The Hamilton-Cartan formalism in the calculus of variations
Annales de l'Institut Fourier, Volume 23 (1973) no. 1, pp. 203-267.

We give an exposition of the calculus of variations in several variables. The introduction of a linear differential form studied by Cartan makes possible an invariant treatment of the Hamiltonian formalism. Noether’s theorem, the Hamilton-Jacobi equation and the second variation are discussed and a Poisson bracket is defined.

Nous donnons un exposé du calcul des variations à plusieurs variables indépendantes. L’introduction d’une forme différentielle de degré un étudiée par Cartan nous permet de donner une version invariante du formalisme hamiltonien. Le théorème de Noether, l’équation de Hamilton-Jacobi et la variation seconde sont abordés et un crochet de Poissson est défini.

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Goldschmidt, Hubert; Sternberg, Shlomo. The Hamilton-Cartan formalism in the calculus of variations. Annales de l'Institut Fourier, Volume 23 (1973) no. 1, pp. 203-267. doi : 10.5802/aif.451. https://aif.centre-mersenne.org/articles/10.5802/aif.451/

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