This demo illustrates the Henon-Heiles system: a point particle moving in the potential

U(x,y) = (x²+y²)/2 + xy² -x³/3.

The user enters the energy and the initial conditions. The demo animates the particle's motion and plots the x position and momentum each time the particle passes through y=0. Such a plot is called a Poincaré section.

Instructions for use

• Using the scrollbars provided, enter the energy (maximum value is 1/6).
• Enter the initial x coordinate and momentum by single-clicking with the mouse at the desired location in the phase plane (right-hand panel). This also starts the animation.
• To stop the animation, click "stop".
• Repeat as often as desired. To clear the screens, click "clear".
• To significantly speed up the generation of points in the phase plane, disable the position 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.