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.