  The consequences of coupling magnetic and elastic degrees of freedom, where
spins and deformations are carried by point-like objects subject to local
interactions, are studied, theoretically and by detailed numerical simulations.
From the constrained Lagrangians we derive consistent equations of motion for
the coupled dynamical variables. In order to probe the dynamics of such a
system, we consider external perturbations, such as spin transfer torques for
the magnetic part, and homogeneous stresses for the elastic part, associated to
their corresponding damping. This approach is applied to the study of ultrafast
switching processes in anti-ferromagnetic systems, which have recently
attracted attention as candidates for anti-ferromagnetic spintronic devices.
Our strategy is then checked in simple, but instructive, situations. We carried
out numerical experiments to study, in particular, how the magnetostrictive
coupling and external stresses affect the nature of the switching processes in
a prototype anti-ferromagnetic material.
