A Set-Valued Force Law for Spatial Coulomb-Contensou Friction

The aim of this paper is to develop a contact law for combined spatial Coulomb friction and normal friction torque (drilling friction) as a function of sliding velocity and spin. We will call this extended contact law the Coulomb-Contensou friction law and derive it from a non-smooth velocity pseudo potential. A Runge-Kutta time-stepping method is briefly presented for the numerical simulation of rigid bodies with Coulomb-Contensou friction. The algebraic inclusion describing the contact problem is solved with an Augmented Lagrangian approach. The theory and numerical methods are applied to the Tippe-Top, which illustrates the importance of Coulomb-Contensou friction for the dynamics of systems with friction.