The main goal of the Muon g-¬2 Experiment (g-¬2) at Fermilab is to measure the muon anomalous magnetic moment to unprecedented precision. This new measurement will allow to test the completeness of the Standard Model (SM) and to validate other theoretical models beyond the SM. The close interplay of the understanding of particle beam dynamics and the preparation of the beam properties with the experimental measurement is tantamount to the reduction of systematic errors in the determination of the muon anomalous magnetic moment. We are developing detailed calculations and modeling of the muon beam delivery system in order to obtain a better understanding of spin¬-energy correlations, nonlinearities, and more realistic aspects that contribute to the systematic errors of the g-¬2 measurement.