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In this work the effects of vehicle vertical vibrations on the tires/road cornering forces, and then consequently on vehicle lateral dynamics are studied. This is achieved through a ride model and a handling model linked together by a non-linear tire model. The ride model is a half vehicle with four degrees of freedom (bounce and pitch motions for vehicle body and two bounce motions for the two axles). The front and rear suspension are a hydro-pneumatic slow-active systems with 6 Hz cut-off frequency designed based on linear optimal control theory. Vehicle lateral dynamics is modeled as two degrees (yaw and lateral motions) incorporating a driver model. An optimal rear wheel steering control in addition to the front steering is considered in the vehicle model to represent a Four Wheel Steering (4WS) system. The tire non-linearity is represented by the Magic Formula tire model.