  Space-time modulation systems have garnered significant attention due to
their resemblance to moving-matter systems and promising applications. Unlike
conventional moving-matter systems, modulation systems do not involve net
motion of matter, and are therefore easier to implement and not restricted to
subluminal velocities. However, canonical wave-medium interaction aspects, such
as scattering and energy-momentum 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
"catch-up" 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.
