Stellar kinematics using a third integral of motion: method and
  application on the Andromeda galaxy
  We probe the feasibility of describing the structure of a multi-component
axisymmetric galaxy with a dynamical model based on the Jeans equations while
taking into account a third integral of motion. We demonstrate that using the
third integral in the form derived by G. Kuzmin, it is possible to calculate
the stellar kinematics of a galaxy from the Jeans equations by integrating the
equations along certain characteristic curves. In cases where the third
integral of motion does not describe the system exactly, the derived kinematics
would describe the galaxy only approximately. We apply our method to the
Andromeda galaxy, for which the mass distribution is relatively firmly known.
We are able to reproduce the observed stellar kinematics of the galaxy rather
well. The calculated model suggests that the velocity dispersion ratios
${\sigma}_z^2/{\sigma}_R^2$ of M31 decrease with increasing R. Moving away from
the galactic plane, ${\sigma}_z^2/{\sigma}_R^2$ remains the same. The velocity
dispersions ${\sigma}_{\theta}^2$ and ${\sigma}_R^2$ are roughly equal in the
galactic plane.
