Home > Calcul Des Variations: Longueur D'Un ARC, Multiplicateur de Lagrange, Formule de Steiner-Minkowski, Theorie Du Transport, Equation D'Euler-La(French)
Calcul Des Variations: Longueur D'Un ARC, Multiplicateur de Lagrange, Formule de Steiner-Minkowski, Theorie Du Transport, Equation D'Euler-La(French)

Calcul Des Variations: Longueur D'Un ARC, Multiplicateur de Lagrange, Formule de Steiner-Minkowski, Theorie Du Transport, Equation D'Euler-La(French)

          
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About the Book

Ce contenu est une compilation d'articles de l'encyclopedie libre Wikipedia. Pages: 25. Non illustre. Chapitres: Longueur d'un arc, Multiplicateur de Lagrange, Formule de Steiner-Minkowski, Theorie du transport, Equation d'Euler-Lagrange, Courbe brachistochrone, Derivee fonctionnelle, Lemme fondamental du calcul des variations, Espace de Finsler. Extrait: En geometrie, la question de la longueur d'un arc est simple a concevoir (intuitive). L'idee d'arc correspond a celle d'une ligne, ou d'une trajectoire d'un point dans un plan ou l'espace par exemple. Sa longueur peut etre vue comme la distance parcourue par un point materiel suivant cette trajectoire ou encore comme la longueur d'un fil prenant exactement la place de cette ligne. La longueur d'un arc est, soit un nombre positif, soit l'infini. Un vieil exemple est celui du demi-cercle de rayon r, ou r designe un nombre reel positif. Sa longueur est egale a r. Un exemple, plus simple, est donne par un segment, sa longueur est egale a la distance qui separe ses deux extremites. Selon l'epoque, differentes methodes permettent de definir et de mesurer la longueur d'un ensemble d'arcs de plus en plus vaste. Eudoxe de Cnide, un mathematicien grec du siecle av. J. C., puis Archimede utilisent une methode, dite d'exhaustion pour calculer celle d'un arc de cercle. La physique de la fin du siecle developpe une nouvelle approche, fondee sur les progres realises en mecanique du point grace en particulier au calcul infinitesimal applique a l'astronomie. La longueur d'un arc est percue comme le produit du temps necessaire a un point materiel pour parcourir l'arc par sa vitesse, si elle est supposee constante. Cette definition est generalisee par Bernhard Riemann et devient la pierre angulaire pour construire une distance sur de nouvelles geometries, maintenant appelees varietes riemanniennes. Pour le mathematicien francais Camille Jordan (1838 - 1922), ces...


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Product Details
  • ISBN-13: 9781159400736
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 26
  • Series Title: French
  • Sub Title: Longueur D'Un ARC, Multiplicateur de Lagrange, Formule de Steiner-Minkowski, Theorie Du Transport, Equation D'Euler-La
  • Width: 189 mm
  • ISBN-10: 1159400733
  • Publisher Date: 12 Oct 2012
  • Binding: Paperback
  • Language: French
  • Returnable: N
  • Spine Width: 1 mm
  • Weight: 68 gr


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