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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2008, Volume 4, Number 1, Pages 87–98
(Mi nd222)
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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.
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
Linking options:
https://www.mathnet.ru/eng/nd222 https://www.mathnet.ru/eng/nd/v4/i1/p87
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Abstract page: | 197 | Full-text PDF : | 75 | First page: | 1 |
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