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Semi-Regular Precession of an Asymmetrical Rigid Solid Body Filled with a Liquid

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Abstract

The Poincaré–Zhukovsky equations are used to describe the rotation of a rigid body with an ellipsoidal cavity filled with an ideal incompressible liquid. We obtain the relationships (called configurational conditions) between the inertia moments of a solid and a cavity with a liquid, at which the solid can perform semi-regular precession when the precession rate is constant and the rate of its proper rotation changes with time. When the axis of its proper rotation coincides with the principal inertia axis, one condition is sufficient, but if the axes do not coincide, then there appear two configuration conditions. It is shown that, under the configuration conditions of semiregular precession, the Poincaré–Zhukovsky equations have an invariant system of three linear functions. Analysis of the configuration conditions for systems close to spherically symmetric is carried out.

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  1. Institute of Precision Mechanics and Control, Russian Academy of Sciences, Saratov, Russia

    V. Yu. Ol’shanskii

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  1. V. Yu. Ol’shanskii
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Correspondence to V. Yu. Ol’shanskii.

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К To the centenary of the birth of academician V.V. Rumyantsev

Translated by G. Dedkov

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Ol’shanskii, V.Y. Semi-Regular Precession of an Asymmetrical Rigid Solid Body Filled with a Liquid. Mech. Solids 56, 1500–1513 (2021). https://doi.org/10.3103/S0025654421080148

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  • DOI: https://doi.org/10.3103/S0025654421080148

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