Highway Vehicle Stability in Braking Maneuvers

The dynamic equations for an automobile in braking maneuvers are simplified in two steps. First, a nominal rectilinear trajectory is considered, with a constant deceleration rate. Secondly, a small perturbation in sideslip angle is examined, and the small disturbance equations of motion are derived. Solutions are obtained in terms of Bessel functions. The vehicle response is deemed stable when initial perturbations to the nominal trajectory are damped, and the perturbed motion is oscillatory. Algebraic expressions for the stability criteria are derived, illustrating the effects of speed, road frictions, tire slip-ratio, and vehicle design characteristics on vehicle response in braking maneuvers.