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Simple analytical models, such as the Hernquist model, are very useful toolsto investigate the dynamical structure of galaxies. Unfortunately, most of theanalytical distribution functions are either isotropic or of theOsipkov-Merritt type, and hence basically one-dimensional. We present threedifferent families of anisotropic distribution functions that self-consistentlygenerate the Hernquist potential-density pair. These families have constant,increasing and decreasing anisotropy profiles respectively, and can hencerepresent a wide variety of orbital structures. For all of the modelspresented, the distribution function and the velocity dispersions can bewritten in terms of elementary functions. These models are ideal tools for awide range of applications, in particular to generate the initial conditionsfor N-body or Monte Carlo simulations.Comment: 14 pages, 7 figures, accepted for publication in A&A - formulae (51)  and (54) and figure 4 correcte

The Hernquist model revisited: Completely analytical anisotropic dynamical models