A new method of determining the 3D phase density for open and globular clusters from observed radial velocities and/or proper motions of stars is proposed. It is shown, that the task is equivalent to a solution of the corresponding (ill-posed) inverse problem.
A knowledge of the phase density enables us to determine the type of the relaxation mechanism which was operating in the system during its evolution. There are three main mechanisms. As a result of the {\it collisional} relaxation, the Maxwellian distribution is formed. The other two relaxation mechanisms are collisionless: they are due to action of the self-consistent field. {\it The Lynden-Bell} violent relaxation leads to the Fermi distribution, i.e. to a constant phase density for energies less than certain maximal value. The third relaxation mechanism is associated with {\it the radial orbit instability}. In this case the initial anisotropy decreases to the value that corresponds to the instability boundary. A typical resulting phase density is a non-monotonic function of the energy $E$: it decreasing for large $E$'s, but increasing for sufficiently small $E$'s.
Thus three main relaxation mechanisms lead to the distribution functions with qualitatively different behaviour. Finding the $E$ -- dependence from observed radial velocities and proper motions of stars, it is possible to determine the type of the principal relaxation mechanism, occurring in each cluster under investigation.
Observations show that in the solar neighbourhood there are different laws of the velocity dispersions of disk stars increase with their age. The correct nature of this phenomenon is still unknown. Several new mechanisms for increasing the stellar velocity dispersion as a result of collisions with giant molecular clouds are proposed. It is shown that these mechanisms result in the observed set of age--velocity dispersion relations. Thus the observed different laws for the heating of the stellar component can be a consequence of different relaxation mechanisms.
Above results were obtained by A.M. Fridman, V.L. Polyachenko, O.V. Khoruzhii, A.E. Piskunov jointly with A.S. Rastorguev (SAI), H. Eichhorn (University of Florida)