  Motivated by the existence of the relationship between the dynamical state of
clusters and the shape of the velocity dispersion profiles (VDP), we study the
VDPs for Gaussian (G) and Non-Gaussian (NG) systems for a subsample of clusters
from the Yang catalog. The groups cover a redshift interval of $0.03\leq
z\leq0.1$ with halo mass $\geq 10^{14}$M$_{\odot}$. We use a robust statistical
method, Hellinger Distance, to classify the dynamical state of the systems
according to their velocity distribution. The stacked VDP of each class, G and
NG, is then determined using either Bright or Faint galaxies. The stacked VDP
for G groups displays a central peak followed by a monotonically decreasing
trend which indicates a predominance of radial orbits, with the Bright stacked
VDP showing lower velocity dispersions in all radii. The distinct features we
find in NG systems are manifested not only by the characteristic shape of VDP,
with a depression in the central region, but also by a possible higher infall
rate associated with galaxies in the Faint stacked VDP.
