Catastrophic or nearly-catastrophic collisions are the most important physical process affecting the evolution of asteroids following the primordial phases. After a generál review of the current ideas about collisional evolution, also in the light of laboratory impact experiments, the problems concerning
the interpretation of asteroid families as outcomes of catastrophic processes are discussed. Finally, it is shown how the present, non completely satisfactory, knowledge of collisional processes
can give important indications on the early phases of evolution of the asteroid belt.
The catologues of visual and eclipsing binaries have been analyzed by means of a mulivariate statistical method, with the purpose of putting into evidence mutual relations among the observed quantities as well as clustering properties in the mulri-dimensional space. Preliminary results of the analysis show several interesting feataures, and a physical interpretation can be attempted. Nevertheless, observational selection effects play an important role. The way back to the understanding of formation and evolutionary properties is extremely difficult, and unbiased conclusions about fundamental parameters as the initial period and mass ratio distributions cannot be obtained.
A thermodynamical approach to the problem of star formation, presented in a previous paper, shows how, at least when the last stages of collapse are assumed as adiabatic, the characteristics of the outcomes depend on the initial conditions (thermal and rotational energies) and on the distribution of the angular momentum among the various parts of the system. In the case of a binary outcome, the distiribution can be profitably expressed in terms of two parameters, roughly corresponding to a) the spin ratio as function of the mass ratio and b) the fraction of a.m. involved in the orbital motion. A systematic exploration of these parameters allows us to analyze the different kinds of results. In this paper we present some preliminary results, assuming that both single and binary outcomes have an equilibrium Mc Laurin ellipsoidal shape, but not taking into account the possible formation of a system star+protoplanetary disc.