Generalized Hamiltonian mechanics

Marsden, J. E.

Arch. Rational Mech. Anal., 28, (1968), 323-361

Abstract:

Our purpose is to generalize Hamiltonian mechanics t the case in which the energy function (Hamiltonian), H , is a distribution (generalized function) in the sense of Schwartz. We follow the same general program as in the smooth case. Familiarity with the smooth case is helpful, although we have striven to make the exposition self-contained, starting from calculus on manifold.