Notes on a paper by F. Génot and B. Brogliato on the Painlevé paradox

Abstract

We reconsider the analysis of the Classical Painlevé Problem developed by F. Génot and B. Brogliato ([1] New results on Painlevé paradoxes. - European Journal of Mechanics-A/Solids, 18(4):653{677, 1999), focusing on the consistency of their results with Galilean invariance. We show that certain conclusions concerning the dynamical evolution of the mechanical system are not invariant under changes of Galilean observer and therefore cannot, in their present form, be interpreted as intrinsic properties of the system. In particular, we show that the classi?cation of motion states depends on the observer through the velocity{dependent characterization of the frictional constraint, and we trace the origin of this dependence to the Galilean velocity-addition theorem. We present and discuss possible reformulations of the model aimed at restoring observer-invariant descriptions of the problem.

16 pages, 4 figures