The conditions of asymptotic stability of the uniform rotation of an asymmetric absolutely rigid body in a resisting medium are obtained in the form of a system of three inequalities. The rotation of the rigid body is maintained by a constant moment that is directed along the third principal axis. These inequalities are estimated analytically. It is shown that these conditions are reduced to three inequalities if the moment is overturning and to two inequalities of the moment is restoring. Conditions for the constant moment and the moment of inertia of the third principal axis are obtained, which under the restoring moment are sufficient for the asymptotic stability of the uniform rotation of the rigid body in the resisting medium. If the body rotates around the axis of the largest moment of inertia and the smallest of the doubles, then for the restoring moment, asymptotic stability is observed if the constant moment is sufficiently large. The stability conditions are generalized to the case where the body contains a cavity with an ideal incompressible fluid that undergoes irrotational motion.
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Translated from Prikladnaya Mekhanika, Vol. 57, No. 4, pp. 68–77, July–August 2021.
The research was partially sponsored by the program of fundamental research of the Ministry of Education and Science (project No. 0119U100042).
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Kononov, Y.M. Stability of a Uniform Rotation of an Asymmetric Rigid Body in a Resisting Medium under a Constant Moment. Int Appl Mech 57, 432–439 (2021). https://doi.org/10.1007/s10778-021-01095-1
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DOI: https://doi.org/10.1007/s10778-021-01095-1