  In the stationary case, atomistic interaction energies can be proved to
$\Gamma$-converge to classical elasticity models in the simultaneous
atomistic-to-continuum and linearization limit [19],[40]. The aim of this note
is that of extending the convergence analysis to the dynamic setting. Moving
within the framework of [40], we prove that solutions of the equation of motion
driven by atomistic deformation energies converge to the solutions of the
momentum equation for the corresponding continuum energy of linearized
elasticity. By recasting the evolution problems in their equivalent
energy-dissipation-inertia-principle form, we directly argue at the variational
level of evolutionary $\Gamma$-convergence [32],[36]. This in particular
ensures the pointwise in time convergence of the energies.
