Abstract: Based on the Landau-Lifshitz-Gilbert formulation, we show that the so-called Stoner-Wohlfarth (SW) limit is exact when the damping constant is infinitely large. Under this limit, the magnetization moves along the steepest energy descent path. The minimal switching field is that at which there is only one stable fixed point in the system. We show that there is a critical value for the damping constant, above which the minimal switching field is the same as that of the SW-limit, for a given magnetic anisotropy. The field of a ballistic magnetization reversal should be along a certain direction window in the presence of energy dissipation. The width of the window depends on both the damping constant and the magnetic anisotropy. The upper and lower bounds of the direction window increase with the damping constant. The window width oscillates with the damping constant for a given magnetic anisotropy, and is zero for both zero and infinite damping.