Study of a driven and braked wheel using maximal monotone differential inclusions: applications to the nonlinear dynamics of wheeled vehicles

Abstract

A wheel subjected to two friction forces, one exerted by the ground and one exerted by the brake pad, is studied. A formalism using multivalued operators allows us to write the constitutive laws of this wheel in the form of a differential inclusion, for which we have the existence and the uniqueness of the solution, as well as the convergence of the associated numerical scheme. This wheel may be connected by itself to a chassis. The chassis may also be connected to two of these wheels. In these two cases, we again obtain a well-posed differential inclusion, in terms of existence, uniqueness, and convergence of the numerical scheme. In a more general manner, numerous applications can be proposed in the domain of the nonlinear dynamics of wheeled vehicles.