Is the Hamilton-Jacobi Equation Enough for Hamiltonian Dynamics?

[Sphinx]

Is Hamilton-Jacobi Equation equivalent to Hamilton equations or it is only a necessary condition ?
Thanks in advance :)

 

[BiGyElLoWhAt]

A quick google search finds:
https://en.wikipedia.org/wiki/Hamilton–Jacobi_equation
In mathematics, the Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations, and is a special case of the Hamilton–Jacobi–Bellman equation.[...]In physics, it is a formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion[citation needed], Lagrangian mechanics and Hamiltonian mechanics.
Does that answer the question? Or am I missing something here?

 

[drvrm]

Is Hamilton-Jacobi Equation equivalent to Hamilton equations

I do not think so please look up the following
http://www.srl.caltech.edu/phys106/p106b01/topic2.pdf