Abstract
The contribution presents four problems connected with the Colloquium topics. They are of theoretical nature in the wider aspect but all refer to the results of practical simulations of rail vehicle motion in a curved track. The first two can be counted to typical non-smooth problems in rail vehicle dynamics. They refer to two-point contact modelling and vehicle stability in curves, respectively. The third problem is closely related to the second one. It refers to railway vehicle dynamics above critical velocity in transition curves. The forth one can also be recognized as the non-smooth problem but not so typical one. It refers to modelling the kinematics in a curved track. All the problems reveal that one needs to be very careful when studying rail vehicle dynamics and trying to simplify its non-linearities at the same time. Non-smooth functions can influence results of numerical analysis strongly, being the features of the physical and modelling nature.
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