  We study the large-scale stellar and gaseous kinematics of the E4 galaxy
NGC2974, based on panoramic integral-field data obtained with SAURON. We
quantify the velocity fields with Fourier methods (kinemetry), and show that
the large-scale kinematics is largely consistent with axisymmetry. We construct
general axisymmetric dynamical models for the stellar motions using
Schwarzschild's orbit-superposition method, and compare the inferred
inclination and mass-to-light ratio with the values obtained by modelling the
gas kinematics. Both approaches give consistent results. However we find that
the stellar models provide fairly weak constraints on the inclination. The
intrinsic orbital distribution of NGC2974, which we infer from our model, is
characterised by a large-scale stellar component of high angular momentum. We
create semi-analytic test models, resembling NGC2974, to study the ability of
Schwarzschild's modelling technique to recover the given input parameters
(mass-to-light ratio and inclination) and the distribution function. We also
test the influence of a limited spatial coverage on the recovery of the
distribution function (i.e. the orbital structure). We find that the models can
accurately recover the input mass-to-light ratio, but we confirm that even with
perfect input kinematics the inclination is only marginally constrained. This
suggests a possible degeneracy in the determination of the inclination, but
further investigations are needed to clarify this issue. For a given potential,
we find that the analytic distribution function of our test model is well
recovered by the three-integral model within the spatial region constrained by
integral-field kinematics.
