Particular attention will be paid to numerical continuation of systems with non-smoothness, motivated by the example of intermittent contacts in a model of orthogonal cutting (turning). Rich dynamical behaviour is present in this model due to the presence of a grazing bifurcation which denotes the transition point from constant contact of the cutting tool with the workpiece to intermittent contact. Using numerical continuation it is possible to elucidate the full bifurcation structure of the system, something that would be extremely difficult with other methods.

Finally, numerical continuation will be demonstrated as applied to a physical experiment (so-called control-based continuation): a nonlinear energy harvesting device. Numerical continuation in this context allows the investigation of a physical device without prior knowledge of a model. Both stable and unstable motions can be investigated and bifurcations found directly. As such these investigations may aid in establishing what an appropriate mathematical model could be. [video]