e pendulum</figcaption> </figure>

    <p> The Lagrangian derivation of the equations of motion (as described in
    the appendix) of the simple pendulum yields: \begin{equation*} m l^2
    \ddot\theta(t) + mgl\sin{\theta(t)} = Q. \end{equation*} We'll consider the
    case where the generalized force, $Q$, models a damping torque (from
    friction) plus a control torque input, $u(t)$: $$Q = -b\dot\theta(t) +
    u(t).$$ </p>

  </section>

  <section class="drake"><h1>Nonlinear dynamics with a
    constan