In this talk, I will present, in a geometric framework, the Hamilton–Jacobi equations for a large variety of mechanical systems. In the first part of the talk, I will show the classical theory for Hamiltonian systems on a cotangent bundle and its relationship with the integrability of these systems. In the second part of the talk, we will see recent developments in the framework of general Poisson, almost-Poisson, contact manifolds and its relation with the integrability by quadrature. Several examples will illustrate the theory.

Meeting ID: 814 591 7621 Passcode: 147983