalaaabaGaeyOaIyRaaG PaVlaadwfadaWgaaWcbaGaamOEaaqabaaakeaacqGHciITcaaMc8Ua amiEaaaacaaMe8UaaGjbVlaaysW7caGGSaGaaGjbVlaaysW7caaMe8 UaaGjbVpaalaaabaGaeyOaIyRaaGPaVlaadwfadaWgaaWcbaGaamyE aaqabaaakeaacqGHciITcaaMc8UaamiEaaaacqGHsisldaWcaaqaai abgkGi2kaaykW7caWGvbWaaSbaaSqaaiaadIhaaeqaaaGcbaGaeyOa IyRaaGPaVlaadMhaaaaaaa@898E@

Note 2 to entry: The rotation of a polar vector is an axial vector and the rotation of an axial vector is a polar vector.

Note 3 to entry: The rotation of the vector field U is denoted by rotU MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiGacogacaGG1bGaai OCaiaacYgacaWHvbaaaa@39F6@ or U MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGWabiab=DGirlabgE na0kaahwfaaaa@3D4D@ . In some English texts, the rotation is denoted by curlU MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiGacogacaGG1bGaai OCaiaacYgacaWHvbaaaa@39F6@ .


Publication date:2008-08
Source:
Replaces:
Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
2017-08-24: Added a <b> tag that was missing for first U. LMO
CO remarks:
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