Abstract
A dicone moving on a pair of cylindrical rails can be considered as a simplified model of a railway wheelset. Taking into account the non-linear friction laws of rolling contact, the equations of motion for this non-linear mechanical system result in a set of differential-algebraic equations. Previous simulations performed with the differential-algebraic solver DASSL, [2], and experiments, [7], indicated non-linear phenomena such as limit-cycles, bifurcations as well as chaotic behaviour. In this paper the non-linear phenomena are investigated in more detail with the aid of special in-house software and the path-following algorithm PATH [10]. We apply Poincaré sections and Poincaré maps to describe the structure of periodic, quasiperiodic and chaotic motions. The analyses show that part of the chaotic behaviour of the non-linear system can be fully understood as a non-linear iterative process. The resulting stretching and folding processes are illustrated by series of Poincaré sections.
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Knudsen, C., Feldberg, R. & Jaschinski, A. Non-linear dynamic phenomena in the behaviour of a railway wheelset model. Nonlinear Dyn 2, 389–404 (1991). https://doi.org/10.1007/BF00045671
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DOI: https://doi.org/10.1007/BF00045671