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.
Funder
Ministerio de Ciencia, Innovación y Universidades
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference57 articles.
1. Mathematical Methods of Classical Mechanics
2. Classical Dynamics: A Contemporary Approach;José,1998
3. Mécanique;Landau,1976
4. Theoretical Mechanics;Saletan,1971
5. Hamilton–Jacobi theory for constrained systems
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献