Equilibrium of a star cluster in the tidal field of the Galaxy

The tensor virial theorem is used to analyze the conditions for the existence of an equilibrium cluster moving in a circular orbit in a stationary axisymmetric galaxy. A general necessary condition is derived, which, for uniform models, coincides with the Bok stability condition. Generalized Mineur ellipsoids are constructed for nonuniform systems with anisotropic velocity distributions. The Hill stability of the cluster is analyzed.