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The Hamilton-Cartan formalism in the calculus of variations. (English) Zbl 0243.49011
Summary: 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.

MSC:
49L99 Hamilton-Jacobi theories
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References:
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