= Sliding-bead gravitational wave detector
{title2=$\ddot L=\tfrac12\epsilon\ddot h_{nn}L_0+O(\epsilon^2)$}
A short rigid nonrotating guide constrains two freely sliding beads to one axis $n$. In its <parallel-propagated orthonormal frame>, the axial <geodesic deviation> is $\ddot L=-R_{n0n0}L$. For a transverse <gravitational wave>, $R_{n0n0}=-\epsilon\ddot h_{nn}/2$, so a wave incident after the beads are at rest changes the measured separation by $\epsilon h_{nn}L_0/2$ to first order. Transverse reaction forces do not supply an axial restoring force. Alignment with the propagation direction gives no first-order length change.
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