  We determine the dynamical distance D, inclination i, mass-to-light ratio M/L
and the intrinsic orbital structure of the globular cluster omega Cen, by
fitting axisymmetric dynamical models to the ground-based proper motions of van
Leeuwen et al. and line-of-sight velocities from four independent data-sets. We
correct the observed velocities for perspective rotation caused by the space
motion of the cluster, and show that the residual solid-body rotation component
in the proper motions can be taken out without any modelling other than
assuming axisymmetry. This also provides a tight constraint on D tan i.
Application of our axisymmetric implementation of Schwarzschild's orbit
superposition method to omega Cen reveals no dynamical evidence for a
significant radial dependence of M/L. The best-fit dynamical model has a
stellar V-band mass-to-light ratio M/L_V = 2.5 +/- 0.1 M_sun/L_sun and an
inclination i = 50 +/- 4 degrees, which corresponds to an average intrinsic
axial ratio of 0.78 +/- 0.03. The best-fit dynamical distance D = 4.8 +/- 0.3
kpc (distance modulus 13.75 +/- 0.13 mag) is significantly larger than obtained
by means of simple spherical or constant-anisotropy axisymmetric dynamical
models, and is consistent with the canonical value 5.0 +/- 0.2 kpc obtained by
photometric methods. The total mass of the cluster is (2.5 +/- 0.3) x 10^6
M_sun. The best-fit model is close to isotropic inside a radius of about 10
arcmin and becomes increasingly tangentially anisotropic in the outer region,
which displays significant mean rotation. This phase-space structure may well
be caused by the effects of the tidal field of the Milky Way. The cluster
contains a separate disk-like component in the radial range between 1 and 3
arcmin, contributing about 4% to the total mass.
