Recent heavy ion fusion target studies show that it is possible to achieve ignition with direct drive and energy gain larger than 100 at 1 MJ. To realize these advanced, high-gain schemes based on direct drive, it is necessary to develop a reliable beam smoothing technique to mitigate instabilities and facilitate uniform deposition on the target. The dynamics of the beam centroid can be explored as a possible beam smoothing technique to achieve a uniform illumination over a suitably chosen region of the target. The basic idea of this technique is to induce an oscillatory motion of the centroid for each transverse slice of the beam in such a way that the centroids of different slices strike different locations on the target. The centroid dynamics is controlled by a set of biased electrical plates called “wobblers.” Using a model based on moments of the Vlasov-Maxwell equations, we show that the wobbler deflection force acts only on the centroid motion, and that the envelope dynamics are independent of the wobbler fields. If the conducting wall is far away from the beam, then the envelope dynamics and centroid dynamics are completely decoupled. This is a preferred situation for the beam wobbling technique, because the wobbler system can be designed to generate the desired centroid motion on the target without considering its effects on the envelope and emittance. A conceptual design of the wobbler system for a heavy ion fusion driver is briefly summarized.