On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat

The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary solutions are found on the invariant set of the zero level of the area integral, and their stability is analyzed. For the case where the suspension point coincides with the center of mass and the action of a gyro...

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Bibliographic Details
Published in:Journal of applied and industrial mathematics 2023-09, Vol.17 (3), p.557-570
Main Authors: Kosov, A. A., Semenov, E. I.
Format: Article
Language:English
Subjects:
Equations of motion
Gyroscopic moment
Integrals
Mathematics
Mathematics and Statistics
Quadratures
Stability
Stability analysis
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Summary:The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary solutions are found on the invariant set of the zero level of the area integral, and their stability is analyzed. For the case where the suspension point coincides with the center of mass and the action of a gyroscopic moment is of a special type, integration by quadratures is performed.
ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478923030092