One of the most relevant problems in vehicle dynamics control is the computational
burden due to optimal trajectory generation. Exploiting the differential flatness property and implementing a different approach to Nonlinear Programming (NLP) it is demonstrated that the computational time to complete the optimization decreases considerably compared to classical direct methods. Two vehicle models, Point-Mass and Torque Vectoring Single-Track, are proven to be flat and employed for offline optimization. Point-Mass is also used as nominal model in the development of an extremely efficient Flatness-Based Model Predictive Control (FMPC) for the Formula SAE race car of the University of Pisa which is validated through simulations. Trajectory generation is formulated in spatial domain, that allows to describe the pose of the vehicle in track reference frame.