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

## TL;DR

This paper analyzes the dynamic behavior of an alpha Stirling engine with a flywheel, focusing on how parameter changes lead to different oscillatory behaviors, including the emergence of limit cycles, using bifurcation theory.

## Contribution

It introduces a dynamical model of an alpha Stirling engine and investigates how bifurcations lead to self-oscillations, providing new insights into engine stability and oscillatory regimes.

## Key findings

- Identification of bifurcation points leading to self-oscillations
- Characterization of limit cycles in the engine model
- Influence of temperature and phase parameters on engine dynamics

## Abstract

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.