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This article is cited in 1 scientific paper (total in 1 paper)
On a Periodic Motion of a Rigid Body Carrying a Material Point in the Presence of Impacts with a Horizontal Plane
Anatoly P. Markeev A. Yu. Ishlinsky Institute for Problems in Mechanics RAS, Vernadskogo 101, block 1, Moscow, 119526 Russia
Abstract:
A material system consisting of an outer rigid body (a shell) and an inner body (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 linear stability is studied.
Keywords:
rigid body dynamics, collision, periodic motion, stability.
Received: 26.12.2011 Accepted: 01.02.2012
Citation:
Anatoly P. Markeev, “On a Periodic Motion of a Rigid Body Carrying a Material Point in the Presence of Impacts with a Horizontal Plane”, Regul. Chaotic Dyn., 17:2 (2012), 142–149
Linking options:
https://www.mathnet.ru/eng/rcd396 https://www.mathnet.ru/eng/rcd/v17/i2/p142
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Abstract page: | 84 |
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