Integrals of a stellar system are the globally 
conserved quantities, such as the energy, angular 
momentum, etc.

Isolating integrals are those which confine the 
system to particular hypersurfaces in the phase 
space (lower the dimensionality of the problem).

In a conservative system, there is always the 
energy; other isolating integrals may exist.  
For example, in our Galactic potential, there 
is also the angular momentum, and the mysterious 
"third integral".

In general, the distribution function can be
expressed through the integrals of motion:



The Jeans' thm. states that in the steady state
(i.e.,               ), the phase space density 
distribution is a function of the isolating 
integrals only:



which greatly simplifies the problem of finding
the consistent models of stellar systems, e.g.,