Dynamics of a driven Stirling engine

We study the nonlinear dynamics of an idealized driven Stirling engine model. The model is analogous to an oscillator with a nonlinear dependence of the spring constant on the state and input signal, with a rich complexity of behaviors depending on frequency ratios and amplitudes. We employ a change of coordinates where input-to-state boundedness questions can be answered. Furthermore, a fixed point argument is used to show that for each periodic input forcing, the system posses at least one periodic orbit of the same period. We elaborate on the significance of this fact to input signal design for the driven Stirling engine.