A Hamilton-Jacobi theory for implicit differential systems
Mathematical Physics
2018-03-14 v1 math.MP
Abstract
In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of generated by Morse families. The implicit character implies the nonexistence of a Hamiltonian function describing the dynamics. This fact is here amended by a generating family of Morse functions which plays the role of a Hamiltonian. A Hamilton--Jacobi equation is obtained with the aid of this generating family of functions. To conclude, we apply our results to singular Lagrangians by employing the construction of special symplectic structures.
Cite
@article{arxiv.1708.01586,
title = {A Hamilton-Jacobi theory for implicit differential systems},
author = {O. Esen and M. de León and C. Sardón},
journal= {arXiv preprint arXiv:1708.01586},
year = {2018}
}