We investigate Cooperrider's complex bogie, a mathematical model of a railw
ay bogie running on an ideal straight track. The speed of the bogie v is th
e control parameter. Taking symmetry into account, we find that the generic
bifurcations from a symmetric periodic solution of the model are Hopf bifu
rcations for maps (or Neimark bifurcations), saddle-node bifurcations, and
pitchfork bifurcations. The last ones are symmetry-breaking bifurcations. B
y variation of an additional parameter, bifurcations of higher degeneracy a
re possible. In particular, we consider mode interactions near a degenerate
bifurcation. The bifurcation analysis and path-finding are done numericall
y.