irst order. This is a general property of
      heavily-damped systems, such as fluids at very low Reynolds number. </p>

      <p> I'd like to ignore one detail for a moment: the fact that $\theta$
      wraps around on itself every $2\pi$.  To be clear, let's write the system
      without the wrap-around as: \begin{equation}b\dot{x} = u_0 -
      mgl\sin{x}.\label{eq:overdamped_pend_ct}\end{equation} Our goal is to
      understand the long-term behavior of this system: to find $x(\infty)$
      given $x