A computing program was developed for simultaneously tracing trajectories and classical, relativistic spin precessions around the zero gradient synchrotron (ZGS). Depolarizing resonances, previously predicted, were found and their properties were computed; there were 36 significant resonances, 12 of which were serious. A method is proposed for avoiding these 12 resonances by using two or four pulsed quadrupole magnets around the ZGS ring. These would rapidly shift &ngr;z, the vertical betatron oscillation frequency, at appropriate energies during the acceleration cycle. With this method, a proton beam, injected into the ZGS withP=1, would haveP>0.7 at the end of the acceleration cycle.