500 Years of History of the Dry Friction Law

The role that such scholars as Amontons, Coulomb, Leonardo da Vinci, Morin, and Euler played in creation of the dry friction law is discussed. In particular, a reference is given to the Euler’s article published in 1748, in which the dry friction law is set forth in the comprehensive statement 37 years before the main publications of Coulomb. The Painleve criticism of the Coulomb’s law is estimated. The Painleve paradox is illustrated by example of the brake shoe scheme. Basic details of theory of polycomponent dry friction are stated.

References

[1] Leonardo da Vinchi. O sebe i o svoey nauke. Izbr. proizv. T. 1 [About himself and his science. Vol. 1]. Moskva-Leningrad, Academia Publ., 1935. 444 p.

[2] Amontons M. De la reistance causee dans les machines. Mem. l’Acad. Roy., 1699, pp. 206-222.

[3] Euler L. Sur la diminution de la r?sistence du frottement. Histoire de L’Academie Royale des Sciences et Belles Lettres a Berlin, 1748, pp. 133-148.

[4] Coulomb C.A. Theorie des machines simples. Mem. Math. et Phys. l’Acad. Sci., 1785, vol. 10, pp. 161-331.

[5] Morin A. Mem. presentees par divers savants a l’Academie des sciences. 1833, t. 4, pp. 1-128, pp. 591-696; 1835, pp. 641-783.

[6] Bellet D. Cours de Mecanique Generale. Toulouse, Cepadues-editions, Collection "La cheveche", 1988. 379 p.

[7] Painleve P. Lecons sur le Frottement. Paris, Hermann, 1895. 120 p. (Russ. ed.: Penleve P. Lektsii o trenii. Moscow, Gostekhizdat Publ., 1954. 316 p.).

[8] Hadamard J. Sur les integrals d’un system d’equations differentielles ordinaires, considers comme fonctions des donnees initiales. Bull. Soc. Math. France, 1900, vol. 28, pp. 64-66.

[9] Zhukovskiy N.E. Uslovie ravnovesiya tverdogo tela, opirayushchegosya na nepodvizhnuyu ploskost’ nekotoroy ploshchadkoy i mogushchego peremeshchat’sya vdol’ etoy ploskosti s treniem. Poln. sobr. soch. T. 1. Obshchaya mekhanika. [Condition for equilibrium of solid body resting on a motionless plane of small area and able to move along this plane with the friction. Collected Papers. Vol. 1. Theoretical mechanics]. Moskva-Leningrad, Gostekhizdat Publ., 1948, pp. 339-354 (640 p.).

[10] Zhukovskiy N.E. Trenie bandazhey zheleznodorozhnykh koles o rel’sy Poln. sobr. soch. T. 8. Teoriya uprugosti. Zheleznye dorogi. Avtomobili. [Friction of binding band of railway wheels on rails. Vol. 8. Theory of elasticity. Railways. Automobiles. Collected Papers]. Moskva-Leningrad, Gostekhizdat Publ., 1948, pp. 426-478.

[11] Coriolis G. Theorie mathematique des effets du jeu de billard. Journal de l’Ecole polytechnique, 1835, 154 p. (Russ. ed.: Koriolis G. Matematicheskaya teoriya yavleniy billiardnoy igry. Moscow, Gostekhizdat Publ., 1954. 316 p.).

[12] Markeev A.P. Dinamika tela, soprikasayushchegosya s tverdoy poverkhnost’yu [The dynamics of the body osculating with a solid surface]. Moscow, Nauka-Fizmatlit Publ., 1992. 336 p.

[13] Routh E.J. An elementary treatise on dynamics of a system of rigid bodies with numerous examples. London, MacMillan and Co, 1877. 601 p. (Russ. ed.: Raus E. Dinamika sistemy tverdykh tel. T. 2. Moscow, Nauka Publ., 1983. 544 p.).

[14] Euler J.A. Recherches plus exactes sur l’effet des moulin a vent. Mem. Acad. Roy. Sci. Berlin, 1758, Bd 12, pp. 165-234.

[15] Kontensu P. Communication between the rubbing and pivoting friction and its accounting in theory of spinning top. Sb. "Problemy giroskopii" [Collect. Pap. "Problems of gyroscopy"], Moscow, Mir Publ., 1967, pp. 60-77 (in Russ.).

[16] Zhuravlev V.F. Frictional moment of a rotating trunnion at movement on the movable base. Voprosy oboronnoy tekhniki [Issues of defense engineering technique], 1969, ser. 9, iss. 2 (in Russ.).

[17] Zhuravlev V.F., Klimov D.M. On the mechanism of the shimmy phenomenon. Dokl. RAN [Proc. Russ. Acad. Sci.], 2009, vol. 428, no. 6, pp. 761-764 (in Russ.).

[18] Andronov V.V., Zhuravlev V.F. Sukhoe trenie v zadachakh mekhaniki [Coulomb friction in mechanics problem]. Moscow-Izhevsk, R&C Dynamics Publ., 2010.183 p.

[19] Kragel’skiy I.V., Shchedrov V.S. Razvitie nauki o trenii. Sukhoe trenie. [Enhancement of tribology. Coulomb friction]. Moscow, AN SSSR Publ., 2010, 183 p.