Nosonovsky Michael, Breki Alexander D
Mechanical Engineering, University of Wisconsin-Milwaukee, 3200 North Cramer St., Milwaukee, WI 53211, USA.
Department of Machine Design, St. Petersburg Polytechnic University, 29 Polytechnicheskaya St., 195251 St. Petersburg, Russia.
Entropy (Basel). 2019 Jun 24;21(6):620. doi: 10.3390/e21060620.
Paradoxes of dry friction were discovered by Painlevé in 1895 and caused a controversy on whether the Coulomb-Amontons laws of dry friction are compatible with the Newtonian mechanics of the rigid bodies. Various resolutions of the paradoxes have been suggested including the abandonment of the model of rigid bodies and modifications of the law of friction. For compliant (elastic) bodies, the Painlevé paradoxes may correspond to the friction-induced instabilities. Here we investigate another possibility to resolve the paradoxes: the introduction of the three-value logic. We interpret the three states of a frictional system as either rest-motion-paradox or as rest-stable motion-unstable motion depending on whether a rigid or compliant system is investigated. We further relate the ternary logic approach with the entropic stability criteria for a frictional system and with the study of ultraslow sliding friction (intermediate between the rest and motion or between stick and slip).
1895年，潘勒韦发现了干摩擦的悖论，引发了一场关于库仑 - 阿蒙顿干摩擦定律是否与刚体牛顿力学相容的争论。人们提出了各种解决悖论的方法，包括放弃刚体模型和修改摩擦定律。对于柔顺（弹性）体，潘勒韦悖论可能对应于摩擦诱发的不稳定性。在这里，我们研究另一种解决悖论的可能性：引入三值逻辑。根据研究的是刚体系统还是柔顺系统，我们将摩擦系统的三种状态解释为静止 - 运动 - 悖论或静止 - 稳定运动 - 不稳定运动。我们进一步将三值逻辑方法与摩擦系统的熵稳定性标准以及超慢滑动摩擦（介于静止和运动之间或粘滞和滑动之间）的研究联系起来。
