1. The Tyre as a Nonlinear System

At a high level of description, the tyre may be thought of as a nonlinear dynamical system, which produces certain outputs, often referred to as tyre characteristics, when subjected to opportune inputs. This interpretation allows defining some fundamental quantities that contribute to determining both the steady-state and the transient response of the tyre. Amongst these, the slip variables play the most important role. In steady-state conditions, the tyre characteristics may be described as real analytic functions of the slips, which may be defined in three main different ways. The Jacobians of the steady-state characteristics with respect to the slip variables are often called matrices of generalised slip stiffnesses. The local properties of the steady-state tyre characteristics may be deduced from the entries of these matrices.