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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, Issue 4, Pages 49–60 (Mi vuu188)  

MECHANICS

The motion of a flat rigid disks bouncing off of a smooth horizontal plane in the gravity field

V. V. Vaskina, O. S. Naymushina

a Udmurt State University, Izhevsk, Russia

Abstract: 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, progections, linear stability, domains of linear stability.

Full text: PDF file (523 kB)
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Document Type: Article
UDC: 531.384+531.662
MSC: 70E18, 70E50, 70H05
Received: 01.12.2010

Citation: V. V. Vaskin, O. S. Naymushina, “The motion of a flat rigid disks bouncing off of a smooth horizontal plane in the gravity field”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 4, 49–60

Citation in format AMSBIB
\Bibitem{VasNai10}
\by V.~V.~Vaskin, O.~S.~Naymushina
\paper The motion of a~flat rigid disks bouncing off of a~smooth horizontal plane in the gravity field
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2010
\issue 4
\pages 49--60
\mathnet{http://mi.mathnet.ru/vuu188}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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