Abstract
SUMMARY In this paper we present the results of a refined investigation of the dynamical behaviour of Cooperrider's complex bogie. The earlier results were presented in [4] and [7]. It was discovered, that one of the solution branches in [4] and [5] was one of an asymmetric, periodic oscillation - albeit with a very small offset, but it indicates, that the asymmetric oscillation is the generic mode at speeds much lower than has hitherto been found. The bifurcation diagram has been completed, a new type of bifurcation discovered and the other asymmetric branch determined. Furthermore we discovered chaotic motion of the bogie at much lower speeds than reported in [5] and [8][, and we present the result here. Finally we present a new solution branch, which represents an unstable, symmetric oscillation. It has the interesting property, that it turns stable in a small speed range for very high speeds. It has a smaller amplitude than the coexisting chaos. Such behaviour is not uncommon in dynamical systems, see e.g.. [9].
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