The expression for the force of a magnetic bearings depends on the applied current and the displacement of the rotor at the point where the bearing is attached (more details can be found in "Magnetic Bearings - Theory, Design, and Application" by Gerhard Schweitzer and Eric Maslen). Regarding the dynamic model of the shaft, it can be developed using the Lagrange's method (more details can be found in "Dynamics of rotating systems" by Giancarlo Genta).