A mechanism for the onset of chaos in mechanical systems with motion-limiting stops

The behaviour of mechanical systems in the neighbourhood of Hopf bifurcations is studied, where it is assumed that the amplitude of the periodic motion is limited by stops. A mechanism is given for the onset of chaotic motion just as the amplitude is large enough to reach the stop. Analytic asymptotic estimates of Liapunov exponents are made. Rigid and flexible but stiff stops are compared. An example of a two-degrees-of-freedom system, consisting of a coupled Duffing and Rayleigh oscillator, is given and analytical predictions are compared with numerical results.