Space-time modulation systems have garnered significant attention due to their resemblance to moving-matter systems and promising applications. Unlike conventional movingmatter systems, modulation systems do not involve net motion of matter, and are therefore easier to implement and not restricted to subluminal velocities. However, canonical wavemedium interaction aspects, such as scattering and energymomentum relations, have remained largely unexplored. In this paper, we address the aforementioned issues for three dynamic systems: moving-matter blocs, moving-perturbation interfaces and moving-perturbation periodic structures, and provide corresponding general formulations along with comparisons. Our investigation reveals the significant roles played by the "catchup" effect between waves and interfaces. Even more interestingly, it reveals different energy and momentum exchanges between moving media and homogenized moving-perturbation structures as a result of conventional and reverse Fresnel-Fizeau drag effects.
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