Institute of Theoretical Astronomy,
10 Kutuzov Quay, St.Petersburg, 191187, Russia
A new approach to the evolution of planetary rings is under way. Irreverible processes in a ring-like system are considered by Boltsmann's equation in the frame of a certain approximation for its collision term. In addition the laws of conservation of a mass and impulse are preserved and the energy losses are related only to non-elasticity of particles at mutual collisions. A simplifiied evolutionary equation may be derived in the two extreme cases: i.e. at very rare and very often collisions.The calculations are performed in a local approximation for each narrow circular zone. We found the velocity 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 condition 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. The local results obtained may be utilized for elaborating a global theory of planetary rings evolution and the interpretation of their observed structures.