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This paper proposes a thorough investigation of steady-state cornering equilibria for cars. Besides equilibria corresponding to normal driving behaviour - herein denoted as stable-normal turn, drifting is attracting increasing attention. When discussing drifting, it is typically assumed that yaw rate and steering angle have opposite signs, i.e. the driver is countersteering, and the rear axle is saturated. Interestingly, another unstable equilibrium is possible, herein referred to as unstable-normal turn. In this work, an attempt to give a comprehensive definition of drift is made. An inverse model is proposed to compute the driver inputs needed to perform a steady-state turn for a given radius and sideslip angle. The mathematical meaning of all equilibria is explored by linearizing the system and analyzing eigenvalues and eigenvectors of the resulting state matrices.

The aim of this work is to improve the performance of a racing motorcycle by means of gearbox tuning. The Optimal Maneuver Method, which essentially simulates an ideal driver and computes the minimum Lap Time for a given motorcycle and a given circuit, is applied. A 1000cc SuperBike motorcycle and two very different racetracks, i.e. a fast one and a slow one, are considered. First the agreement between the Optimal Maneuver Method results and the logged telemetry data is proven, in order to fully justify its application. Next the relationship between gearbox ratio, lap performance and circuit characteristics is investigated and potential improvements are highlighted. Finally gearbox tuning is achieved by a Lap Time optimization procedure, and subsequent performance improvements are discussed.