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V. Ph. Zhuravlev and A. A. Kireenkov, "Padé expansions in the two-dimensional model of Coulomb friction," Mech. Solids. 40 (2), 1-10 (2005)
Year 2005 Volume 40 Number 2 Pages 1-10
Title Padé expansions in the two-dimensional model of Coulomb friction
Author(s) V. Ph. Zhuravlev (Moscow)
A. A. Kireenkov (Moscow)
Abstract In [1-3], a model of dry friction that generalizes the simplest one-dimensional Coulomb model to the case where the relative motion of the rubbing bodies is the combination of slip and drilling has been discussed. The model constructed in the cited papers involves a linear-fractional approximation to integral expressions for the force and torque that are calculated by summing up the elementary interactions represented by Coulomb's law in the differential form. In the present paper, the possibilities for refining this model by proceeding to higher-order approximations in terms of the Padé expansions are considered.
References
1.  V. Ph. Zhuravlev, "On the model of dry friction in the problem of rolling of rigid bodies," PMM [Applied Mathematics and Mechanics], Vol. 62, No. 5, pp. 762-767, 1998.
2.  V. Ph. Zhuravlev, "Friction laws in the case of combination of slip and spin," Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 81-88, 2003.
3.  A. A. Kireenkov, "On the motion of a homogeneous rotating disk along a plane in the case of combined friction," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 60-67, 2002.
4.  I. G. Goryaceva and M. N. Dobychin, Contact Problems in Tribology [in Russian], Mashinostroenie, Moscow, 1988.
5.  G. K. Pozharitskii, "Vanishing slips of mechanical systems subject to dry friction," PMM [Applied Mathematics and Mechanics], Vol. 29, No. 3, pp. 558-563, 1965.
6.  A. Yu. Ishlinskii, B. N. Soklov, and F. L. Chernous'ko, "On the motion of plane bodies subject to dry friction," Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 17-28, 1981.
7.  F. L. Chernous'ko, "Equilibrium conditions for bodies on a rough plane," Izv. AN SSSR. MTT [Mechanics of Solids], No. 6, pp. 6-17, 1988.
8.  Ya. G. Panovko and I. I. Gubanova, Stability and Vibration of Elastic Systems [in Russian], Nauka, Moscow, 1967.
9.  P.-A. Bliman and M. Sorine, "Easy-to-use realistic dry friction models for automatic control," in Proc. of the 3rd Europ. Control Conf., pp. 3788-3794, Rome, 1995.
10.  N. E. Zhukovskii, "Friction of railway wheel tires against rails," in N. E. Zhukovskii, Collected Works. Volume 7 [in Russian], pp. 426-478, Gostekhizdat, Moscow, Leningrad, 1950.
11.  N. E. Zhukovskii, "Equilibrium conditions for a body based on a fixed plane with an area and able to move along this plane with friction," in N. E. Zhukovskii, Collected Works. Volume 1 [in Russian], pp. 339-354, Gostekhizdat, Moscow, Leningrad, 1948.
12.  V. V. Andronov, "Mechanical systems with transformed dry friction," Izv. AN SSSR. MTT [Mechanics of Solids], No. 1, pp. 40-49, 1988.
13.  P. Contensou, "Couplage entre frottement de glissement et Ftottement de pivotement dans la théorie de la touplie," in Kreiselprobleme Gyrodynamics: IUTAM Symp. Celerina, 1962, pp. 201-216, Springer, Berlin, 1963.
14.  M. Paskal, "An asymptotic solution of the equations of motion of the Celtic stone," PMM [Applied Mathematics and Mechanics], Vol. 47, No. 2, pp. 321-329, 1983.
15.  A. P. Ivanov, "On the motion of planar bodies in the presence of static friction," Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 89-94, 2003.
16.  G. Baker and P. Graves-Morris, Padé approximants [Russian translations], Mir, Moscow, 1986.
Received 22 April 2004
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