An unusual Hopf bifurcation: The railway bogie

The railway bogie model introduced by Cooperrider [1972] exhibits a Hopf bifurcation as the speed of the train v(tr) is increased. This Hopf bifurcation is unusual because the amplitude of the family of,periodic solutions that arises, behaves locally like v(tr)(c)-v(tr) rather than like root v(tr)(c)-v(tr). The explanation seems to lie with the form of the creep forces. Because of these forces, the model is of class C-1 but not C-2 at the origin.