Notes on a paper by F. Génot and B. Brogliato on the Painlevé paradox
Stefano Pasquero
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):653677, 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 velocitydependent 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.
Create a lesson
Related papers
2-Morita Theory of E2-Algebras and Module Categories
Rongge Xu, Holiverse Yang
Multiscale Loop Vertex Expansion for Cumulants, the ϕ42 Model
Vincent Rivasseau
Quasi-polynomiality and N-point functions of single connected leaky completed Hurwitz numbers
Chongyu Wang, Chenglang Yang
Coupled stochastic variational principles for multiscale surface gravity waves -- Part I: theoretical framework
Etienne Mémin, Arnaud Debussche
The Sharp Spectral Transition for Almost Mathieu Operators via Alternating Resonances
Jiawei He, Xueyin Wang
Dynamical classical-field limit of Bosonic Gibbs states: Renormalized Hartree NLS correlations in 2D and 3D
Phan Thành Nam, Rongchan Zhu, Xiangchan Zhu