2025MNRAS.544..988B

We present a kinematic and dynamical analysis of six Galactic open clusters - NGC 2204, NGC 2660, NGC 2262, Czernik 32, Pismis 18, and NGC 2437, using Gaia DR3. We used Bayesian and Gaussian Mixture Model (GMM) methods to identify cluster members, but chose GMM because it is more appropriate for low-mass stars. Estimated distances range from 1.76 to 4.20 kpc and ages from 0.199 to 1.95 Gyr, confirming their intermediate-age nature. King model fits indicate compact morphologies, with core radii of 1-10 arcmin and cluster radii of 5-24 arcmin. We identify 13 blue straggler stars and 3 yellow straggler stars members, whose central concentrations suggest origins via mass transfer or stellar collisions. The mass function slopes (0.96-1.19) are flatter than the Salpeter value, which indicates that these clusters have undergone dynamical mass segregation. Orbit integration within a Galactic potential indicates nearly circular orbits (eccentricities 0.02-0.10), vertical excursions within $\pm$132 pc, and guiding radii near the solar circle, suggesting disc confinement. These clusters likely formed in the thin disc and are shaped by Galactic tidal perturbations, facilitating the rapid loss of low-mass members. Additionally, 12 variable stars were found across 4 clusters using Transiting Exoplanet Survey Satellite (TESS) light curves, including $\gamma$ Doradus and SPB pulsators, eclipsing binaries, and a yellow straggler candidate. Periods were derived via Lomb-Scargle analysis. Two eclipsing binaries (TIC 94229743 and TIC 318170024) were modelled using PHOEBE, yielding mass ratios of 1.37 and 2.16, respectively. Our findings demonstrate that integrating orbital dynamics and variable star studies presents valuable insights into the evolutionary pathways of open clusters.