= Strong-shock polar for a perfect gas
{title2=$u_Y^2=(U-u_X)(u_X-qU),\quad q=(\gamma-1)/(\gamma+1)$}
The normal <velocity> is reduced by $q$ in the strong-shock limit while tangential <velocity> is unchanged. If the upstream speed is $U$ and the shock normal makes angle $\beta$ with its direction, then $u_X=U[1-(1-q)\cos^2\beta]$ and $u_Y=\pm U(1-q)\cos\beta\sin\beta$. Eliminating the angle gives the displayed circle, centered at $\gamma U/(\gamma+1)$ with radius $U/(\gamma+1)$. It is the limiting <shock polar> in downstream <velocity> space.
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