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IssuesArchive of Issues2021-7pp.1157-1166

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G.V. Gorr and T.V. Belokon, "On Solutions of the Equations of Motion of a Gyrostat with a Variable Gyrostatic Moment," Mech. Solids. 56 (7), 1157-1166 (2021)
Year 2021 Volume 56 Number 7 Pages 1157-1166
DOI 10.3103/S002565442107013X
Title On Solutions of the Equations of Motion of a Gyrostat with a Variable Gyrostatic Moment
Author(s) G.V. Gorr (Department of Applied Mechanics, Institute of Applied Mathematics and Mechanics, Donetsk, 84100 Ukraine, gvgorr@gmail.com)
T.V. Belokon (M. Tugan-Baranovsky National University of Economics and Trade, Donetsk, 50005 Ukraine, B.Tatyana13@mail.ru)
Abstract The problem of the motion of a gyrostat with a variable gyrostatic moment under the action of potential and gyroscopic forces is considered. Three new solutions of the equations of motion are obtained, which are determined by three linear invariant relations for the components of the angular velocity vector of the gyrostat. In the case of a heavy gyrostat, a solution is found when the gyrostat mass distribution is characterized by the Kovalevskaya and Goryachev–Chaplygin generalized conditions. The next two solutions are valid for equations of the Kirchhoff–Poisson class. One of them exists in the case of dynamically symmetric gyrostats, and in the other solution the gyrostat mass distribution is arbitrary.
Keywords gyrostatic moment, invariant relations, potential and gyroscopic forces, Kovalevskaya and Goryachev–Chaplygin generalized conditions
Received 22 June 2020Revised 12 October 2020Accepted 20 October 2020
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