Limit cycles at oversteer vehicle

Handling and stability properties of automobiles are most often studied from a practical point of view by applying a reduced set of equations, where the forward velocity is kept constant. At studying the full set of equations of a basic nonlinear two-wheel vehicle model, a supercritical Hopf bifurcation is found for an oversteer vehicle. All state variables of the vehicle are involved at small amplitude limit cycles in the vicinity of the Hopf bifurcation point with the steering angle (drive torque) as bifurcation parameter. At the transition to large amplitude relaxation cycles, the cyclic motion of the vehicle may be separated into ‘slow’ longitudinal velocity-related segments, and ‘fast’ vehicle yaw and side slip-related segments, indicating a singular perturbed system. Moreover, Canard phenomenon is observed for both steering angle and drive torque bifurcation parameters.