On the origin and bifurcations of stick-slip oscillations

A recently proposed model of macroscopic friction is investigated using methods of dynamical systems analysis. Particular emphasis is put on the bifurcations associated with the appearance of stick-slip oscillations. In the model it is found that the existence of these oscillations is a result of a periodic orbit straddling a discontinuity in the first derivative of the vector field. A local analysis tool is developed to discuss the stability of such an orbit and its bifurcations due to changes in system parameters. The analysis tool is found to be highly efficient at quantitatively predicting the location and type of bifurcations. It is argued that the method and the general results are applicable to a large class of friction models containing similar discontinuities and thus, hopefully, to actual frictional dynamics.