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Area Mathematics - Functions / Sinusoidal quantities

IEV ref 103-07-12

en
instantaneous complex value
rotating phasor
complex representation, <of a sinusoidal quantity>
for a sinusoidal quantity a(t)= A ^ cos(ωt+ ϑ 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadggacaGGOaGaam iDaiaacMcacqGH9aqpceWGbbGbaKaajugabiGacogacaGGVbGaai4C aOGaciikaiabeM8a3jaayIW7caWG0bGaey4kaSIaeqy0dO0aaSbaaS qaaKqzadGaaGimaaWcbeaakiaacMcaaaa@4817@ , complex quantity

a _ (t)= A ^ [cos(ωt+ ϑ 0 )+jsin(ωt+ ϑ 0 )]= A ^ exp[j(ωt+ ϑ 0 )]= A ^ exp(jωt)exp(j ϑ 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaamaaabaGaamyyaa aacaGGOaGaamiDaiaacMcacqGH9aqpceWGbbGbaKaajugGbiaacUfa jugqbiGacogacaGGVbGaai4CaOGaciikaiabeM8a3jaayIW7caWG0b Gaey4kaSIaeqy0dO0aaSbaaSqaaKqzaeGaaGimaaWcbeaakiaacMca cqGHRaWkjugqbiGacQgakiaaysW7jugqbiaacohacaGGPbGaaiOBaO GaciikaiabeM8a3jaayIW7caWG0bGaey4kaSIaeqy0dO0aaSbaaSqa aKqzaeGaaGimaaWcbeaakiaacMcajugGbiaac2facqGH9aqpkiqadg eagaqcaKqzafGaciyzaiaacIhacaGGWbqcLbyaciGGBbqcLbuaciGG QbGcciGGOaGaeqyYdCNaaGjcVlaadshacqGHRaWkcqaHrpGsdaWgaa WcbaqcLbqacaaIWaaaleqaaOGaaiykaKqzagGaaiyxaiabg2da9OGa bmyqayaajaqcLbuaciGGLbGaaiiEaiaacchakiGacIcajugqbiGacQ gakiabeM8a3jaayIW7caWG0bGaaiykaKqzafGaciyzaiaacIhacaGG WbGcciGGOaqcLbuaciGGQbGccqaHrpGsdaWgaaWcbaqcLbqacaaIWa aaleqaaOGaaiykaaaa@8771@

where j is the imaginary unit, A ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiqadgeagaqcaaaa@3628@ is complex amplitude, ω MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeM8a3baa@371F@ is angular frequency, and ϑ 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeg9aknaaBaaale aajugabiaaicdaaSqabaaaaa@385A@ is initial phase

Note 1 to entry: The instantaneous value of the quantity is the real part of its complex representation.


fr
valeur instantanée complexe, f
phaseur tournant, m
représentation complexe, <d'une grandeur sinusoïdale> f
pour une grandeur sinusoïdale a(t)= A ^ cos(ωt+ ϑ 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadggacaGGOaGaam iDaiaacMcacqGH9aqpceWGbbGbaKaajugabiGacogacaGGVbGaai4C aOGaciikaiabeM8a3jaayIW7caWG0bGaey4kaSIaeqy0dO0aaSbaaS qaaKqzadGaaGimaaWcbeaakiaacMcaaaa@4817@ , grandeur complexe

a _ (t)= A ^ [cos(ωt+ ϑ 0 )+jsin(ωt+ ϑ 0 )]= A ^ exp[j(ωt+ ϑ 0 )]= A ^ exp(jωt)exp(j ϑ 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaamaaabaGaamyyaa aacaGGOaGaamiDaiaacMcacqGH9aqpceWGbbGbaKaajugGbiaacUfa jugqbiGacogacaGGVbGaai4CaOGaciikaiabeM8a3jaayIW7caWG0b Gaey4kaSIaeqy0dO0aaSbaaSqaaKqzaeGaaGimaaWcbeaakiaacMca cqGHRaWkjugqbiGacQgakiaaysW7jugqbiaacohacaGGPbGaaiOBaO GaciikaiabeM8a3jaayIW7caWG0bGaey4kaSIaeqy0dO0aaSbaaSqa aKqzaeGaaGimaaWcbeaakiaacMcajugGbiaac2facqGH9aqpkiqadg eagaqcaKqzafGaciyzaiaacIhacaGGWbqcLbyaciGGBbqcLbuaciGG QbGcciGGOaGaeqyYdCNaaGjcVlaadshacqGHRaWkcqaHrpGsdaWgaa WcbaqcLbqacaaIWaaaleqaaOGaaiykaKqzagGaaiyxaiabg2da9OGa bmyqayaajaqcLbuaciGGLbGaaiiEaiaacchakiGacIcajugqbiGacQ gakiabeM8a3jaayIW7caWG0bGaaiykaKqzafGaciyzaiaacIhacaGG WbGcciGGOaqcLbuaciGGQbGccqaHrpGsdaWgaaWcbaqcLbqacaaIWa aaleqaaOGaaiykaaaa@8771@

où j est l’unité imaginaire, A ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiqadgeagaqcaaaa@3628@ est l'amplitude complexe, ω MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeM8a3baa@371F@ est la pulsation et ϑ 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeg9aknaaBaaale aajugabiaaicdaaSqabaaaaa@385A@ est la phase à l'origine

Note 1 à l'article: La valeur instantanée de la grandeur est la partie réelle de la représentation complexe.


ar
قيمة لحظية مركبة
الطور الدوار
التمثيل المركب للقيمة الجيبية

cs
okamžitá komplexní hodnota
komplexní reprezentace, (sinusoidální veličiny)

de
rotierender Amplitudenzeiger, m
Drehzeiger, m

es
valor instantáneo complejo

it
valore istantaneo complesso
fasore (rotante)
rappresentazione complessa (di una grandezza sinusoidale)

ko
순시 복소값

ja
瞬時複素数
回転位相ベクトル
複素表現, <正弦量の>

nl
be ogenblikkelijke complexe waarde, f
draaiende fasor, m

pl
fazor wirujący
wartość chwilowa zespolona
reprezentacja zespolona (wielkości sinusoidalnej)

pt
valor instantâneo complexo
fasor rotativo
representação complexa (de uma grandeza complexa)

sr
тренутна комплексна вредност, ж јд
обртни фазор, м јд
комплексно представљање, <синусне величине> с јд

sv
komplex representation (av en sinusformad storhet)
roterande visare
momentant komplext värde

zh
瞬时复值
旋转相量
复表示, <一个正弦量的>

Publication date: 2009-12
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