  In textbooks of geophysical fluid dynamics, the Coriolis force and the
centrifugal force in a rotating fluid system are derived by making use of the
fluid parcel concept. In contrast to this intuitive derivation to the apparent
forces, more rigorous derivation would be useful not only for the pedagogical
purpose, but also for the applications to other kinds of rotating geophysical
systems rather than the fluid. The purpose of this paper is to show a general
procedure to derive the transformed equations in the rotating frame of
reference based on the local Galilean transformation and rotational coordinate
transformation of field quantities. The generality and usefulness of this
Eulerian approach is demonstrated in the derivation of apparent forces in
rotating fluids as well as the transformed electromagnetic field equation in
the rotating system.
