  Motivated by the experimentally observed shear-induced destabilization and
reorientation of smectic A like systems, we consider an extended formulation of
smectic A hydrodynamics. We include both, the smectic layering (via the layer
displacement u and the layer normal p) and the director n of the underlying
nematic order in our macroscopic hydrodynamic description and allow both
directions to differ in non equilibrium situations. In an homeotropically
aligned sample the nematic director does couple to an applied simple shear,
whereas the smectic layering stays unchanged. This difference leads to a finite
(but usually small) angle between n and p, which we find to be equivalent to an
effective dilatation of the layers. This effective dilatation leads, above a
certain threshold, to an undulation instability of the layers. We generalize
our earlier approach [Rheol. Acta, vol.39(3), 15] and include the cross
couplings with the velocity field and the order parameters for orientational
and positional order and show how the order parameters interact with the
undulation instability. We explore the influence of various material parameters
on the instability. Comparing our results to recent experiments and molecular
dynamic simulations, we find a good qualitative agreement.
