= Sedimentation drift of a weighted two-rod body
{title2=$\Delta x=2L/3$}
Attach weights $mg$ at the joint and $\lambda mg$ at each outer endpoint of the <right-angle two-rod resistance matrix> geometry. With the first rod initially horizontal and the second vertically upwards, quasistatic <Stokes flow> gives $\dot\theta=(1-\lambda)mg(\cos\theta-\sin\theta)/(4CL^2)$. For $\lambda<1$ the orientation tends to $\pi/4$; for $\lambda>1$ it tends to $-3\pi/4$. Eliminating time gives $x-x_0=(2L/3)(1+\sin\theta-\cos\theta)$ and the same rightward net displacement $2L/3$ in both cases. For $\lambda>1$ the initial drift is leftwards before reversing. At $\lambda=1$ there is no rotation or lateral drift, illustrating noncommuting infinite-time and parameter limits.
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