  Open Clusters (OCs) can trace with a great accuracy the evolution of the
Galactic disk. The aim of this work is to study the kinematical behavior of the
OC population over time. We take advantage of the latest age determinations of
OCs to investigate the correlations of the 6D phase space coordinates and
orbital properties with age. We also investigate the rotation curve of the
Milky Way traced by OCs and we compare it to that of other observational or
theoretical studies. We gathered nearly 30000 Radial Velocity (RV) measurements
of OC members from both Gaia-RVS data and ground based surveys and catalogues.
We computed the weighted mean RV, Galactic velocities and orbital parameters of
1382 OCs. We investigated their distributions as a function of age, and by
comparison to field stars. We provide the largest RV catalogue available for
OCs, half of it based on at least 3 members. Compared to field stars, we note
that OCs are not exactly on the same arches in the radial-azimuthal velocity
plane, while they seem to follow the same diagonal ridges in the Galactic
radial distribution of azimuthal velocities. Velocity ellipsoids in different
age bins all show a clear anisotropy. The heating rate of the OC population is
similar to that of field stars for the radial and azimuthal components but
significantly lower for the vertical component. The rotation curve drawn by our
sample of clusters shows several dips, which match the wiggles derived from
non-axisymmetric models of the Galaxy. From the computation of orbits, we
obtain a clear dependence of the maximum height and eccentricity with age.
Finally, the orbital characteristics of the sample of clusters as shown by the
action variables, follow the distribution of field stars. The additional age
information of the clusters points towards some (weak) age dependence of the
known moving groups.
