raphical depiction of this system is not a line, but a
      vector field where the vectors $[\dot x_1, \dot x_2]^T$ are plotted over
      the domain $(x_1,x_2)$.  This vector field is known as the <em>phase
      portrait</em> of the system.</p>

      <p> In this section we restrict ourselves to the simplest case when $u_0 =
      0$. Let's sketch the phase portrait.  First sketch along the
      $\theta$-axis. The $x$-component of the vector field here is zero, the
      $y$-component is $-\frac{g}{l}\s