C.N. Jensen, M. Golubitsky and H. True

Symmetry, generic bifurcations, and mode interaction in nonlinear railway dynamics

In: IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics. (F.C. Moon, ed.) Kluwer Acad. Publ., 1999, 387-396.

• Abstract

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