Kinematic Properties of Open Star Clusters with Data from the Gaia DR2
  Catalogue
  We consider open star clusters (OSCs) with the proper motions, parallaxes,
and line-of-sight velocities calculated by various authors from Gaia DR2 data.
The distance scale factor has been found by analyzing the separate solutions of
the basic kinematic equations to be $p=1.00\pm0.04.$ It shows that the
distances calculated using the parallaxes from the Gaia DR2 catalogue do not
need any correction factor. We have investigated the solutions obtained from
various OSC samples differing in both age and accuracy of their parallax and
line-of-sight velocity measurements. The solution obtained from a sample of 930
OSCs satisfying the constraints on the age logt<9 and the relative
trigonometric parallax error <30% is recognized to be the best one, with 384
OSCs in this sample having the mean line-of-sight velocities calculated from at
least three probable members of the corresponding clusters. As a result of the
simultaneous solution of all the basic kinematic equations, we have found the
following kinematic parameters from this sample:
$(U,V,W)_\odot=(8.53,11.22,7.83)\pm(0.38,0.46,0.32)$ km s$^{-1}$,
$\Omega_0=28.71\pm0.22$ km s$^{-1}$ kpc$^{-1}$, $\Omega'_0=-4.100\pm0.058$ km
s$^{-1}$ kpc$^{-2}$, and $\Omega''_0= 0.736\pm0.033$ km s$^{-1}$ kpc$^{-3}$.
The linear rotation velocity at the adopted at the adopted solar distance
$R_0=8\pm0.15$ kpc is $V_0=229.7\pm4.6$ km s$^{-1}$. An analysis of the proper
motions for these 930 OSCs has shown that, apart from the rotation around the
Galactic z axis, there is rotation of the entire sample around the x axis with
an angular velocity of $0.48\pm0.15$ km s$^{-1}$ kpc$^{-1}$ differing
significantly from zero.
