  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 Schwarzschild's orbit-superposition method. We find that
Schwarzschild's method is able to recover the internal dynamics and
three-integral distribution function of realistic models of early-type
galaxies.
