Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelin. Dinam., 2010, Volume 6, Number 4, Pages 855–868 (Mi nd9)  

This article is cited in 9 scientific papers (total in 10 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.

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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
\by V.~V.~Kozlov
\paper Lagrangian mechanics and dry friction
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 4
\pages 855--868

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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
    6. Putkaradze V. Rogers S., “On the Dynamics of a Rolling Ball Actuated By Internal Point Masses”, Meccanica, 53:15 (2018), 3839–3868  crossref  mathscinet  isi  scopus
    7. Mikheyev V.V., Saveliev S.V., Xi International Scientific and Technical Conference - Applied Mechanics and Dynamics Systems, Journal of Physics Conference Series, 944, IOP Publishing Ltd, 2018  crossref  isi  scopus
    8. Vaganian A., “on Generalized Coulomb-Amontons' Law in the Context of Rigid Body Dynamics”, Nonlinear Dyn., 101:4 (2020), 2145–2155  crossref  isi  scopus
    9. Kireenkov A.A., Zhavoronok I S., “Anisotropic Combined Dry Friction in Problems of Pneumatics' Dynamics”, J. Vib. Eng. Technol., 8:2, SI (2020), 365–372  crossref  isi  scopus
    10. A. A. Kireenkov, S. I. Zhavoronok, D. V. Nyshtaev, “On tire models accounting for both deformed state and coupled dry friction in a contact spot”, Kompyuternye issledovaniya i modelirovanie, 13:1 (2021), 163–173  mathnet  crossref
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