The Large Magellanic Cloud (LMC) has a complex dynamics driven by both internal and external processes. The external forces are due to tidal interactions with the Small Magellanic Cloud (SMC) and the Milky Way, while internally its dynamics mainly depends on the stellar, gas, and dark matter mass distributions. Despite the overall complexity of the system, very often simple physical models can give us important insights about the main driving factors. Here we focus on the internal forces and attempt to model the proper motions (PM) of ~1 000 000 stars in the LMC as measured by Gaia with an axisymmetric dynamical model, based on the Jeans equations. We test both cored and cusped spherical Navarro-Frenk-White (NFW) dark matter halos to fit the LMC gravitational potential. We find that this simple model is very successful at selecting a clean sample of genuine LMC member stars and correctly predicts the geometry and orientation of the LMC with respect to the observer without additional prior information. Our Jeans dynamical models describes well the mean velocity and velocity dispersion of the LMC stellar disc, however it fails to describe the motions of the LMC bar, which is a non-axisymmetric feature dominating the central region. We plan a triaxial Schwarzschild approach as a next step for the dynamical modelling of the LMC.
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