Modes of a stellar system II: non-ergodic systems
  An equation is derived for the energy of a small disturbance in a system that
is generated by a distribution function (DF) of the form $f(\vJ)$ -- most
galaxies and star clusters can be closely approximated by such a DF. The theory
of van Kampen modes is extended to such general systems. An inner product on
the space of DFs is defined such that the energy of a disturbance is its norm
under this product. It is shown that van Kampen modes that differ in frequency
are then orthogonal, with the consequence that the energies of van Kampen modes
are additive. Consequently, most of the insight into the dynamics of ergodic
systems that was gained in a recent paper on the van Kampen modes of ergodic
systems applies to real clusters and galaxies.
