  Interaction of electromagnetic, acoustic and even gravitational waves with
accelerating bodies forms a class of nonstationary time-variant processes.
Scattered waves contain intrinsic signatures of motion, which manifest in a
broad range of phenomena, including Sagnac interference, Doppler and
micro-Doppler frequency shifts. While general relativity is often required to
account for motion, instantaneous rest frame approaches are frequently used to
describe interactions with slowly accelerating objects. Here we investigate
theoretically and experimentally an interaction regime, which is neither
relativistic nor adiabatic. The test model considers an accelerating scatterer
with a long-lasting relaxation memory. The slow decay rates violate the
instantaneous reaction assumption of quasi-stationarity, introducing
non-Markovian contributions to the scattering process. Memory signatures in
scattering from a rotating dipole are studied theoretically, showing symmetry
breaking of micro-Doppler combs. A quasi-stationary numeric analysis of
scattering in the short memory limit is proposed and validated experimentally
with an example of electromagnetic pulses interacting with a rotating wire.
