= Particle attraction in an elliptical shearing-sheet vortex
{title2=$r\geq3\quad\text{for every finite positive drag rate in Keplerian shear}$}
The material-boundary and <vorticity> conditions give $\alpha=S/[r(r-1)]$ and $\beta=Sr/(r-1)$. A pressureless particle subject to <linear drag>, <Coriolis acceleration> and tidal gravity has the <drag-polynomial stability for all positive stopping rates> with $K=2\Omega(2\Omega-S)$, $L=\Omega(\alpha+\beta-S)$ and $P=\alpha\beta$. In <Keplerian shear>, $K/\Omega^2=1$, $L/\Omega^2=3(r+1)/[2r(r-1)]$ and $P/\Omega^2=9/[4(r-1)^2]$. The exact criterion is $r\geq3$, including the boundary $K=L>P$ at $r=3$. Attraction is local to the centre under the prescribed interior velocity field; a trajectory leaving the patch cannot be followed using that field alone.
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