As a consequence, non-autonomous mechanics (in particular, non-autonomous Hamiltonian mechanics) can be formulated as a covariant classical field theory (in particular covariant Hamiltonian field theory) on X = R . Accordingly, the velocity phase space of non-autonomous mechanics is the jet manifold J 1 Q of Q → → R provided with the coordinates ( t , q i , q t i ) . Its momentum phase space is the vertical cotangent bundle V Q of Q → → R coordinated by ( t , q i , p i ) and endowed with the canonical Poisson structure. The dynamics of Hamiltonian non-autonomous mechanics is defined by a Hamiltonian form p i d q i − − H ( t , q i , p i ) d t .