 can we tell?  One technique is to linearize the
      system at the fixed point.  A smooth, time-invariant, nonlinear system
      that is locally exponentially stable <i>must</i> have a stable
      linearization; we'll discuss linearization more in the next chapter. </p>

      <p>Here's a thought exercise.  If $u$ is no longer a constant, but a
      function $\pi(\theta,\dot{\theta})$, then how would you choose $\pi$ to
      stabilize the vertical position.  Feedback cancellation is the trivial
      