[en] The precessional switching process of a magnetic nanoparticle subject to external field pulses applied along the hard-axis is considered. The critical field pulse amplitude necessary to realize the switching is determined. Then, the analytical solution of magnetization switching dynamics is derived in the lossless limit by using elliptic functions. Moreover, expressions for the field pulse duration tolerances which guarantee successful switching are also obtained. The theoretical predictions are verified by macrospin numerical simulations of ultra-fast magnetization switching.