At first, the explanations on the coordinate axes to be used for the description of vehicle motion and how the tire lateral forces act on the moving vehicle are given. Then the equations of linear two degree-of-freedom vehicle motion, side slip and yaw rate, to steering input are introduced based on Newton's second law. The description of the steady state cornering of the vehicle is introduced by the development of the equations of motion and by applying the geometrical relation to the vehicle circular turning as well. Hence the description is extended to under tire nonlinear region. Examining the steady state cornering with the equations, the concepts of the vehicle steer characteristics—under-steer, neutral-steer, and over-steer—and the vehicle stability are investigated. In addition to the examination on the characteristic equation, the transfer functions of side slip angle, yaw rate, and lateral acceleration are derived from the equations of motion and the transient response characteristics of the vehicle motion are discussed. The response characteristics to periodical steer input are also investigated.
