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In this paper, the nonsmooth dynamics of two contacting rigid bodies is analysed in the presence of dry friction. In three dimensions, slipping can occur in continuously many directions. Then, the Coulomb friction model leads to a system of differential equations, which has a codimension-2 discontinuity set in the phase space. The new theory of extended Filippov systems is applied to analyse the dynamics of a rigid body moving on a fixed rigid plane to explore the possible transitions between the slipping and rolling behaviour. The paper focuses on finding the so-called limit directions of the slipping equations at the discontinuity. This leads to a complete qualitative description of the possible scenarios of the dynamics in the vicinity of the discontinuity. It is shown that the new approach consistently extends the information provided from the static friction force of the rolling behaviour. The methods are demonstrated on an application example.

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In this paper, nonlinear dynamics of a railway wheelset is investigated during kinematic oscillations. Based on the nonlinear differential equations, the notion of nonlinearity factor is introduced, which expresses the effect of the vibration amplitude on the frequency of the oscillations. The analytical formula of this nonlinearity factor is derived from the local geometry of the rail and wheel profiles. The results are compared to the ones obtained from the rolling radius difference (RRD) function.

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