  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 by
others a multitude of times, with consequences of cratering, erosion, spin
increments, fragmentation, and occasional catastrophic disruption and
dispersion. Extensive information for asteroid orbits, sizes, shapes,
composition, and rotation rates of those asteroids is now available. Those are
a result of their history, but to interpret them requires understanding the
processes. That understanding can be improved by simulations of the history. A
simulation needs robust models of the dynamical and collisional events. Such
models have evolved substantially in the last few decades. Here I present
current models, a method, and a code "SSAH" for stochastic simulations of the
history of the main belt. That code gives a framework upon which existing and
future models can be based. The results lead to new paradigms for asteroid
histories including the distribution of spins; the irrelevance of strength spin
limits; the "unusual" spins of 2001 OE84; and of large slow-spinning tumbling
objects (Mathilde); the "V-shape" in the spin versus diameter plot; the
non-Maxwellian distribution of spins of a given diameter range; the numbers of
expected tumblers, and more. At the same time, the simulations expose gaps in
our knowledge that require further research. The SSAH code is freely available
for the use of others.
