We study theoretically a chain of precessing classical magnetic impurities in an $s$-wave superconductor. Utilizing a rotating wave description, we derive an effective Hamiltonian that describes the emergent Shiba band. We find that this Hamiltonian shows non-trivial topological properties, and we obtain the corresponding topological phase diagrams both numerically and analytically. We show that changing the precession frequency offers a control over topological phase transitions and the emergence of Majorana bound states. We propose driving the magnetic impurities or magnetic texture into precession by means of spin-transfer torque in a spin-Hall setup, and manipulate it using spin superfluidity in the case of planar magnetic order.
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