  A generalization of the Hamilton-Jacobi theory to arbitrary dynamical
systems, including non-Hamiltonian ones, is considered. The generalized
Hamilton-Jacobi theory is constructed as a theory of ensemble of identical
systems moving in the configuration space and described by the continual
equation of motion and the continuity equation. For Hamiltonian systems, the
usual Hamilton-Jacobi equations naturally follow from this theory. The proposed
formulation of the Hamilton-Jacobi theory, as the theory of ensemble, allows
interpreting in a natural way the transition from quantum mechanics in the
Schrodinger's form to classical mechanics.
