Geodesic
Using the Dirac approach to model the motion of a railway vehicle when its wheel flange climbs the rail
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2013), pp. 67-71 
A. V. Vlakhova. Using the Dirac approach to model the motion of a railway vehicle when its wheel flange climbs the rail. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2013), pp. 67-71. http://geodesic.mathdoc.fr/item/VMUMM_2013_2_a15/
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     author = {A. V. Vlakhova},
     title = {Using the {Dirac} approach to model the motion of a railway vehicle when its wheel flange climbs the rail},
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     pages = {67--71},
     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_2_a15/}
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An approach to formulate a mathematical model is proposed to describe the railway vehicle motion when its wheel flange is rolling on the railhead. This model makes it possible to construct an analytical estimate of the vehicle derailment with respect to the vehicle construction and the motion conditions. This model is based on the primary Dirac constraints and its solution is not similar to the solution of the classical no-slip nonholonomic model. The primary Dirac constraints are caused by the degeneration of the system's Lagrange function when the contact creep force stiffness tends to infinity and the ratio of the wheelpair mass to the vehicle mass tends to zero.

[1] Ermakov V.M., Pevzner V.O., “O skhodakh porozhnikh vagonov”, Zheleznodorozhnyi transport, 2002, no. 3, 29–33

[2] Novozhilov I.V., Filippov V.N., “K otsenke uslovii vkatyvaniya grebnya zheleznodorozhnoi kolesnoi pary na golovku relsa”, Izv. RAN. Mekhan. tverdogo tela, 2002, no. 4, 21–29 | MR

[3] Kharris U.Dzh., Zakharov S.M., Landgren Dzh., Turne Kh., Ebersen V., Obobschenie peredovogo opyta tyazhelovesnogo dvizheniya: voprosy vzaimodeistviya kolesa i relsa, Per. s angl., Intekst, M., 2002

[4] Novozhilov I.V., “Razdelenie dvizhenii relsovogo ekipazha”, Izv. AN SSSR. Mekhan. tverdogo tela, 1980, no. 1, 55–59

[5] Novozhilov I.V., Fraktsionnyi analiz, Izd-vo MGU, M., 1995 | MR

[6] Dzhonson K., Mekhanika kontaktnogo vzaimodeistviya, Mir, M., 1989

[7] Arnold V.I., Kozlov V.V., Neishtadt A.I., Matematicheskie aspekty klassicheskoi i nebesnoi mekhaniki, URSS, M., 2009

[8] Vasileva A.B., “Asimptoticheskie metody v teorii obyknovennykh differentsialnykh uravnenii s malymi parametrami pri starshikh proizvodnykh”, Zhurn. vychisl. matem. i matem. fiz., 3:4 (1963), 611–642

[9] Pogorelov D.Yu., Simonov V.A., “Pokazatel dlya otsenki opasnosti skhoda podvizhnogo sostava putem vkatyvaniya kolesa na golovku relsa”, Visnik SNU im. V. Dalya, 5(147):1 (2010), 64–70