A century has now passed since the origins of the Abraham-Minkowski controversy pertaining to the correct form of optical momentum in media. Since, the debate has come to reference the general debate over optical momentum, including a number of competing formulations. The pervasive modern view is that the Abraham momentum represents the optical momentum contained within the fields and the Minkowski momentum includes a material component which is coupled with the fields. A recently proposed resolution to the debate identified Abraham’s kinetic momentum as responsible for the overall center-of-mass translations of a medium
and Minkowski’s canonical momentum as responsible for local translations of a medium within or with respect to another medium. Still, current literature reveals significant confusion as to how systems of light and matter should be modeled as to deduce the equations of motion when multiple material types are present. For example, the state-of-the-art model for optical dynamics of submerged particles assumes over damped systems such that the mass of the particles is ignored in the equations of motion. In this paper, we apply the subsystem approach to deduce the electrodynamics of such systems. We show that regardless of which electromagnetic momentum continuity law is applied, the equations of motion can be correctly deduced as long as the continuity law is consistent with Maxwells equations and the overall system is closed such that momentum is conserved. Because the closed system includes the material response, the model can be very complex. However, we demonstrate with simple, well-known examples.