The research works of Coulomb and Amontons and generalized laws of friction


The paper is devoted to the contributions of Coulomb and Amontons to the physics of friction from the viewpoint of current discussions and attempts to formulate generalized laws of friction.


  1. [1]

    Dowson D. In History of Tribology. London: Longman Group Limited, 1979: 678.

  2. [2]

    Amontons G. De la resistance cause’e dans les machines (About resistance and force in machines). Mem l’Acedemie R A: 257–282 (1699)

  3. [3]

    Barber J R. Multiscale surfaces and Amontons’ law of friction. Trib Lett 49: 539–543 (2013)

  4. [4]

    He G, Müser M H, Robbins M O. Adsorbed layers and the origin of static friction. Science 284: 1650–1652 (1999)

  5. [5]

    Stewart Gillmor C. In Coulomb and the Evolution of Physics and Engineering in Eighteenth-Century France. Princeton: Princeton University Press, 1971: 328.

  6. [6]

    Coulomb C A. Sur une application des regles de maximis & minimis a quelques problemes de statique, relatifs a I’ architecture. Memoires de Mathematique & de Physique, presentes a I’ Academie. Royale des Sciences par divers Savans, & Ius dans ses Assemblees 7: 343–382 (1773)

  7. [7]

    Heyman J. In Coulomb’s Memoir on Statics. An Essay in the History of Civil Engineering. London: Imperial College Press, 1997: 212.

  8. [8]

    Popov V L. Contact Mechanics and Friction. Physical Principles and Applications. Berlin: Springer, 2010.

  9. [9]

    Coulomb C A. Theorie des machines simple (Theory of simple machines). Bachelier, Paris, 1821.

  10. [10]

    Coulomb C A. Memoire sur les frottemens de la pointe des pivots. Paris, 1797: 448–471.

  11. [11]

    Coulomb C A. Experiences destinees a determiner la coherence des fluides et les lois de leur resistance dans les movements tre lents. Paris, 1801: 246–305

  12. [12]

    Popov V L, Dimaki A, Psakhie S, Popov M. On the role of scales in contact mechanics and friction between elastomers and randomly rough self-affine surfaces. Sci Rep in press (2015)

  13. [13]

    Greenwood J A, Tabor D. The friction of hard sliders on lubricated rubber-The importance of deformation losses. Proc Roy Soc London 71: 989–1001 (1958)

  14. [14]

    Grosch K A. Relation between friction and visco-elastic properties of rubber. Proc Roy Soc London A 274: 21–39 (1963)

  15. [15]

    Li Q, Popov M, Dimaki A, Filippov A E, Kürschner S, Popov V L. Friction between a viscoelastic body and a rigid surface with random self-affine roughness. Phys Rev Lett 111: 034301 (2013)

  16. [16]

    Popov V L, Voll L, Li Q, Chai Y S, Popov M. Generalized law of friction between elastomers and differently shaped rough bodies. Sci Rep 4: 3750 (2014)

  17. [17]

    Rhee S K. Wear equation for polymer sliding against metal surfaces. Wear 16: 431–445 (1970)

  18. [18]

    Dieterich J H. Time dependent friction and the mechanics of stick-slip. Pure Appl Geophys 116: 790–806 (1978)

  19. [19]

    Dieterich J H. Modeling of rock friction: 1. Experimental results and constitutive equations. J Geophys Res Solid Earth 84: 2161–2168 (1979)

  20. [20]

    Rice J R, Ruina A L. Stability of steady frictional slipping. J Appl Mech 50: 343–349 (1983)

  21. [21]

    Müser M H, Urbakh M, Robbins M O. Statistical mechanics of static and low-velocity kinetic friction. In Advance in Chemical Physics, Ed. by Prigogine I, Rice S A. John Wiley & Sons, Inc., 2003.

  22. [22]

    Grzemba B. New experimental investigations on the Dieterich-Ruina law. Facta Universitatis, Ser Mech Eng 13(1) (2015)

  23. [23]

    Otsuki M, Matsukawa H. Systematic breakdown of Amontons’ law of friction for an elastic object locally obeying Amontons’ law. Sci Rep 3: 1586 (2013)

  24. [24]

    Rubinstein S M, Cohen G, Fineberg J. Detachment fronts and the onset of dynamic friction. Nature 430: 1005–1009 (2004)

Download references

Author information

Correspondence to Elena Popova.

Additional information

This article is published with open access at

Elena POPOVA. She studied Slavistics at the Tomsk State University, Russia (graduated in 1987 with degree Dipl.-Phil.) and German literature studies and philosophy at the University of Paderborn, Germany (graduated in 2003 with degree Magistra Artium). She worked at the Tomsk Pedagogical University, Russian Academy of Sciences and later at the University of Potsdam. Since 2007 she coordinated double degree programs in Engineering Science with Russia and China at the Berlin University of Technology and carried out research in the field of history of tribology.

Valentin L. POPOV. He is a full professor at the Berlin University of Technology. He studied physics (1976–1982) and obtained his PhD degree in 1985 from the Moscow State Lomonosov University. He worked at the Institute of Strength Physics of the Russian Academy of Sciences. After a guest-professorship in the field of theoretical physics at the University of Paderborn (Germany) from 1999 to 2002, he has headed the Department of System Dynamics and the Physics of Friction in the Institute of Mechanics at the Berlin University of Technology. His areas of interest include tribology, nanotribology, tribology at low temperatures, biotribology, the influence of friction through ultrasound, numerical simulation of frictional processes, research regarding earthquakes, as well as themes relating to materials sciences such as the mechanics of elastoplastic media with microstructures, strength of metals and alloys, and shape memory alloys. He has published 30 papers in leading international journals during the past 5 years. He is the author of the book “Contact Mechanics and Friction: Physical principles and applications” which appeared in German, English, Chinese, and Russian editions. He is the joint editor of international journals and regularly organizes international conferences and workshops over diverse tribological themes. He is a member of the Scientific Council of the German Tribological Society. He has intensively collaborated with many industrial corporations and possesses experience in implementing the results of scientific research in industrial applications.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Popova, E., Popov, V.L. The research works of Coulomb and Amontons and generalized laws of friction. Friction 3, 183–190 (2015) doi:10.1007/s40544-015-0074-6

Download citation


  • static friction
  • sliding friction
  • kinetics of friction
  • material dependency
  • history of science