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arXiv · 1708.01586

A Hamilton-Jacobi theory for implicit differential systems

O. Esen·M. de León·C. Sardón
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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 $TT^*Q$ 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.

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O. Esen, M. de León, C. Sardón. 2017-08-04. A Hamilton-Jacobi theory for implicit differential systems. https://doi.org/10.1063/1.4999669

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