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Area Physics for electrotechnology / Relativistic physics for electrotechnology

IEV ref 113-07-45

Symbol
Rot

en
four-rotation
four-dimensional generalization of three-dimensional rotation

Rot A _ _ :={ A ν x μ A μ x ν } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaaiOuaiaac+gacaGG0b WaaWqaaeaacaWGbbaaaiaacQdacqGH9aqpdaGadaqaamaalaaabaGa eyOaIyRaamyqamaaBaaaleaacaaH9oaabeaaaOqaaiabgkGi2kaayI W7caWG4bWaaSbaaSqaaiaaeY7aaeqaaaaakiabgkHiTmaalaaabaGa eyOaIyRaamyqamaaBaaaleaacaaH8oaabeaaaOqaaiabgkGi2kaayI W7caWG4bWaaSbaaSqaaiaae27aaeqaaaaaaOGaay5Eaiaaw2haaaaa @4E6E@

where A _ _ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaWaaWqaaeaacaWGbbaaaa aa@347D@ is an arbitrary four-vector

Note 1 to entry: Four-rotation is useful in STR. In general theory of relativity (GTR) for non-flat space-time, a more sophisticated method is used.

Note 2 to entry: Whereas three-dimensional rotation is described by a pseudovector, four-rotation is described by an antisymmetric four-dimensional tensor.

Note 3 to entry: In the International System of Quantities, the dimension of four-rotation is L 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacaabaaGcbaGaciitamaaCaaaleqaba GaeyOeI0IaaGymaaaaaaa@35AD@ .


fr
quadrirotationnel, m
généralisation quadridimensionnelle du rotationnel tridimensionnel

Rot A _ _ :={ A ν x μ A μ x ν } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaaiOuaiaac+gacaGG0b WaaWqaaeaacaWGbbaaaiaacQdacqGH9aqpdaGadaqaamaalaaabaGa eyOaIyRaamyqamaaBaaaleaacaaH9oaabeaaaOqaaiabgkGi2kaayI W7caWG4bWaaSbaaSqaaiaaeY7aaeqaaaaakiabgkHiTmaalaaabaGa eyOaIyRaamyqamaaBaaaleaacaaH8oaabeaaaOqaaiabgkGi2kaayI W7caWG4bWaaSbaaSqaaiaae27aaeqaaaaaaOGaay5Eaiaaw2haaaaa @4E6E@

A _ _ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaWaaWqaaeaacaWGbbaaaa aa@347D@ est un quadrivecteur arbitraire

Note 1 à l’article: Le quadrirotationnel est utile en relativité restreinte. En relativité générale pour un espace-temps non plat, une méthode plus élaborée est utilisée.

Note 2 à l’article: Alors que le rotationnel tridimensionnel est décrit par un pseudovecteur, le quadrirotationnel est décrit par un tenseur quadridimensionnel antisymétrique.

Note 3 à l’article: Dans le Système international de grandeurs, la dimension du quadrirotationnel est L 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacaabaaGcbaGaciitamaaCaaaleqaba GaeyOeI0IaaGymaaaaaaa@35AD@ .


Publication date: 2022-06
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