Advanced brush tyre modelling 1. Tyre inputs and equations 2 Steady state theory of tyre forces and moments generation 3 Transient theory of tyre forces and moments generation 4 Exact solutions to the rolling contact problem 5 Approximate theories of tyre forces and moments generation 6 Additional material. This book provides an in depth understanding of tyre dynamics. In the first three chapters new concepts are introduced in respect to the classic theory. Analytical results are derived step by step to guide the reader through the governing equations of the model. Transient phenomena are explained in a relatively simple way according to the brush theory. The analysis is extended to cover the case of large camber angles which is often disregarded. The principal mechanisms behind the transient generation of tyre forces and moment are discussed in general terms and exact solutions to the rolling contact problem are given for simple contact geometries. The last part of the book is dedicated to the approximated theories of transient generation of tyre forces and moment. Two different models suitable for use in vehicle dynamics applications are presented and compared.