We present an analytical model to identify thin discs in galaxies, and apply this model to a sample of SDSS MaNGA galaxies. This model fits the velocity and velocity dispersion fields of galaxies with regular kinematics. By introducing two parameters $zeta$ related to the comparison of the models asymmetric drift correction to the observed gas kinematics and $eta$ related to the dominant component of a galaxy, we classify the galaxies in the sample as disc-dominated, non-disc-dominated, or disc-free indicating galaxies with a dominating thin disc, a non-dominating thin disc, or no thin disc detection with our method, respectively. The dynamical mass resulting from our model correlates with stellar mass, and we investigate discrepancies by including gas mass and variation of the initial mass function. As expected, most spiral galaxies in the sample are disc-dominated, while ellipticals are predominantly disc-free. Lenticular galaxies show a dichotomy in their kinematic classification, which is related to their different star formation rates and gas fractions. We propose two possible scenarios to explain these results. In the first scenario, disc-free lenticulars formed in more violent processes than disc-dominated ones, while in the second scenario, the quenching processes in lenticulars lead to a change in their kinematic structures as disc-dominated lenticulars evolve to disc-free ones.
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