  We investigate the effects of halo kinematics on the dynamics of stellar
discs by simulating the evolution of isolated disc-halo systems from
equilibrium initial conditions. Our main results come from four simulations
where the initial disc is identical and the halo is either treated as a rigid
potential or is live with isotropic orbits or orbits that preferentially rotate
with or counter to the disc. We confirm previous results that bar formation is
more vigorous in models with a live halo than a rigid one and is further
enhanced when halo orbits preferentially rotate with the disc. We discuss two
types of buckling events with different symmetries about the mid plane, one
that occurs just as the bar is forming and the other well after the bar has
been established. We also show that warps are most easily excited and
maintained when the halo is counter-rotating with the disc, in agreement with
theoretical predictions. Our most novel result is the discovery of a rotating
halo instability, which causes the disc and halo cusp to spiral outward from
the centre of mass of the system whether the halo rotates with the disc or
counter to it and also occurs in a disc bulge halo system that does not form a
bar. We provide a heuristic linear model that captures the essential dynamics
of the instability.
