Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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 Nelin. Dinam., 2012, Volume 8, Number 1, Pages 71–81 (Mi nd304)

On a periodic motion of a rigid body carrying a material point in the presence of impacts with a horizontal plane

A. P. Markeev

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526, Russia

Abstract: A material system consisting of a “carrying” rigid body (a shell) and a body“being carried” (a material point) is considered. The system moves in a uniform field of gravity over a fixed absolutely smooth horizontal plane. The central ellipsoid of inertia of the shell is an ellipsoid of rotation. The material point moves according to the harmonic law along a straight-line segment rigidly attached to the shell and lying on its axis of dynamical symmetry. During its motion, the shell may collide with the plane. The coefficient of restitution for an impact is supposed to be arbitrary. The periodic motion of the shell is found when its symmetry axis is situated along a fixed vertical, and the shell rotates around this vertical with an arbitrary constant angular velocity. The conditions for existence of this periodic motion are obtained, and its stability in the linear approximation is studied.

Keywords: rigid body dynamics, collision, periodic motion, stability

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UDC: 531.36,531.38,531.66
MSC: 70E55, 70F35, 70K42, 70E50
Accepted:26.12.2011

Citation: A. P. Markeev, “On a periodic motion of a rigid body carrying a material point in the presence of impacts with a horizontal plane”, Nelin. Dinam., 8:1 (2012), 71–81

Citation in format AMSBIB
\Bibitem{Mar12} \by A.~P.~Markeev \paper On a periodic motion of a rigid body carrying a material point in the presence of impacts with a horizontal plane \jour Nelin. Dinam. \yr 2012 \vol 8 \issue 1 \pages 71--81 \mathnet{http://mi.mathnet.ru/nd304} 

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This publication is cited in the following articles:
1. A. P. Markeev, “K dinamike tverdogo tela, nesuschego materialnuyu tochku”, Nelineinaya dinam., 8:2 (2012), 219–229
2. Markeyev A.P., “Approximate Equations of Rotational Motion of a Rigid Body Carrying a Movable Point MASS”, Pmm-J. Appl. Math. Mech., 77:2 (2013), 137–144
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