{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T17:08:36Z","timestamp":1770138516445,"version":"3.49.0"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,24]],"date-time":"2019-06-24T00:00:00Z","timestamp":1561334400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Paradoxes of dry friction were discovered by Painlev\u00e9 in 1895 and caused a controversy on whether the Coulomb\u2013Amontons 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 Painlev\u00e9 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).<\/jats:p>","DOI":"10.3390\/e21060620","type":"journal-article","created":{"date-parts":[[2019,6,24]],"date-time":"2019-06-24T18:14:08Z","timestamp":1561400048000},"page":"620","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Ternary Logic of Motion to Resolve Kinematic Frictional Paradoxes"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0980-3670","authenticated-orcid":false,"given":"Michael","family":"Nosonovsky","sequence":"first","affiliation":[{"name":"Mechanical Engineering, University of Wisconsin\u2014Milwaukee, 3200 North Cramer St., Milwaukee, WI 53211, USA"}]},{"given":"Alexander D.","family":"Breki","sequence":"additional","affiliation":[{"name":"Department of Machine Design, St. Petersburg Polytechnic University, 29 Polytechnicheskaya St., 195251 St. Petersburg, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,24]]},"reference":[{"key":"ref_1","unstructured":"Persson, B.N.J. 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