ON THE STABILITY OF ONE PERMANENT ROTATION IN A NEIGHBORHOOD OF THE APPELROTH EQUALITY

In mechanical autonomous conservative systems that admit a partial integral, there are sometimes stationary motions that exist both with and without a partial integral. A system is considered in which the Hess integral exists when the Appelroth equality is satisfied and the stationary motion is dist...

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Bibliographic Details
Published in:Mechanics of solids 2021-07, Vol.56 (4), p.478-484
Main Author: Novikov, M. A.
Format: Article
Language:English
Subjects:
Classical Mechanics
Equality
Integrals
Motion stability
Physics
Physics and Astronomy
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Summary:In mechanical autonomous conservative systems that admit a partial integral, there are sometimes stationary motions that exist both with and without a partial integral. A system is considered in which the Hess integral exists when the Appelroth equality is satisfied and the stationary motion is distinguished, which takes place even without the Appelroth equality. In the article, the stability of such a stationary motion is studied by the second Lyapunov method. It is found that the boundary of the region of sufficient stability conditions does not coincide with the boundary of the region of necessary stability conditions.
ISSN:0025-6544
1934-7936
DOI:10.3103/S0025654421040130