Self-oscillations in an Alpha Stirling Engine: a bifurcation analysis

We study a thermo-mechanical system comprised of an alpha Stirling engine and a flywheel from the perspective of dynamical systems theory. Thermodynamics establish a static relation between the flywheel's angle and the forces exerted by the two power pistons that constitute the engine. Mechanics, in turn, provide a dynamic relation between the forces and the angle, ultimately leading to a closed dynamical model. We are interested in the different behaviors that the engine displays as parameters are varied. The temperature of the hot piston and the mechanical phase between both pistons constitute our bifurcation parameters. Considering that energy conversion in the engine can only take place through cyclic motions, we are particularly interested in the appearance of limit cycles.