  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 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 of $\sim10^6$ stars in the LMC as measured by Gaia Data Release 3 with
an axisymmetric dynamical model, based on the Jeans equations. We test both
cored and cusped spherical Navarro-Frenk-White 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 predicts the geometry
and orientation of the LMC with respect to the observer within the constraint
of axisymmetry. Our Jeans dynamical models describe well the rotation profile
and the velocity dispersion of the LMC stellar disc, however they fail 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.
