This application simulates the movement of a pendulum in three dimensions, also known as a spherical pendulum. There is no damping.

If you're on a touchscreen device, use the usual touchscreen gestures:

• One finger: moves the viewing angle.
• Two fingers, pinch gesture: zooms.
• Two fingers, swiping in the same direction: shifts the camera position.

Buttons:

• : Restarts the simulation.
• : Accesses the parameters and initial conditions of the system: initial angle, pendulum length, etc.

This is a simulation of the spherical pendulum, or pendulum in two dimensions, whose Lagrangian is given by

$$ \mathcal{L} = \dfrac{1}{2}mL^2\dot{\theta}^2 + \dfrac{1}{2}mL^2\dot{\phi}^2\sin^2\ theta + $$ $$ + mgL\cos\theta, $$

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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