  We study the deterministic dynamics of rotator chain that subjected to purely
mechanical driving on the boundary by stability analysis and numerical
simulation. Globally synchronous rotation, clustered synchronous rotation, and
split synchronous rotation states are identified. In particular, we find that
the single-peaked variance distribution of angular momenta is the consequence
of the deterministic dynamics. As a result, the operational definition of
temperature used in the previous studies on rotator chain should be revisited.
