  A general theoretical framework for the study of electronic stopping of
particle projectiles in crystalline solids is proposed. It neither relies on
perturbative or linear response approximations, nor on an ideal metal host.
Instead, it exploits the discrete translational symmetries in a space-time
diagonal determined by a projectile with constant velocity moving along a
trajectory with crystalline periodicity. This allows for the characterisation
of (stroboscopically) stationary solutions, by means of Floquet theory for
time-periodic systems. Previous perturbative and non-linear jellium models are
recovered from this general theory. An analysis of the threshold velocity
effect in insulators is presented based on Floquet quasi-energy conservation.
