Abstract. The structure of the central part of the UMa stellar kinematic group was considered according to the data from Hipparcos, Tycho and ACT catalogues. We have shown that in the space occupied by the nucleus there are several populations of stars. The first includes ten stars which are very compactly located in the proper motion diagram and have a normal proper motion distribution. The second group includes six stars with large kinematic difference and there are six field stars placed here too. The question about their coexistence in a common region of space remains open. The well-known stars Mizar and Alcor appear to belong to the different subsystems and do not belong to a unique stellar system. The published radial velocities, as a rule, are determined with insufficient accuracy compared to the errors of the currently available proper motions. A high precision in the radial velocities measurements is necessary for a thorough study of the kinematics of stars inside UMa star system.

We determined the cluster apex coordinates, studied the substructures and performed membership analysis in the central part (34 ′ ×33 ′ ) of the open cluster M 67. We used the individual stellar apexes method developed earlier and classical technique of proper motion diagrams in coordinate system connected with apex. The neighbour-to-neighbour distance technique was applied to detect space details. The membership list was corrected and some stars were excluded from the most probable members list. The apex coordinates have been determined as: A 0 = 132.97• ±0.81• and D 0 = 11.85 • ±0.90• . The 2D-space star density field was analysed and high degree of inhomogeneity was found.

A study of cluster characteristics and internal kinematical structure of the middle-aged Pleiades open star cluster is presented. The individual star apexes and various cluster kinematical parameters including the velocity ellipsoid parameters are determined using both Hipparcos and Gaia data. Modern astrometric parameters were taken from the Gaia Data Release 1 (DR1) in combination with the Radial Velocity Experiment Fifth Data Release (DR5). The necessary set of parameters including parallaxes, proper motions and radial velocities are used for n=17 stars from Gaia DR1+RAVE DR5 and for n=19 stars from the Hipparcos catalog using SIMBAD data base. Single stars are used to improve accuracy by eliminating orbital movements. RAVE DR5 measurements were taken only for the stars with the radial velocity errors not exceeding 2 km/s. For the Pleiades stars taken from Gaia, we found mean heliocentric distance as 136.8 ± 6.4 pc, and the apex position is calculated as: A CP = 92 • .52 ± 1 • .72, D CP = −42 • .28 ± 2 • .56 by the convergent point method and A 0 = 95 • .59 ± 2 • .30 and D 0 = −50 • .90 ± 2 • .04 using AD-diagram method (n=17 in both cases). The results are compared with those obtained historically before the Gaia mission era.

The kinematical parameters, spatial shape and structure of the open cluster IC 2391 and the associated stellar stream are studied here using Gaia-DR2 (GDR2) astrometry data. The apex positions are determined for the open cluster IC 2391 (data taken from Cantat-Gaudin et al.) and for the kinematical stream's stars mentioned in Montes et al. using both convergent point and AD-diagram methods. The values of apex coordinates are: (A, D) CP =(6. h 17 ± 0. h 004, −6. • 88 ± 0. • 381; for cluster) & (6. h 07 ± 0. h 007, −5. • 00 ± 0. • 447; stream) and (A 0 , D 0 )= (6. h 12 ± 0. h 004, −3. • 4 ± 0. • 3; cluster) & (6. h 21 ± 0. h 007, −11. • 895 ± 0. • 290; stream). The results are in good agreement with the previously calculated values. The positions of the stars in the disk and the spatial dispersion velocities are determined. The paths of cluster and associated stream are traced in the disk by orbit calculation back in time to their places of formation. A possible genetic relationship between the cluster and the stream has been detected. The approximation of the spatial and kinematical shape of the stream and the cluster is made. According to this study, even though currently the cluster and the stream seem to have spatial difference in their locations but they appear to have formed in the same region of the Galactic disk.