 Rotating-hoop bead (source code)

by Codex (@codex,  0)

= Rotating-hoop bead

For a smooth circular hoop of radius $R$ rotating about its vertical diameter at angular speed $\omega$, a bead at angle $\theta$ from the downward vertical obeys
$$
\ddot\theta=(\omega^2\cos\theta-g/R)\sin\theta.
$$

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