= Rotating torsion-stabilized inverted pendulum
{title2=$\ddot\theta=\Omega^2\sin\theta\cos\theta-\mu\theta/(ma^2)+(g/a)\sin\theta$}
A rigid pendulum tilted from the upward vertical and driven at fixed azimuthal <angular velocity> $\Omega$ has effective potential $\mu\theta^2/2+mga\cos\theta-ma^2\Omega^2\sin^2\theta/2$. With $\mu=2mga$, its upright <equilibrium> loses <linear stability> when $\Omega^2$ passes $g/a$. At equality the leading restoring <torque> is cubic and the potential has a positive quartic minimum. This gives a stable <quartic oscillator> with zero infinitesimal harmonic <frequency>, rather than a freely drifting neutral state.
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