On statistic mechanics of planetary rings
           V.A. Antonov, A.S. Baranov

 Institute for Theoretical Astronomy, 10, Kutuzov Quay, St Petersburg, 
                 191187, Russia


   A new approach to the dynamical evolution of planetary rings and the
other analogous objects is under way.
   Irreversible processes in a ring-like systems are considered by the
Boltsmann's equation in the frame of a certain approximation for its
collision term. In addition the laws of energy conservation of a mass
and impilse are preserved and the energy losses are related only to
non-elasticity  of particles at mutual collisions. The calculations are
performed in a local approximation for each narrow circular zone. We
found the velosity distribution , which turned out to steady-state in
the sense that the energy influx of relative motions at the expense of
a differential rotation is balanced by non-elastic losses. Such an
equilibrium suggests a certain relation between the elasticity
coefficient and the other parameters. If the stationary conditions are
disturbed, the velocity dispersion is either progressively increasing
or vice versa is decreasing. In either case the adopted initial
premises will be finally violated: the system becomes either
essentially three-dimensional or, on the contrary, completely plane.
   A simplified evolutionary equation may be derived in the two extreme
cases: i.e. at very rare and very often collisions. The local results
obtained may be utilized for elaborating a global theory of planetary
rings evolution and the interpretation of their observed structures.