Abstract
The paper deals with the problem of a disk sliding on a rough inclined plane under the action of an arbitrary (symmetric) law of normal stress distribution and the classical differential Euler-Coulomb dry friction law. Some qualitative results concerned with the global dynamics of motion of such a disk are obtained. In several cases where the Galin distribution of normal stresses and the corresponding Zhuravlev formulas for friction forces and moments are used, one can succeed in obtaining the first integrals for the corresponding equations of motion of an annular disk. The limit cases concerned with the well-posedness of transition from a disk to a material point, which is directly related to the problem of justification of the point contact with sliding friction or a nonholonomic constraint, are also discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Yu. Ishlinskii, B. N. Sokolov, and F. L. Chernousko, “On Motion of Plane Bodies with Dry Friction,” Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 4, 17–28 (1981) [Mech. Solids (Engl. Transl.)].
S. Goyal, A. Ruina, and J. Papadopoulos, “Planar Sliding with Dry Friction. Pt. 2: Dynamics of Motion,” Wear 143, 331–352 (1991).
Z. Farkas, G. Bartels, T. Unger, and D. Wolf, “Frictional Coupling between Sliding and Spinning Motion,” Phys. Rev. Lett. 90(24), 248302 (2003).
G. M. Rozenblat, Dynamical Systems with Dry Friction (NITs “Regular and Chaotic Dynamics,” Moscow-Izhevsk, 2006) [in Russian].
N. N. Dmitriev, “Motion of Disk and Ring on a Plane with Anisotropic Friction,” Trenie i Iznos 23(1), 10–15 (2002) [J. Frict. Wear (Engl. Transl.)].
V. Ph. Zhuravlev, “Friction Laws in the Case of Combination of Slip and Spin,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 81–88 (2003) [Mech. Solids (Engl. Transl.) 38 (4), 52–58 (2003)].
V. Ph. Zhuravlev, “The Model of Dry Friction in the Problem of the Rolling of Rigid Bodies,” Prikl. Mat. Mekh. 62(5), 762–767 (1998) [J. Appl. Math. Mech. (Engl. Transl.) 62 (5), 705–710 (1998)].
G. M. Rozenblat, “Integration of the Equations of Motion of a Disk on a Rough Plane,” Izv. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 65–71 (2007) [Mech. Solids (Engl. Transl.) 42 (4), 552–557 (2007)].
L. A. Galin, Contact Problems of Elasticity and Viscoelasticity (Nauka, Moscow, 1980) [in Russian].
V. V. Andronov and V. Ph. Zhuravlev, Dry Friction in Problems of Mechanics (NITs “Regular and Chaotic Dynamics,” Moscow-Izhevsk, 2010) [in Russian].
A. P. Ivanov, “A Dynamically Consistent Model of the Contact Stresses in the Plane Motion of a Rigid Body,” Prikl. Mat. Mekh. 73(2), 189–203 (2009) [J. Appl. Math. Mech. (Engl. Transl.) 73 (2), 134–144 (2009)].
T. V. Sal’nikova, D. V. Treshchev, and S. R. Gallyamov, Motion of a Free Hollow Disk on a Rough Horizontal Plane,” Nelin. Din. 8(1), 83–101 (2012).
O. B. Fedichev and P. O. Fedichev, “Deceleration and Stop of Plane Bodies Sliding on a Rough Horizontal Plane,” Nelin. Din. 7(3), 549–558 (2011).
A. V. Karapetyan and A. M. Rusinova, “A Qualitative Analysis of the Dynamics of a Disc on an Inclined Plane with Friction,” Prikl. Mat. Mekh. 75(5), 731–737 (2011) [J. Appl. Math. Mech. (Engl. Transl.) 75 (5), 511–516 (2011)].
V. Ph. Zhuravlev and G. M. Rozenblat, Theoretical Mechanics in Solutions of Problems from I. V. Meshcherskii’s Collection (LIBROKOM, Moscow, 2013) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © G. M. Rozenblat, 2013, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2013, No. 5, pp. 109–117.
About this article
Cite this article
Rozenblat, G.M. On a disk sliding on a rough inclined plane under an arbitrary law of normal stresses. Mech. Solids 48, 573–580 (2013). https://doi.org/10.3103/S0025654413050130
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654413050130