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Area Mathematics - Functions / Sinusoidal quantities

IEV ref103-07-12

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

de
rotierender Amplitudenzeiger, m
Drehzeiger, m

es
valor instantáneo complejo

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

ja
瞬時複素数
回転位相ベクトル
複素表現, <正弦量の>

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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