Geodesic
Dynamics of Chaplygin skate on a horizontal plane with dry anisotropic friction
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2020), pp. 61-63 
A. V. Karapetyan; A. A. Shishkov. Dynamics of Chaplygin skate on a horizontal plane with dry anisotropic friction. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2020), pp. 61-63. http://geodesic.mathdoc.fr/item/VMUMM_2020_2_a12/
@article{VMUMM_2020_2_a12,
     author = {A. V. Karapetyan and A. A. Shishkov},
     title = {Dynamics of {Chaplygin} skate on a horizontal plane with dry anisotropic friction},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {61--63},
     year = {2020},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_2_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of Chaplygin's skate motion on the horizontal plane with dry friction is considered. It is supposed that the friction force depends on an angle between the sliding velocity and the skate plane. It is shown that the time of the skate sliding is defined by a transcendental equation and depends on the initial values of the angular velocity, the sliding velocity and the angle between the sliding velocity and the skate plane. The countable set of initial values of the sliding velocity such that the sliding time does not depend on this angle is found.

[1] Chaplygin S. A., “K teorii dvizheniya negolonomnykh sistem. Teorema o proizvodyaschem mnozhitele”, Matem. sb., 28:2 (1911), 303–314 | Zbl

[2] Caratheodory C., “Der Schlitten”, Z. angew. Math. und Mech., 13 (1933), 71–76 | DOI

[3] Neimark Yu. I., Fufaev N. A., Dinamika negolonomnykh sistem, Nauka, M., 1967

[4] Leine R. I., Gloker Ch., “A set-valued force for spatial Coulomb–Contensou friction”, Eur. J. Mech., 22:2 (2003), 193–216 | DOI | MR | Zbl

[5] Le Saux C., Leine R. I., Gloker Ch., “Dynamics of a rolling disk in the presence of dry friction”, J. Nonlinear Sci., 15:1 (2005), 28–61 | MR

[6] Ivanov A. P., Osnovy teorii sistem s treniem, RKhD, M.–Izhevsk, 2011

[7] Sumbatov A. S., Yunin E. K., Izbrannye zadachi mekhaniki sistem s treniem, Fizmatlit, M., 2013

[8] Zobova A. A., “Obzor modelei raspredelennogo sukhogo treniya”, Prikl. matem. i mekhan., 80:2 (2016), 194–206 | MR | Zbl

[9] Karapetyan A. V., Shamin A. Yu., “O dvizhenii sanei Chaplygina po gorizontalnoi ploskosti s sukhim treniem”, Prikl. matem. i mekhan., 83:2 (2019), 251–256