  Quantum wires subject to the combined action of spin-orbit and Zeeman
coupling in the presence of \emph{s}-wave pairing potentials (superconducting
proximity effect in semiconductors or superfluidity in cold atoms) are one of
the most promising systems for the developing of topological phases hosting
Majorana fermions. The breaking of time-reversal symmetry is essential for the
appearance of unpaired Majorana fermions. By implementing a
\emph{time-dependent} spin rotation, we show that the standard magnetostatic
model maps into a \emph{non-magnetic} one where the breaking of time-reversal
symmetry is guaranteed by a periodical change of the spin-orbit coupling axis
as a function of time. This suggests the possibility of developing the
topological superconducting state of matter driven by external forces in the
absence of magnetic fields and magnetic elements. From a practical viewpoint,
the scheme avoids the disadvantages of conjugating magnetism and
superconductivity, even though the need of a high-frequency driving of
spin-orbit coupling may represent a technological challenge. We describe the
basic properties of this Floquet system by showing that finite samples host
unpaired Majorana fermions at their edges despite the fact that the bulk
Floquet quasienergies are gapless and that the Hamiltonian at each instant of
time preserves time-reversal symmetry. Remarkably, we identify the mean energy
of the Floquet states as a topological indicator. We additionally show that the
localized Floquet Majorana fermions are robust under local perturbations. Our
results are supported by complementary numerical Floquet simulations.
