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This is a study of the history of the asteroids in the main asteroid belt.Collisions have been the dominant process. Every asteroid has been impacted byothers a multitude of times, with consequences of cratering, erosion, spinincrements, fragmentation, and occasional catastrophic disruption anddispersion. Extensive information for asteroid orbits, sizes, shapes,composition, and rotation rates of those asteroids is now available. Those area result of their history, but to interpret them requires understanding theprocesses. That understanding can be improved by simulations of the history. Asimulation needs robust models of the dynamical and collisional events. Suchmodels have evolved substantially in the last few decades. Here I presentcurrent models, a method, and a code "SSAH" for stochastic simulations of thehistory of the main belt. That code gives a framework upon which existing andfuture models can be based. The results lead to new paradigms for asteroidhistories including the distribution of spins; the irrelevance of strength spinlimits; the "unusual" spins of 2001 OE84; and of large slow-spinning tumblingobjects (Mathilde); the "V-shape" in the spin versus diameter plot; thenon-Maxwellian distribution of spins of a given diameter range; the numbers ofexpected tumblers, and more. At the same time, the simulations expose gaps inour knowledge that require further research. The SSAH code is freely availablefor the use of others.

Main Belt Asteroid Histories: Simulations of erosion, cratering, catastrophic dispersions, spins, binaries and tumblers