Geodesic
The motion of a flat rigid disks bouncing off of a smooth horizontal plane in the gravity field
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2010), pp. 49-60 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the motion of a flat rigig disks bouncing off a horizontal plane in the gravity field. The plane is assumed to be absolutely smooth and the impact absolutely elastic. The disks move in vertical plane and rotate around horizontal axis, while the disks are able to break off from the plane with following impacts and bounces. For different values of the energy, 2D projections of the disk's trajectories onto the phase plane are given. The stationary points are determined and their linear stability is studied in detail. It is shown, there are alternating domains of linear stability and instability in the first approximation in the plane parameters. The stability conditions are expressed analytically in terms of the parameters of the problem.
Keywords: flat rigid disc, elastic impact, linear stability, domains of linear stability.
Mots-clés : progections 
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     title = {The motion of a~flat rigid disks bouncing off of a~smooth horizontal plane in the gravity field},
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V. V. Vaskin; O. S. Naymushina. The motion of a flat rigid disks bouncing off of a smooth horizontal plane in the gravity field. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2010), pp. 49-60. http://geodesic.mathdoc.fr/item/VUU_2010_4_a5/

[1] Ivanov A. P., Dinamika sistem s mekhanicheskimi soudareniyami, Mezhdunarodnaya programma obrazovaniya, M., 1997, 336 pp. | MR

[2] Markeev A. P., “Dinamika tverdogo tela pri nalichii ego soudarenii s tverdoi poverkhnostyu”, Nelineinaya dinamika, 4:1 (2008), 1–38 | MR

[3] Ivanov A. P., “O bezudarnykh pryzhkakh neodnorodnogo kolesa. Sluchai gladkoi opory”, Mekhanika tverdogo tela, 1992, no. 1, 25–31

[4] Markeev A. P., “Issledovanie ustoichivosti periodicheskogo dvizheniya tverdogo tela pri nalichii soudarenii s gorizontalnoi ploskostyu”, Prikladnaya matematika i mekhanika, 58:3 (1992), 71–81 | MR

[5] Alekhin A. K., Markeev A. P., “Ob ustoichivochti periodicheskogo dvizheniya diska nad gorizontalnoi ploskostyu”, Mekhanika tverdogo tela, 2000, no. 4, 16–22