Each asteroid is a massless test particle in the field of the Sun and Jupiter, with Jupiter on a prescribed circular orbit of radius 5.2 AU about the common centre of mass (the circular restricted three-body problem). Units: AU, years, solar masses, so GMsun = 4π². The acceleration is a = −GMs(r − rs)/|r − rs|³ − GMJ(r − rJ)/|r − rJ|³, integrated with a kick-drift-kick leapfrog (step 0.01 yr).
Without Jupiter every orbit obeys Kepler's third law T = a3/2 years. With it, orbits whose period is a simple fraction of Jupiter's (3:1 at 2.50 AU, 5:2 at 2.82, 7:3 at 2.96, 2:1 at 3.27) are kicked repeatedly in phase and their eccentricity grows chaotically, which clears the Kirkwood gaps. The conserved quantity of the restricted problem is the Jacobi integral J = E − ω Lz; the check tracks its drift. At the Lagrange points 60 degrees ahead of and behind Jupiter (switch to the rotating frame) the Trojans librate.
Honest simplifications: Jupiter is on a fixed circular orbit (no eccentricity, no Saturn), asteroids do not interact, the plane is flat, and real gap formation takes up to millions of years: raise Jupiter's mass or use the fast preset to see it in minutes of run time.