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Nelin. Dinam., 2008, Volume 4, Number 1, Pages 87–98 (Mi nd222)  

This article is cited in 1 scientific paper (total in 1 paper)

A method for determination of the parameters of motion of a top that moves without bouncing on a smooth plane

G. M. Rozenblat

Moscow Automobile and Road Institute

Abstract: The problem of motion of an axisymmetric rigid body on a horizontal plane in the presence of gravity is considered. The body touches the plane at one point, and the plane is assumed to be perfectly smooth. In the already-known and integrable case of symmetric body the normal reaction force exerted by the plane onto the body is calculated and its sign is examined. The condition that the body remains in contact with the plane is that the reaction is positive because the constraint at the point of contact is assumed to be unilateral. In some cases a comparatively trivial analytical representation (a polynomial of degree two) for the reaction force is obtained which allows determination of the initial conditions and the body's parameters for the body to remain in contact with the plane.

Keywords: rigid body(tip-top), unilateral constraint, bouncing.

Full text: PDF file (224 kB)
UDC: 531.36
MSC: 37N15
Received: 29.11.2007

Citation: G. M. Rozenblat, “A method for determination of the parameters of motion of a top that moves without bouncing on a smooth plane”, Nelin. Dinam., 4:1 (2008), 87–98

Citation in format AMSBIB
\Bibitem{Roz08}
\by G.~M.~Rozenblat
\paper A method for determination of the parameters of motion of a top that moves without bouncing on a smooth plane
\jour Nelin. Dinam.
\yr 2008
\vol 4
\issue 1
\pages 87--98
\mathnet{http://mi.mathnet.ru/nd222}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Rozenblat G.M., “Motions of a TOP on a Smooth Plane Without Separation”, Mech. Sol., 48:2 (2013), 128–133  crossref  isi  elib  scopus
  • Нелинейная динамика
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