Abstract For engineering electromagnetism, media/objects have shapes and sizes and may move with accelerations along complex trajectories in reference to the observers in the Laboratory frame. To describe the electromagnetic behavior of a system that is made of multiple moving objects, we have developed the Maxwell’s equations for a mechano-driven media system (MEs-f-MDMS) under low-speed approximation (v << c) [Advances in Physics: X, 9 (2024) 2354767]. Through extensive studies, the MEs-f-MDMS are required for describing the electrodynamics inside a moving object, while the classical Maxwell’s equations are to describe the electrodynamics in the region that is at stationary with respect to the Laboratory frame. The full solutions of the two regions satisfy the boundary conditions. The accelerated movement of a medium is a source for generating electromagnetic wave at its vicinity, but this component was missed in classical Maxwell’s equations. In this paper, we present the strategies for solving the MEs-f-MDMS for a generate case with considering the dispersion of the medium and the related constitutive relations both in time and frequency spaces. The theory is rather general and will serve as general guidance for numerical calculations toward practical applications.
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