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NASA's Double Asteroid Redirection Test (DART) mission will kinetically impact Dimorphos, the secondary component of the Didymos binary asteroid system, which will excite Dimorphos's dynamical state and lead to significant libration about the synchronous state and possibly chaotic non-principal axis rotation. Although this particular outcome is human caused, many other secondary components of binary systems are also prone to such exotic spin states. For a satellite in an excited spin state, the time-varying tidal and rotational environment can lead to significant surface accelerations. Depending on the circumstances, this mechanism may drive granular motion on the surface of the secondary. We modeled the dynamical evolution of a Didymos-like binary asteroid system using a fully coupled, three-dimensional simulation code. Then, we computed the time-varying gravitational and rotational accelerations felt over the entire surface resulting from the secondary's perturbed dynamical state. We find that an excited spin and orbit can induce large changes in the effective surface slope, potentially triggering granular motion and surface refreshment. However, for the case of the DART impact, this effect is highly dependent on many unknowns, such as Dimorphos's detailed shape, bulk density, surface geology, and the momentum transferred. Aside from the Didymos system and the DART mission, this effect also has important implications for binary systems in general.