Covariant hydrodynamics of Hamiltonian systems

The theory of hydrodynamic reduction of non-autonomous Hamiltonian mechanics (V. Kozlov, 1983) is presented in the geometric formalism of bundles over the time axis $R$. In this formalism, time is one of the coordinates, not a parameter; the connections describe reference frames and velocity fields of mechanical systems. The equations of the theory are presented in a form that is invariant with respect to time-dependent coordinate transformations and the choice of reference frames.