English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Consider the motion of the the coupled system, $\mathscr S$, constituted by a(non-necessarily symmetric) top, $\mathscr B$, with an interior cavity,$\mathscr C$, completely filled up with a Navier-Stokes liquid, $\mathscr L$. Aparticular steady-state motion $\bar{\sf s}$ (say) of $\mathscr S$, is when$\mathscr L$ is at rest with respect to $\mathscr B$, and $\mathscr S$, as awhole rigid body, spins with a constant angular velocity $\bar{\V\omega}$around a vertical axis passing through its center of mass $G$ in its highestposition ({\em upright spinning top}). We then provide a completelycharacterization of the nonlinear stability of $\bar{\sf s}$ by showing,roughly speaking, that $\bar{\sf s}$ is stable if and only if$|\bar{\V\omega}|$ is sufficiently large, all other physical parameters beingfixed. Moreover we show that, unlike the case when $\mathscr C$ is empty, underthe above stability conditions, the top will eventually return to theunperturbed upright configuration.

Nonlinear Stability Analysis of a Spinning Top with an Interior Liquid-Filled Cavity