We present a theoretical study of optically induced dynamics in a homeotropic nematic liquid crystal excited at normal incidence. By retaining the first symmetric and antisymmetric reorientation modes, the dynamical equations are reduced to a four-dimensional problem. The main advantage of this minimal approach is to emphasize the role of twisted mode and asymmetry of the light-induced molecular reorientation in a manner suitable for a clear physical interpretation. Theoretical results are compared with experiments in the particular case of circularly polarized light beams to show the physical origin of mode competition and of the breakdown of chiral and longitudinal symmetry. The model successfully describes previous experimental studies such as time-dependent three-dimensional molecular dynamics, light-induced stabilized helical reorientation, and in-plane precession regime in achiral nematics. While a recent experiment has revealed a new spatiotemporal transition, the model succeeds to describe all the features of such a bifurcation pointing out anew the importance of asymmetry. Finally, the first quantitative description of the appearance of a giant mirrorless optical bistability when twisted reorientation modes are excited is demonstrated. A qualitative physical interpretation is suggested for all these phenomen