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An Overview of the Hamilton–Jacobi Theory: the Classical and Geometrical Approaches and Some Extensions and Applications

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  • Narciso Román-Roy

    (Department of Mathematics, Campus Nord, Universitat Politècnica de Catalunya, Ed. C3, 08034 Barcelona, Spain)

Abstract

This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton–Jacobi theory. The relation with the “classical” Hamiltonian approach using canonical transformations is also analyzed. Furthermore, a more general framework for the theory is also briefly explained. It is also shown how, from this generic framework, the Lagrangian and Hamiltonian cases of the theory for dynamical systems are recovered, as well as how the model can be extended to other types of physical systems, such as higher-order dynamical systems and (first-order) classical field theories in their multisymplectic formulation.

Suggested Citation

  • Narciso Román-Roy, 2021. "An Overview of the Hamilton–Jacobi Theory: the Classical and Geometrical Approaches and Some Extensions and Applications," Mathematics, MDPI, vol. 9(1), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:1:p:85-:d:474046
    as

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    References listed on IDEAS

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    1. Lembke B., 1918. "√ a. p," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 111(1), pages 709-712, February.
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