  We systematically investigate the multi-stability behaviour and cooling of
both librational and translational modes of an optically levitated nonspherical
nanoparticle. By expanding the trapping potential to the fourth order of both
the translational and librational freedom degrees, we deduce the nonlinearity
of them and their nonlinear coupling. Through stability analysis, we find that
the system presents multi-stability when either the librational or the
translational drive is red-detuned. The system will be stabilized if and only
if these two drives are both blue-detuned. In the steady state region, we study
the synthetic cooling scheme of translational mode by utilising librational
mode. We find that matching the driving amplitude of these two modes and
appropriate air pressure can optimize synthetic cooling. The synthetic cooling
limit can be greatly improved, if we combine the feedback cooling with the
synthetic cooling.
