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

@article{AIF_1973__23_1_203_0,
     author = {Goldschmidt, Hubert and Sternberg, Shlomo},
     title = {The Hamilton-Cartan formalism in the calculus of variations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {23},
     number = {1},
     year = {1973},
     pages = {203-267},
     doi = {10.5802/aif.451},
     zbl = {0243.49011},
     mrnumber = {49 \#6279},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1973__23_1_203_0}
}
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. http://www.numdam.org/item/AIF_1973__23_1_203_0/

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