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IssuesArchive of Issues2023-7pp.2544-2556

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G.V. Gorr, "One Class of Resonance Precession Motions of a Rigid Body under the Action of Three Homogeneous Force Fields," Mech. Solids. 58 (7), 2544-2556 (2023)
Year 2023 Volume 58 Number 7 Pages 2544-2556
DOI 10.3103/S0025654423070105
Title One Class of Resonance Precession Motions of a Rigid Body under the Action of Three Homogeneous Force Fields
Author(s) G.V. Gorr (State Budgetary Institution Institute of Applied Mathematics and Mechanics, Donetsk, Russia, gvgorr@gmail.com)
Abstract The article considers the problem of the motion of a rigid body with a fixed point in a force field which is a superposition of three homogeneous force fields. The conditions for the existence of precessional motions, characterized by the property that the velocity of the body’s precession is twice the velocity of its own rotation, are studied. It is shown that the body has dynamic symmetry with respect to the axis which forms a constant angle with a vector fixed in space. In the case of a body with the spherical mass distribution, it is equal to arccos(1/4). The solution of the equations of body motion is described by elliptic functions of time.
Keywords precessions of a rigid body, resonance motions, homogeneous force fields
Received 05 September 2022Revised 22 November 2022Accepted 22 November 2022
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