A differential equations approach to Hamiltonian systems

We present an intrinsic definition of a (possibly time-dependent) Hamiltonian differential equation as a submanifold of the first-order jet bundle over a fibred cosymplectic manifold. The equivalence of the standard constraint algorithm in mechanics to the completion procedure in differential equations theory is explicitly demonstrated. As an application, we study covariant classical mechanics. Finally, some problems with constraint algorithms in field theories are indicated.