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In rigid-body dynamics, the Painlevé paradox (also called frictional paroxysms by Jean Jacques Moreau) is the paradox that results from inconsistencies between the contact and Coulomb models of friction. It is named for former French prime minister and mathematician Paul Painlevé.

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  • Painlevé paradox (en)
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  • In rigid-body dynamics, the Painlevé paradox (also called frictional paroxysms by Jean Jacques Moreau) is the paradox that results from inconsistencies between the contact and Coulomb models of friction. It is named for former French prime minister and mathematician Paul Painlevé. (en)
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  • In rigid-body dynamics, the Painlevé paradox (also called frictional paroxysms by Jean Jacques Moreau) is the paradox that results from inconsistencies between the contact and Coulomb models of friction. It is named for former French prime minister and mathematician Paul Painlevé. To demonstrate the paradox, a hypothetical system is constructed where analysis of the system requires assuming the direction of the frictional force. Using that assumption, the system is solved. However, once the solution is obtained, the final direction of motion is determined to contradict the assumed direction of the friction force, leading to a paradox. 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. (en)
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