A novel simulator of the translational and rotational motion of rigid aggregates of aerosol particles has been developed, taking into account the stochastic Brownian force, gravity, and the hydrodynamic drag as functions of the size, overall shape and internal structure of the aggregate. The simulator is used to determine the dynamics of aerosol aggregates of various sizes, overall shape, and internal structure, in order to extract the corresponding diffusion coefficient values. The diffusion coefficient is shown to be a strong function of the number of particles forming the aggregate (N), as well as of the detailed structure of the aggregate. It is found that for large values of N the "fractal dimension" is a convenient parameter characterizing the internal structure of the aggregates with roughly spherical overall shape. A key result is that the norm of the diffusion coefficient tensor of such aggregates is much smaller than the values which are estimated using the various "equivalent sphere" approximations. It should be noted that the new simulator, in its present form, can also be used in cases of aggregates with virtually arbitrary overall shape and non-uniform internal structure. (C) 2005 Published by Elsevier Ltd.