  The Eulerian variational principle for the Vlasov-Poisson-Amp\`{e}re system
of equations in a general coordinate system is presented. The invariance of the
action integral under an arbitrary spatial coordinate transformation is used to
obtain the momentum conservation law and the symmetric pressure in a more
direct way than using the translational and rotational symmetries of the
system. Next, the Eulerian variational principle is given for the collisionless
drift kinetic equation, where particles' phase-space trajectories in given
electromagnetic fields are described by Littlejohn's guiding center
equations~[R. G. Littlejohn, J. Plasma Phys.\ {\bf 29}, 111 (1983)]. Then, it
is shown that, in comparison with the conventional moment method, the
invariance under a general spatial coordinate transformation yields a more
convenient way to obtain the momentum balance as a three-dimensional vector
equation in which the symmetric pressure tensor, the Lorentz force, and the
magnetization current are properly expressed. Furthermore, the Eulerian
formulation is presented for the extended drift kinetic system, for which, in
addition to the drift kinetic equations for the distribution functions of all
particle species, the quasineutrality condition and Amp\`{e}re's law to
determine the self-consistent electromagnetic fields are given. Again, the
momentum conservation law for the extended system is derived from the
invariance under the general spatial coordinate transformation. Besides, the
momentum balances are investigated for the cases where the collision and/or
external source terms are added into the Vlasov and drift kinetic equations.
