= Energy dissipation of a damped pendulum
{title2=$\dot E=-c\dot\theta^2$}
For the normalized <damped pendulum>, $E=\dot\theta^2/2+1-\cos\theta$ obeys $\dot E=-c\dot\theta^2\leq0$. Its <mechanical energy> is constant only along an equilibrium trajectory, and strictly decreases over every positive-length interval on a nonstationary trajectory. At an individual turning point its derivative vanishes. This excludes nonconstant periodic trajectories despite oscillatory approach to a <stable focus>.
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