ANALYTICAL DETERMINATION OF BIFURCATIONS IN AN IMPACT OSCILLATOR

It is well known that some solutions for a sinusoidally driven oscilla tor with linear stiffness and impacts at rigid stops modelled with a c oefficient of restitution impact law can be located analytically. Rece ntly, new co-dimension one bifurcations called grazing bifurcations ha ve been found in such systems. Here we present analytical results whic h show how the type of grazing bifurcation changes with parameter, and that when the type of grazing bifurcation changes a codimension two b ifurcation occurs. The simplest grazing bifurcations involve orbits of period-1, but we show that the same analytical methods can be used to locate some subharmonics and their bifurcations.