Chaos in the Driven Pendulum

This applet illustrates the driven pendulum: a rigid, plane pendulum whose point of attachment oscillates vertically. The user enters the amplitude and frequency of oscillation of the attachment point, and the initial conditions. The applet animates the pendulum's motion and plots the angle and angular velocity each time the attachment point reaches the bottom of its cycle. Such a plot is called a Poincare section.

Instructions for use

Using the scrollbars provided, enter the amplitude in units of the length of the pendulum rod, and the frequency in units of the frequency of small oscillations of the undriven pendulum.
Enter the initial angle and angular velocity by single-clicking with the mouse at the desired location in the phase plane. This also starts the animation.
To stop the animation, click "stop".
Repeat as often as desired. To clear the screen, click "clear".
To significantly speed up the generation of points in the phase plane, disable the pendulum animation using the checkbox provided. This may be done while the animation is running.
Use the checkbox provided to change the size of the points plotted. This may be done while the animation is running.