Characterisation of the dynamics of a four-dimensional stick-slip system by a scalar variable

In this paper some aspects of the dynamics of a 4-dimensional system are described by means of a scalar variable. The two degrees-of-freedom system undergoes self excited vibrations brought on by an instantaneous change in the friction law. The subsequent mathematical system is non-smooth and its phase space has a variable dimension so that, for instance, the usual calculation of Lyapunov exponents is precluded. A 1-dimensional variable is introduced that allows a numerical diagnosis of the chaotic state of the system dynamics and a mechanism proposed for the bifurcation at which the attractor loses stability.