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Area Physics for electrotechnology / Mechanics

IEV ref113-03-76

Symbol
L

en
Lagrange function
difference of kinetic energy T( q i ,  q ˙ i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadsfacaGGOaGaam yCamaaBaaaleaacaWGPbaabeaakiaacYcacaqGGaGabmyCayaacaWa aSbaaSqaaiaadMgaaeqaaOGaaiykaaaa@408F@ and potential energy V(qi), where qi is a generalized coordinate and q ˙ i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiqadghagaGaamaaBa aaleaacaWGPbaabeaaaaa@3AE6@ is a generalized velocity, thus L( q i ,  q ˙ i )=T( q i ,  q ˙ i )V( q i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadYeacaGGOaGaam yCamaaBaaaleaacaWGPbaabeaakiaacYcacaqGGaGabmyCayaacaWa aSbaaSqaaiaadMgaaeqaaOGaaiykaiabg2da9iaadsfacaGGOaGaam yCamaaBaaaleaacaWGPbaabeaakiaacYcacaqGGaGabmyCayaacaWa aSbaaSqaaiaadMgaaeqaaOGaaiykaiabgkHiTiaadAfacaGGOaGaam yCamaaBaaaleaacaWGPbaabeaakiac+aOGPaaaaa@4F50@

NOTE 1 The potential energy V(qi) can be generalized to dynamic potential V( q i q ˙ i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadAfacaGGOaGaam yCamaaBaaaleaajug4aiaadMgaaSqabaqcLbsacaqGSaGaaeiiaOGa bmyCayaacaWaaSbaaKqzGeqaaKqzGdGaamyAaaqcLbsabeaakiaabc cajugibiac+aOGPaaaaa@46D1@ .

NOTE 2 The coherent SI unit of Lagrange function is joule, J.


fr
fonction de Lagrange, f
différence entre l’énergie cinétique T( q i ,  q ˙ i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadsfacaGGOaGaam yCamaaBaaaleaacaWGPbaabeaakiaacYcacaqGGaGabmyCayaacaWa aSbaaSqaaiaadMgaaeqaaOGaaiykaaaa@408F@ et l’énergie potentielle V(qi), où qi est une coordonnée généralisée et q ˙ i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiqadghagaGaamaaBa aaleaacaWGPbaabeaaaaa@3AE6@ est une vitesse généralisée, soit L( q i ,  q ˙ i )=T( q i ,  q ˙ i )V( q i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadYeacaGGOaGaam yCamaaBaaaleaacaWGPbaabeaakiaacYcacaqGGaGabmyCayaacaWa aSbaaSqaaiaadMgaaeqaaOGaaiykaiabg2da9iaadsfacaGGOaGaam yCamaaBaaaleaacaWGPbaabeaakiaacYcacaqGGaGabmyCayaacaWa aSbaaSqaaiaadMgaaeqaaOGaaiykaiabgkHiTiaadAfacaGGOaGaam yCamaaBaaaleaacaWGPbaabeaakiac+aOGPaaaaa@4F50@

NOTE 1 L’énergie potentielle V(qi) peut être généralisée au potentiel dynamique V( q i q ˙ i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadAfacaGGOaGaam yCamaaBaaaleaajug4aiaadMgaaSqabaqcLbsacaqGSaGaaeiiaOGa bmyCayaacaWaaSbaaKqzGeqaaKqzGdGaamyAaaqcLbsabeaakiaabc cajugibiac+aOGPaaaaa@46D1@ .

NOTE 2 L’unité SI cohérente de fonction de Lagrange est le joule, J.


ar
معادلة لاجرانج

de
Lagrange-Funktion, f

es
función de Lagrange

fi
Lagrangen funktio

it
funzione di Lagrange

ja
ラグランジュ関数

pl
funkcja Lagrange’a

pt
função de Lagrange

sv
lagrangefunktion

zh
拉格朗日函数

Publication date: 2011-04
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