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Nelin. Dinam., 2010, Volume 6, Number 4, Pages 855–868 (Mi nd9)  

This article is cited in 4 scientific papers (total in 5 papers)

Lagrangian mechanics and dry friction

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A generalization of Amantons' law of dry friction for constrained Lagrangian systems is formulated. Under a change of generalized coordinates the components of the dry-friction force transform according to the covariant rule and the force itself satisfies the Painlevé condition. In particular, the pressure of the system on a constraint is independent of the anisotropic-friction tensor. Such an approach provides an insight into the Painlevé dry-friction paradoxes. As an example, the general formulas for the sliding friction force and torque and the rotation friction torque on a body contacting with a surface are obtained.

Keywords: Lagrangian system, anisotropic friction, Painlevé condition.

Full text: PDF file (191 kB)
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Document Type: Article
UDC: 531.01
MSC: 70F40
Received: 29.10.2010

Citation: V. V. Kozlov, “Lagrangian mechanics and dry friction”, Nelin. Dinam., 6:4 (2010), 855–868

Citation in format AMSBIB
\Bibitem{Koz10}
\by V.~V.~Kozlov
\paper Lagrangian mechanics and dry friction
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 4
\pages 855--868
\mathnet{http://mi.mathnet.ru/nd9}


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    This publication is cited in the following articles:
    1. A. V. Borisov, “Otvet V. F. Zhuravlevu”, Nelineinaya dinam., 6:4 (2010), 897–901  mathnet
    2. T. V. Salnikova, D. V. Treschev, S. R. Gallyamov, “Dvizhenie svobodnoi shaiby po sherokhovatoi gorizontalnoi ploskosti”, Nelineinaya dinam., 8:1 (2012), 83–101  mathnet
    3. V. V. Chistyakov, “O chastnykh sluchayakh dinamiki vrascheniya tverdogo tela vokrug neglavnoi tsentralnoi osi inertsii pri sukhom trenii v oporakh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 153–163  mathnet
    4. Alexander A. Burov, Ekaterina S. Shalimova, “On the Motion of a Heavy Material Point on a Rotating Sphere (Dry Friction Case)”, Regul. Chaotic Dyn., 20:3 (2015), 225–233  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    5. Zhavoronok S.I., Kireenkov A.A., “On the Effect of the Anisotropic Dry Friction and the Deformed State of Tires on the Shimmy Initiation”, Coupled Problems in Science and Engineering Vii (Coupled Problems 2017), eds. Papadrakakis M., Onate E., Schrefler B., Int Center Numerical Methods Engineering, 2017, 216–226  isi
  • Нелинейная динамика
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