  The kinematics and dynamics of stellar and substellar populations within
young, still-forming clusters provides valuable information for constraining
theories of formation mechanisms. Using Keck II NIRSPEC+AO data, we have
measured radial velocities for 56 low-mass sources within 4' of the core of the
Orion Nebula Cluster (ONC). We also re-measure radial velocities for 172
sources observed with SDSS/APOGEE. These data are combined with proper motions
measured using $HST$ ACS/WFPC2/WFC3IR and Keck II NIRC2, creating a sample of
135 sources with all three velocity components. The velocities measured are
consistent with a normal distribution in all three components. We measure
intrinsic velocity dispersions of ($\sigma_{v_\alpha}$, $\sigma_{v_\delta}$,
$\sigma_{v_r}$) = ($1.64\pm0.12$, $2.03\pm0.13$, $2.56^{+0.16}_{-0.17}$) km
s$^{-1}$. Our computed intrinsic velocity dispersion profiles are consistent
with the dynamical equilibrium models from Da Rio et al. (2014) in the
tangential direction, but not in the line of sight direction, possibly
indicating that the core of the ONC is not yet virialized, and may require a
non-spherical potential to explain the observed velocity dispersion profiles.
We also observe a slight elongation along the north-south direction following
the filament, which has been well studied in previous literature, and an
elongation in the line of sight to tangential velocity direction. These 3-D
kinematics will help in the development of realistic models of the formation
and early evolution of massive clusters.
