Lyapunov-Bautin bifurcation and the hunting of a railway wheelset

This paper presents results of the analytical investigation of the dynamics of a single railway wheelset. Above a critical speed, the stationary motion of the wheelset loses its stability. The methods of the Lyapunov-Bautin bifurcation theory provide the parameters of a domain where unstable periodic motions appear around the stable stationary motion. We use the Bautin formulae to determine the Lyapunov constant. Conditions to determine the regime of safe or dangerous motion are investigated. Computer algebra is involved because of the complexity of the Bautin formulae.