Abstract
In dynamics, both the concepts of rigid body and Coulomb’s law of friction are well established, although it is known at least since Painlevé’s time that they may lead to irregularities and contradictions, such as loss of uniqueness or existence of the solution of the equations of motion. The problem is still of very actual interest, since it can be of practical significance also for the industrially used rigid body codes. One of the simplest mechanical systems in which these difficulties can be well described is the Painlevé–Klein apparatus. As most other systems discussed in this context in the literature, this is a holonomic system. In the present note, we briefly examine a nonholonomic oscillatory system which is an extension of the classical Painlevé–Klein apparatus and we study its dynamics with respect to the Painlevé paradox. Both the borders of paradoxical regions and their reachability are addressed.
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Wagner, A., Heffel, E., Arrieta, A.F. et al. Analysis of an Oscillatory Painlevé–Klein Apparatus with a Nonholonomic Constraint. Differ Equ Dyn Syst 21, 149–157 (2013). https://doi.org/10.1007/s12591-012-0131-9
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DOI: https://doi.org/10.1007/s12591-012-0131-9