Solution
= Solution
Near $\theta=0$, the linearized equation is $\ddot\theta+(g-a)\theta/\ell=0$. When $a<g$ this is an <harmonic oscillator>, so the downward configuration is stable. Writing $\theta=\pi+\varepsilon$ instead gives $\ddot\varepsilon-(g-a)\varepsilon/\ell=0$, with an exponentially growing solution. \b[Downward is stable; upward is unstable.]