Minimum separation of phase-shifted sphere oscillations
= Minimum separation of phase-shifted sphere oscillations
{title2=$\ell_{\min}=\ell_0-2\delta|\sin(\phi/2)|$}
The centre separation for equal-amplitude oscillations has minimum $\ell_0-2\delta|\sin(\phi/2)|$. A bound $\ell_0\geq\delta$ alone cannot guarantee nonoverlap. An asymptotic mobility calculation needs this minimum much larger than the sphere radii.