In this paper we develop a Hamilton-Jacobi theory in the setting of almost Poisson manifolds. The theory extends the classical Hamilton-Jacobi theory and can be also applied to very general situations including nonholonomic mechanical systems and time dependent systems with external forces.
@article{arxiv.1209.5351,
title = {A Universal Hamilton-Jacobi Theory},
author = {Manuel de León and David Martín de Diego and Miguel Vaquero},
journal= {arXiv preprint arXiv:1209.5351},
year = {2012}
}