} = \frac{1}{2},$$ yielding
\begin{gather*}
t = \frac{2I}{E+mgl} \int_{\phi(0)}^{\phi(t)} \frac{d\phi}{\sqrt{1 -
    k_1^2 \sin^2(\phi)}} \\
\theta(t) = 2 \tan^{-1} \left[ \frac{ \text{sn} \left( t
    \sqrt{\frac{E+mgl}{2I}} + F\left( \frac{\theta(0)}{2}, k_1 \right)
    \right) } { \text{cn} \left( t
    \sqrt{\frac{E+mgl}{2I}} + F\left( \frac{\theta(0)}{2}, k_1 \right)
    \right) }
 \right]
\end{gather*}
Notes: Use MATLAB's <code>atan2</code> and <code>unwrap</code> to recover the
complete trajectory.</