Hopf-Friedrichs bifurcation and the hunting of a railway axle

Abstract

After deriving the equations of motion which govern the lateral and yaw motions of a railway axle, these are cast in the form of a system of first-order nonlinear differential equations. To this system the Hopf-Friedrichs bifurcation theory is applied to determine when a periodic orbit will bifurcate from the equilibrium position. Sufficient conditions to guarantee the stability of the orbit are investigated.