Draft:Maxwell's equations for a mechano-driven media system

Maxwell's equations for a mechano-driven media system (MEs-f-MDMS), are a set of coupled partial differential equations, obtained by the expansion from classical Maxwell's equations, which are utilized to describe the electromagnetism of multi-moving-media. The equations include the object moving cases, which are about one observer who is observing two electromagnetic phenomena, which are associated with two moving objects/media located in the two reference frames that may relatively move at v << c, but may with acceleration. Classical Maxwell's equations are to describe the electrodynamics in the region where there is no local medium movement, such as in vacuum or in stationary objects.

The partial differential form of Maxwell's equations with considering the moving of medium boundary, can be written as

$$\nabla\cdot D=\rho_f$$

$$\nabla\cdot B=0$$

$$\nabla\times\bigl(E+v_r\times{B}\bigr)= -{ \partial \over \partial t}B$$

$$\nabla\times\bigl(H-v_r\times{D}\bigr)= J+\rho{v}+{ \partial \over \partial t}D$$

where v is moving velocity of the origin of the reference frame S′, which is only time-dependent so that it can be viewed as a "rigid translation", and vr is the relative moving velocity of the point charge with respect to the reference frame S′, which is considered as the "rotation speed" that may be space- and time-dependent.

If the medium moves at a constant velocity: v = constant and vr = 0, the MEs-f-MDMS resume the format of the classical MEs, so there is no logic inconsistency with the existing theory.