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Stationary-state solutions to the rotation of solid bodies with liquid-filled cavities and their stability

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Abstract

In this paper, we discuss all the possible equilibrium states of axi-symmetrical solid bodies with liquid-filled cavities rotating around fixed axes according to the extremum conditions on the potential energy, and conclude that there exists a unique stable final-state solution, for which the system uniformly rotates around its vertical symmetrical axis, for both the inverted and suspended ones. And then applying the Lyapunov direct approach for a continuous system, we investigate the stability of the rotating systems subject to large disturbances. In addition, we describe an interesting analogue between the rotation of a solid body with a liquid-filled cavity in the inverted case and the motion of a small ball in a spinning spherical bowl. The results obtained herein theoretically provide an evidence of the reality of the secular stability.

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References

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Authors and Affiliations

  1. Institute of Mechanics, Academia Sinica, Beijing, China

    Xu Shuo-chang

  2. Shanghai institute of Applied Mathematics and Mechanics, Shanghai, China

    Dai Shi-qiang

Authors
  1. Xu Shuo-chang
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  2. Dai Shi-qiang
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Shuo-chang, X., Shi-qiang, D. Stationary-state solutions to the rotation of solid bodies with liquid-filled cavities and their stability. Applied Mathematics and Mechanics 6, 605–615 (1985). https://doi.org/10.1007/BF03250483

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  • DOI: https://doi.org/10.1007/BF03250483

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