  We use the Illustris simulation to study the distributions of ellipticities
and kinematic misalignments of galactic projections, as well as the intrinsic
shapes and rotation of the simulated galaxies. Our results for the projections
of galaxies display clear trends of an overall increase of kinematic
misalignment and a slight decrease of ellipticity for fast rotators with
increasing masses, while revealing no clear distinction between slow rotators
of different mass. It is also found that the number of very slow rotators with
large ellipticities is much larger than found in observations. The intrinsic
properties of the galaxies are then analysed. The results for the intrinsic
shapes of the galaxies are mostly consistent with previous results inferred
from observational data. The distributions of intrinsic misalignment of the
galaxies suggest that some of the galaxies produced by Illustris have
significant rotation around their medium axes. Further analysis reveals that
most of these galaxies display signs of non-equilibrium. We then study the
evolution of the intrinsic misalignments and shapes of three specific Illustris
galaxies, which we consider as typical ones, along the main progenitor line of
their merger trees, revealing how mergers influence the intrinsic shapes and
kinematics: the spin axis in general stays close to the shortest axis, and
tends to quickly relax to such an equilibrium state within a few dynamical
times of the galaxy after major perturbations; triaxiality and intrinsic
flatness in general decrease with time, however, sometimes increases occur that
are clearly seen to correlate with major merger events.
