<p>
This is a simulation of the spherical pendulum, or pendulum in two dimensions, whose Lagrangian is given by
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$$
\mathcal{L} = \dfrac{1}{2}mL^2\dot{\theta}^2 + \dfrac{1}{2}mL^2\dot{\phi}^2\sin^2\ theta + 
$$

$$
+ mgL\cos\theta,
$$

<p>
where $\theta$ and $\phi$ are the traditional spherical coordinates. 
The equations of motion are integrated using the fourth order Runge-Kutta method with time step $h$. 
For large initial angles (greater than 120º), 
it is necessary to decrease $h$ to guarantee the convergence of the solution. 
The acceleration of gravity is defined as $g = 9.8$ m/s².
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<p>
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