  This work presents a mechanism by which non-reciprocal wave transmission is
achieved in a class of gyric metamaterial lattices with embedded rotating
elements. A modulation of the device's angular momentum is obtained via
prescribed rotations of a set of locally housed spinning motors and are then
used to induce space-periodic, time-periodic, as well as space-time-periodic
variations which influence wave propagation in distinct ways. Owing to their
dependence on gyroscopic effects, such systems are able to break reciprocal
wave symmetry without stiffness perturbations rendering them consistently
stable as well as energy self-reliant. Dispersion patterns, band gap emergence,
as well as non-reciprocal wave transmission in the space-time-periodic gyric
metamaterials are predicted both analytically from the gyroscopic system
dynamics as well as numerically via time-transient simulations. In addition to
breaking reciprocity, we show that the energy content of a frictionless gyric
metamaterial is conserved over one temporal modulation cycle enabling it to
exhibit a stable response irrespective of the pumping frequency.
