Math. Model. Nat. Phenom.
Volume 16, 2021
|Number of page(s)||21|
|Published online||09 April 2021|
Nonlinear stability analysis of a spinning top with an interior liquid-filled cavity
Department of Mechanical Engineering and Materials Science, University of Pittsburgh,
2 Department of Mathematics and Statistics, Queen’s University, Kingston, Canada.
* Corresponding author: firstname.lastname@example.org
Accepted: 30 November 2020
Consider the motion of the coupled system, 𝒮, constituted by a (non-necessarily symmetric) top, ℬ, with an interior cavity, 𝒞, filled up with a Navier-Stokes liquid, ℒ. A particular steady-state motion (say) of 𝒮, is when ℒ is at rest with respect to ℬ, and 𝒮, as a whole rigid body, spins with a constant angular velocity around a vertical axis passing through its center of mass G in its highest position (upright spinning top). We then provide a complete characterization of the nonlinear stability of by showing, roughly speaking, that is stable if and only if is sufficiently large, all other physical parameters being fixed. Moreover we show that, unlike the case when 𝒞 is empty, under the above stability conditions, the top will eventually return to the unperturbed upright configuration.
Mathematics Subject Classification: 35Q35 / 35Q30 / 35B35 / 35B40 / 75D05
Key words: Fluid-solid interaction / Navier-Stokes equations / rigid body / stabilty
© The authors. Published by EDP Sciences, 2021
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