  We investigate the effects of rotation about the axis of an astigmatic
two-mirror cavity on its optical properties. This simple geometry is the first
example of an optical system that can be destabilized and, more surprisingly,
stabilized by rotation. As such, it has some similarity with both the Paul trap
and the gyroscope. We illustrate the effects of rotational (de)stabilization of
a cavity in terms of the spatial structure and orbital angular momentum of its
modes.
