  A generalization of the classical electrodynamics for systems in absolute
motion is presented using a possible alternative to the Lorentz transformation.
The main hypothesis assumed in this work are: a) The inertial transformations
relate two inertial frames: the privileged frame S and the moving frame S' with
velocity v with respect to S. b) The transformation of the fields from S to the
moving frame S' is given by H'=a(H - v D) and E'=a(E + v B) where a is a matrix
whose elements depend of the absolute velocity of the system. c) The
constitutive relations in the moving frame S' are given by D'= \epsilon E', B'=
\mu H' and J'=\eta E'. It is found that Maxwell's equations, which are
transformed to the moving frame, take a new form depending on the absolute
velocity of the system. Moreover, differing from classical electrodynamics, it
is proved that the electrodynamics proposed explains satisfactorily the Wilson
effect.
