We construct axisymmetric and triaxial galaxy models with a phase-space distribution function that depends on linear combinations of the three exact integrals of motion for a separable potential. These Abel models, first introduced by Dejonghe & Laurent and subsequently extended by Mathieu & Dejonghe, are the axisymmetric and triaxial generalisations of the well-known spherical Osipkov-Merritt models. We show that the density and higher order velocity moments, as well as the line-of-sight velocity distribution (LOSVD) of these models can be calculated efficiently and that they capture much of the rich internal dynamics of early-type galaxies. We build a triaxial and oblate axisymmetric galaxy model with projected kinematics that mimic the two-dimensional kinematic observations that are obtained with integral-field spectrographs such as SAURON. We fit the simulated observations with axisymmetric and triaxial dynamical models constructed with our numerical implementation of Schwarzschilds orbit-superposition method. We find that Schwarzschilds method is able to recover the internal dynamics and three-integral distribution function of realistic models of early-type galaxies.
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