First space and kinematical analysis of newly discovered southern UFMGs
  clusters with Gaia
  The work on the kinematical parameters and spatial shape structure have been
performed with Gaia DR2 astrometry data of the new recently southern discovered
open clusters; UFMG 1, UFMG 2, and UFMG 3 in the vicinity (1.3 degrees radius)
of the rarely studied NGC 5999. The apexes positions with AD-diagram method are
computed for about 107, 168, 98, and 154 members of these star clusters,
respectively, our calculated values of apex coordinates, seems like: (A, D) =
(102.40 +/- 1.02 & -4.60 +/- 0.47; NGC 5999), (96.69 +/- 1.10 & -0.58 +/-
0.045; UFMG 1), (97.47 +/- 1.09 & 1.56 +/- 0.051; UFMG 2), and (98.65 +/- 1.12
& -0.26 +/- 0.060; UFMG 3). On the other hand, Velocity Ellipsoid Parameters
VEPs for those are also computed; e.g. space velocities due to Galactic
coordinates, dispersion velocities (sigma_1, sigma_2, sigma_3) due to matrix
elements for all ij, projected distances (X_sun, Y_sun, Z_sun) on the plane
disc, and the Solar elements (S_sun, l_A, b_A). According to an approximation
of spatial and kinematical shape, UFMGs and NGC 5999 seem to have a spatial
difference in their space locations but they appear to have formed in the same
region of the Galactic disc. The total cumulative mass MC; including total
number of main-sequence NMS and non-main-sequence Nnon-MS of these clusters
also evaluated here with a second-order polynomial of mass-luminosity relation
in order to get clusters tidal radii (pc). Finally, we concluded that NGC 5999,
UFMG 1, and UFMG 2 are dynamically relaxed (i.e. tau >> 1), and the fourth one
in non-relaxed.
