"Hamilton-Jacobi theory and geometric mechanics"

From the viewpoint of geometric mechanics, any dynamical system should be described in a coordinate-independent way, by means of the tools of differential geometry. Thinking about the geometric structures involved may lead to new interesting questions. We focus on Hamilton-Jacobi equation, which is in some regards equivalent to Hamilton’s equation. In particular, we will give an interpretation of Hamilton-Jacobi equation on a manifold in terms of a family of differential equations on a lower-dimensional manifold.