Accelerator physics needs advanced modeling and simulation techniques, for beam stability studies but also for the measurement of beam parameters like the Twiss parameters. A deeper understanding of magnetic field non-linearities effects will greatly help in the improvement of future circular collider design, performance, and diagnostics. This paper studies the variation of the \beta-beating with the action of the particle generated by non-linear Resonance Driving Terms, both from a theoretical and an experimental point of view.