  The origin of multiple stellar populations in Globular Clusters (GCs) is one
of the greatest mysteries of modern stellar astrophysics. N-body simulations
suggest that the present-day dynamics of GC stars can constrain the events that
occurred at high redshift and led to the formation of multiple populations.
Here, we combine multi-band photometry from the Hubble Space Telescope (HST)
and ground-based facilities with HST and Gaia Data Release 2 proper motions to
investigate the spatial distributions and the motions in the plane of the sky
of multiple populations in the type II GCs NGC 5139 ($\omega\,$Centauri) and
NGC 6656 (M 22). We first analyzed stellar populations with different
metallicities. Fe-poor and Fe-rich stars in M 22 share similar spatial
distributions and rotation patterns and exhibit similar isotropic motions.
Similarly, the two main populations with different iron abundance in
$\omega\,$Centauri share similar ellipticities and rotation patterns. When
analyzing different radial regions, we find that the rotation amplitude
decreases from the center towards the external regions. Fe-poor and Fe-rich
stars of $\omega\,$Centauri are radially anisotropic in the central region and
show similar degrees of anisotropy. We also investigate the stellar populations
with different light-element abundances and find that their N-rich stars
exhibit higher ellipticity than N-poor stars. In $\omega\,$Centauri Centauri
both stellar groups are radially anisotropic. Interestingly, N-rich, Fe-rich
stars exhibit different rotation patterns than N-poor stars with similar
metallicities. The stellar populations with different nitrogen of M 22 exhibit
similar rotation patterns and isotropic motions. We discuss these findings in
the context of the formation of multiple populations.
