  Motivated by kinematic observations of young embedded clusters, this paper
explores possible kinematic signatures produced by asphericity and departures
from initial virial equilibrium in these systems. Specifically, the kinematic
quantity that is measured and calculated in this study is the distribution of
the line-of-sight velocities as a function of position along the cluster.
Although clusters are found within a wide range of sizes, we focus on the
regime with stellar membership $N \sim 10^3$. The gravitational potential of
these young clusters is dominated by the gas, and the geometry of the gas
distribution is generalized to include axisymmetric (and triaxial) forms. With
this loss of symmetry, the kinematic results thus depend on viewing angle. This
work also considers the stars to begin their trajectories with subvirial
speeds, as indicated by observations of core motions in such clusters. Our
results determine the conditions necessary for the kinematic signature to
display interesting structure, i.e., a non-spherical potential, a viewing angle
that is not along one of the principal axes, and subvirial starting conditions.
We characterize the effects on this signature due to projection angle, initial
stellar velocities, cluster elongation, and star formation efficiency. Finally,
we compare our theoretical results to recent kinematic observations of the
Orion Nebula Cluster; we find that the observations can be explained provided
that the cluster is non-spherical, starts with subvirial initial velocities,
and is not viewed along a principal axis.
