A set-valued force law for spatial Coulomb-Contensou friction

The aim of this paper is to develop a set-valued contact law for combined spatial Coulomb-Contensou friction, taking into account a normal friction torque (drilling friction) and spin. The set-valued Coulomb-Contensou friction law is derived from a non-smooth velocity pseudo potential. A higher-order Runge-Kutta time-stepping method is 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. The analysis and numerical results on the Tippe-Top illustrate the importance of Coulomb-Contensou friction for the dynamics of systems with friction.