  We consider the rotational dynamics in an ensemble of globally coupled
identical pendulums. This model is essentially a generalization of the standard
Kuramoto model, which takes into account the inertia and the intrinsic
nonlinearity of the community elements. There exists the wide variety of
in-phase and out-of-phase regimes. Many of these states appear due to broken
symmetry. In the case of small dissipation our theoretical analysis allows one
to find the boundaries of the instability domain of in-phase rotational mode
for ensembles with arbitrary number of pendulums, describe all arising
out-of-phase rotation modes and study in detail their stability. For the system
of three elements parameter sets corresponding to the unstable in-phase
rotations we find a number of out-of-phase regimes and investigate their
stability and bifurcations both analytically and numerically. As a result, we
obtain a sufficiently detailed picture of the symmetry breaking and existence
of various regular and chaotic states.
