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IssuesArchive of Issues2018-8pp.95-106

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V.Yu. Ol'shanskii, "On the Regular Precessions of an Asymmetric Liquid-Filled Rigid Body," Mech. Solids. 53 (S2), 95-106 (2018)
Year 2018 Volume 53 Number S2 Pages 95-106
DOI 10.3103/S0025654418050138
Title On the Regular Precessions of an Asymmetric Liquid-Filled Rigid Body
Author(s) V.Yu. Ol'shanskii (Institute of Precision Mechanics and Control, Russian Academy of Sciences, Saratov, Russia, olshanskiy_vlad@mail.ru)
Abstract The conditions for the existence of a linear invariant system of Poincaré–Zhukovsky equations have been found. In a linear invariant system, three configuration conditions have been obtained that are sufficient to allow a mechanical system without dynamic symmetry to undergo regular precession. The explicit expression of the moments of inertia of a system consisting of a rigid body with an ellipsoidal cavity filled an ideal vorticity fluid is given in terms of the cavity dimensions; the velocities of precession and self-rotation are found. The particular case of the permanent rotation of an asymmetric rigid shell around the angular momentum vector is considered; in this case, any axis rigidly bound to the shell can be used as the axis of permanent rotation.
Keywords liquid-filled rigid body, Poincaré–Zhukovsky equations, regular precession
Received 23 December 2017
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