Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2015-2pp.132-141

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A.V. Sakharov, "Rotation of a body with two movable internal masses on a rough plane," J. Appl. Math. Mech. 79 (2), 132-141 (2015)
Year 2015 Volume 79 Issue 2 Pages 132-141
DOI 10.1016/j.jappmathmech.2015.07.003
Title Rotation of a body with two movable internal masses on a rough plane
Author(s) A.V. Sakharov (Dolgoprudnyi, Russia, sah.aleksandr@gmail.com)
Abstract The two-dimensional motion of a system consisting of a hollow rigid body, resting on a rough plane, and two internal mobile point masses, capable of moving parallel to the longitudinal axis of symmetry of the body is considered. Friction in the contact area is modelled by a local Amonton-Coulomb law. A dynamically matched linear model is used to describe the normal stress distribution. The possibility of achieving rotation of the system by a certain relative motion of internal masses is investigated. Two control laws for the movable masses are considered: piecewise-linear and harmonic, for which the equations of motion are integrated numerically for different values of the parameters of the control laws. The features of the motion of the system for the chosen laws are analysed. It is established that, for a two-phase piecewise-linear control law, rotation of the system reaches a steady state. The parameters of the piecewise-linear control law, which deliver a maximum of the mean angular velocity of the body in the steady mode of motion are obtained.
Received 10 May 2014
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