  We study a model colloidal liquid crystal consisting of hard spherocylinders
under the influence of an external aligning potential by Langevin dynamics
simulation. The external field that rotates in a plane acts on the orientation
of the individual particles and induces a variety of collective nonequilibrium
states. We characterize these states by the time-resolved orientational
distribution of the particles and explain their origin using the single
particle behavior. By varying the external driving frequency and the packing
fraction of the spherocylinders we construct the dynamical state diagram.
