Analytical results in transient brush tyre models: theory for large camber angles and classic solutions with limited friction

Abstract This paper establishes new analytical results in the mathematical theory of brush tyre models. In first part, exact problem which considers large camber angles is analysed from perspective linear dynamical systems. Under assumption vanishing sliding, most salient properties model are discussed with some insights on concepts as existence and uniqueness solution. A comparison against classic steady-state suggests that latter represents a very good approximation even case angles. Furthermore, respect to theory, more general situation limited friction explored. It demonstrated that, transient conditions, sliding solutions can be determined for all one-dimensional problems. For pure lateral slip, investigation conducted under strictly concave pressure distribution rolling direction.