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.
At present, the Amplitude-Magnitude (AM) method is largely applied for determining the spin axis direction of asteroids; such a method gives results which are in general in a good agreement with those
obtained by means of essentially different methods. However, one of the crltical assumptions of the AM method is that asteroids are modelled as triaxial ellipsoids with semiaxes a>b>c. Although
such an hypothesis appears reasonable for large objects on the basis of physical considerations about their expected equilibrium shapes, very irregular figures are more plausible for smaller objects, probably dominated by solid-state forces. Therefore, it is worth-while to study the influence that deviations from a purely triaxial ellipsoid shape can háve on the derived spin axis direction. For this purpose, a numerlcal program has been developed in order to compute the lightcurves of irregularly shaped objects at given aspect angles. The present paper reports some preliminary results concerning the uncertainty of the rotation axis direction of asteroids when non-triaxial shapes are considered.
In tne last few decades new observational techniques have provided a wealth of physical information on several hundreds of asteroids. These objects are no longer seen as pointlike bodies
mainly interesting as a 'dynamical zoo', but have become small 'worlds' with known sizes, gross shapes, surface compositions, rotational properties and collisional histories. The diversity of these 'worlds' 3 is astonishing: they range in size from less than 1 to 10^3 km, in spin period from a few hours to many days, in shape from nearly spherical to very elongated and/or irregular, in surface reflectivity from about 0.02 .to 0.4, in composition from metal-rich and silicate rocks to volatile-rich carbonaceous assemblages. Of course there are many peculiar objects: asteroids with surface patches of different brightness and colour; bodies, which have suffered internal heating and have developed a core-mantlecrust
structure; asteroids converted by catastrophic impacts into gravitationally bound 'piles of rubble'; objects with triaxial equilibrium figures or splitted into binary systems; outer-belt
asteroids whose spectrophotometric properties are very much alike those of cometary nuclei. This paper reviews some of these recent findings, which are currently being interpreted in the frame of
complex theoretical models for the formation and evolution of orbiting and collisionally interacting bodies.
The external accuracy of photometric parameters of asteroids is investigated by comparison of published lists. Absolute magnitudes are consistent at the ±0.1 mag level but phase coefficients are still rather uncertain.
The physics of the two types of resonances characterizing the dynamical structure of the asteroidal belt are presented. In the case of mean motion resonances, the frequency of Jupiter´s rotation about the Sun determines the various resonance frequencies. For secular resonances, the resonance frequencies corxespond to eigenfrequencies of the system of differential equations descríbing the motions of nodal and apsidal lines of planetary orbits. Both
types of resonances are related to gaps in the asteroidal belt. The computing theories for the formation of these gaps are reviewed. The secular resonances gained considerable interest because of their alleged role as source of Earth-crossing objects like Apollo asteroids and meteorites. Recent numerical model calculations on secular resonances are reviewed under this aspect.