Geodesic
The dynamics of rigid body whose sharp edge is in contact with a inclined surface with dry friction
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 3, pp. 567-593.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider the dynamics of rigid body whose sharp edge is in contact with a rough plane. The body can move so that its contact point does not move or slips or loses touch with the support. In this paper, the dynamics of the system is considered within three mechanical models that describe different modes of motion. The boundaries of definition range of each model are given, the possibility of transitions from one mode to another and their consistency with different coefficients of friction on the horizontal and inclined surfaces is discussed.
Keywords: rod, Painlevé paradox, dry friction, separation, frictional impact. 
@article{ND_2013_9_3_a10,
     author = {Ivan S. Mamaev and Tatyana B. Ivanova},
     title = {The dynamics of rigid body whose sharp edge is in contact with a inclined surface with dry friction},
     journal = {Russian journal of nonlinear dynamics},
     pages = {567--593},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2013_9_3_a10/}
}
TY  - JOUR
AU  - Ivan S. Mamaev
AU  - Tatyana B. Ivanova
TI  - The dynamics of rigid body whose sharp edge is in contact with a inclined surface with dry friction
JO  - Russian journal of nonlinear dynamics
PY  - 2013
SP  - 567
EP  - 593
VL  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2013_9_3_a10/
LA  - ru
ID  - ND_2013_9_3_a10
ER  - 
%0 Journal Article
%A Ivan S. Mamaev
%A Tatyana B. Ivanova
%T The dynamics of rigid body whose sharp edge is in contact with a inclined surface with dry friction
%J Russian journal of nonlinear dynamics
%D 2013
%P 567-593
%V 9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2013_9_3_a10/
%G ru
%F ND_2013_9_3_a10
Ivan S. Mamaev; Tatyana B. Ivanova. The dynamics of rigid body whose sharp edge is in contact with a inclined surface with dry friction. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 3, pp. 567-593. http://geodesic.mathdoc.fr/item/ND_2013_9_3_a10/

[1] Genot F., Brogliato B., “New results on Painlevé paradoxes”, Eur. J. Mech. A Solids, 18:4 (1999), 653–677 | DOI | MR | Zbl

[2] Kessler P., O'Reilly O. M., “The ringing of Euler's disk”, Regul. Chaotic Dyn., 7:1 (2002), 49–60 ; Кесcлер П., О'Рейли О. М., “Звон диска Эйлера”, Нелинейная динамика, 1:2 (2005), 247–260 | DOI | MR | Zbl

[3] Song P., Kraus P., Kumar V., “Analysis of rigid body dynamic models for simulation of systems with frictional contacts”, J. Appl. Mech., 68:1 (2000), 118–128 | DOI

[4] Stewart D. E., Dynamics with inequalities: Impacts and hard constraints, SIAM, Philadelphia, PA, 2011, 387 pp. ; Cтюарт Д. Е., Динамика систем с неравенствами. Удары и жесткие связи, НИЦ «Регулярная и хаотическая динамика», М.–Ижевск, 2012, 551 с. | MR

[5] Thiry R., “Étude d'un problème particulier ou intervient le frottement de glissement”, Nouv. Ann. de Math. Sér. 5, 1 (1922), 208–216

[6] Zhao Zh., Liu C., Ma W., Chen B., “Experimental investigation of the Painlevé paradox in a robotic system”, J. Appl. Mech., 75 (2008), 041006, 11 pp. | DOI

[7] Or Y., Rimon E., “Investigation of Painlevé's paradox and dynamic jamming during mechanism sliding motion”, Nonlinear Dynam., 67 (2012), 1647–1668 | DOI | MR | Zbl

[8] Bolotov A. E., “O dvizhenii materialnoi ploskoi figury, stesnennom svyazyami s treniem”, Matem. sb., 25:4 (1906), 562–708

[9] de Sparr M., “O trenii skolzheniya”: Penleve P., Lektsii o trenii, Gostekhizdat, M., 1954, 232–235

[10] Ivanov A. P., “Bifurkatsii v sistemakh s treniem: Osnovnye modeli i metody”, Nelineinaya dinamika, 5:4 (2009), 479–498

[11] Ivanov A. P., “Ob usloviyakh otryva v zadache o dvizhenii tverdogo tela po sherokhovatoi ploskosti”, Nelineinaya dinamika, 4:3 (2008), 287–302

[12] Ivanov A. P., Osnovy teorii sistem s treniem, NITs «Regulyarnaya i khaoticheskaya dinamika», Izhevskii institut kompyuternykh issledovanii, M.–Izhevsk, 2011, 304 pp.

[13] Ivanov A. P., “Usloviya odnoznachnoi razreshimosti uravnenii dinamiki sistem s treniem”, PMM, 72:4 (2008), 531–546 | MR | Zbl

[14] Ivanov A. P., Shuvalov N. D., Ivanova T. B., “Ob usloviyakh otryva volchka na absolyutno sherokhovatoi opore”, Vestn. UdGU. Matem. Mekhan. Kompyut. nauki, 3 (2012), 103–113

[15] Kuleshov A. S., Treschev D. V., Ivanova T. B., Naimushina O. S., “Tverdyi tsilindr na vyazkouprugoi ploskosti”, Nelineinaya dinamika, 7:3 (2011), 601–625

[16] Lekornyu L., “O trenii skolzheniya”: Penleve P., Lektsii o trenii, Gostekhizdat, M., 1954, 221–224 | MR

[17] Le Suan An, “Paradoksy Penleve i zakon dvizheniya mekhanicheskikh sistem s kulonovym treniem”, PMM, 54:4 (1990), 520–529 | MR | Zbl

[18] Neimark Yu. I., “Esche raz o parodoksakh Penleve”, MTT, 1995, no. 1, 17–21

[19] Neimark Yu. I., Fufaev N. A., “Paradoksy Penleve i dinamika tormoznoi kolodki”, PMM, 59:3 (1995), 366–375 | MR

[20] Penleve P., Lektsii o trenii, Gostekhizdat, M., 1954, 105 pp.

[21] Pfeifer F., “K voprosu o tak nazyvaemykh kulonovykh zakonakh treniya”: Penleve P., Lektsii o trenii, Gostekhizdat, M., 1954, 264–316

[22] Rozenblat G. M., “O dvizhenii ploskogo tverdogo tela po sherokhovatoi pryamoi”, Nelineinaya dinamika, 2:3 (2006), 293–306

[23] Samsonov V. A., “Dinamika tormoznoi kolodki i «udar treniem»”, PMM, 69:6 (2005), 912–921 | MR | Zbl

[24] Samsonov V. A., Ocherki o mekhanike: Nekotorye zadachi, yavleniya i paradoksy, Nauka, M., 1980, 64 pp.

[25] Fufaev N. A., “Dinamika sistemy v primere Penleve–Kleina. O paradokse Penleve”, MTT, 1991, no. 4, 48–53