Systematic numerical simulations have been carried out systematically in order to clarify the effect of rotation on the dynamics of core collapse in the supernova explosions. We have utilized a simple phenomenological equation of state with a polytropic form to approximate the complicated microphysics, and we have not solved neutrino transport, either. The infalling matter is found to be clearly divided into two parts, one of which is the inner core contracting subsonically, and the other is the outer core falling supersonically as in the spherically symmetric collapse. The inner core becomes more massive and deformed as the rotational energy increases or as the degree of the differential rotation becomes greater. On the other hand, it is also clear that the explosion energy monotonically decreases as the rotational energy increases or as the degree of differential rotation becomes greater. This is because the centrifugal force prevents the inner core from contracting sufficiently and less gravitational energy is available to push the outer core. This feature is insensitive to the degree of neutrino trapping. It is, therefore, concluded that in general rotation of the core has a negative effect on the prompt explosion mechanism.
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