Painlevé paradox

The Painlevé paradox (also called by Jean Jacques Moreau frictional paroxysms) is a well-known example by Paul Painlevé in rigid-body dynamics that showed that rigid-body dynamics with both contact friction and Coulomb friction is inconsistent. This result is due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in the Coulomb friction law, especially when dealing with large coefficients of friction. There exist, however, simple examples which prove that the Painlevé paradoxes can appear even for small, realistic friction. The Painlevé paradox (also called by Jean Jacques Moreau frictional paroxysms) is a well-known example by Paul Painlevé in rigid-body dynamics that showed that rigid-body dynamics with both contact friction and Coulomb friction is inconsistent. This result is due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in the Coulomb friction law, especially when dealing with large coefficients of friction. There exist, however, simple examples which prove that the Painlevé paradoxes can appear even for small, realistic friction.