  We present analysis of the gas kinematics of the Integral Shaped Filament
(ISF) in Orion~A using four different molecular lines, $^{12}$CO (1-0),
$^{13}$CO (1-0), NH$_3$ (1,1), and N$_2$H$^+$ (1-0). We describe our method to
visualize the position-velocity (PV) structure using the intensity-weighted
line velocity centroid, which enables us to identify structures that were
previously muddled or invisible. We observe a north to south velocity gradient
in all tracers that terminates in a velocity peak near the center of the Orion
Nebula Cluster (ONC), consistent with the previously reported "wave-like"
properties of the ISF. We extract the velocity dispersion profiles and compare
the non-thermal line widths to the gas gravitational potential. We find
supersonic Mach number profiles, yet the line widths are consistent with the
gas being deeply gravitationally bound. We report the presence of two $^{12}$CO
velocity components along the northern half of the ISF; if interpreted as
circular rotation, the angular velocity is $\omega=1.4\,{\rm Myr}^{-1}$. On
small scales we report the detection of N$_2$H$^+$ and NH$_3$ "twisting and
turning" structures, with short associated timescales that give the impression
of a torsional wave. Neither the nature of these structures nor their relation
to the larger scale wave is presently understood.
