  In the general setting of the problem, the explicit compact formulae are
derived for the ponderomotive forces in the macroscopic electrodynamics of
moving media in the Minkowski and Abraham approaches. Taking account of the
Minkowski constitutive equations and making use of a special representation for
the Abraham energy-momentum tensor enable one to obtain a compact expression
for the Abraham force in the case of arbitrary dependence of the medium
velocity on spatial coordinates and the time and for nonstationary external
electromagnetic field. We term the difference between the ponderomotive forces
in the Abraham and Minkowski approaches as the Abraham force not only under
consideration of media at rest but also in the case of moving media. The
Lorentz force is found which is exerted by external electromagnetic field on
the conduction current in a medium, the covariant Ohm law and the constitutive
Minkowski relations being taken into account. The physical argumentation is
traced for definition of the 4-vector of the ponderomotive force as the
4-divergence of the energy-momentum tensor of electromagnetic field in a
medium.
