An overview of the Hamilton–Jacobi theory: the classical and geometrical approaches and some extensions and applications
Visualitza/Obre
Cita com:
hdl:2117/361018
Tipus de documentArticle
Data publicació2021-01-01
EditorMultidisciplinary Digital Publishing Institute (MDPI)
Condicions d'accésAccés obert
Llevat que s'hi indiqui el contrari, els
continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
:
Reconeixement 4.0 s
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.
CitacióRoman-Roy, N. An overview of the Hamilton–Jacobi theory: the classical and geometrical approaches and some extensions and applications. "Mathematics", 1 Gener 2021, vol. 9, núm. 1, article 85.
ISSN2227-7390
Versió de l'editorhttps://www.mdpi.com/2227-7390/9/1/85
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
mathematics-09-00085-v2.pdf | 384,6Kb | Visualitza/Obre |