  Motivated by understanding the liquid core dynamics of tidally deformed
planets and moons, we present a study of incompressible flow driven by
latitudinal libration within rigid triaxial ellipsoids. We first derive a
laminar solution for the inviscid equations of motion under the assumption of
uniform vorticity flow. This solution exhibits a res- onance if the libration
frequency matches the frequency of the spin-over inertial mode. Furthermore, we
extend our model by introducing a reduced model of the effect of viscous Ekman
layers in the limit of low Ekman number (Noir and C\'ebron 2013). This
theoretical approach is consistent with the results of Chan et al. (2011) and
Zhang et al. (2012) for spheroidal geometries. Our results are validated
against systematic three-dimensional numerical simulations. In the second part
of the paper, we present the first linear sta- bility analysis of this uniform
vorticity flow. To this end, we adopt different methods (Lifschitz and Hameiri
1991; Gledzer and Ponomarev 1977) that allow to deduce upper and lower bounds
for the growth rate of an instability. Our analysis shows that the uniform
vorticity base flow is prone to inertial instabilities caused by a parametric
resonance mechanism. This is confirmed by a set of direct numerical
simulations. Applying our results to planetary settings, we find that neither a
spin-over resonance nor an inertial instability can exist within the liquid
core of the Moon, Io and Mercury.
