Surface of Section Applet
Controls Explained

SOS Home
APPLET INSTRUCTIONS:

To start the applet, click anywhere in the black square on the right.

You will then see two panes appear. On the left is the xy plane, where you can watch the star trace out its orbit. On the right is the surface of section plot. Every time the star crosses the y axis, its phase space coordinate (y, vy) is plotted on the surface of section. The white curve on the surface of section marks the region of allowed orbits. Outside this curve orbits are not allowed for the energy you have chosen; if you click there nothing will happen. Clicking on the surface of section starts a new orbit which starts at x = 0, y and vy given by where you clicked on the surface of section, and vx determined from x, y, vy and the energy chosen.

As you click again in the surface of section, the xy plot gets erased and a new orbit started. The old orbit's surface of section remains, however, so by starting different orbits you can make a "map" of phase space with the surface of section. If you want to erase the surface of section as well, hit the "reset" button.

CONTROLS:
Galaxy Type:
Singular, Core. This sets the core radius of the potential. If you choose Singular, rc = 0 and you get the singular logarithmic potential. If you choose Core, rc = 1 and you get the logarihmic potential with a core.
Galaxy Shape:
1.0, 0.9, 0.7, 0.5. This is the "q" parameter for the flattening of the potential along the y axis. If q = 1.0, the potential is round. Smaller values of q give flatter potentials.
Energy:
-1, -0.5, 0.0, 0.5, 1.0, 1.5. This is the binding energy of the orbits for which you are making a surface of section. Note that for the singular logarithmic potential, even orbits with positive energy are bound, contrary to how we usually think of the definition of binding energy.
Disable sleep:
Normally when the applet runs, it pauses for a few milliseconds between updating the graphics. This slows the applet down, but also makes it behave well. If you disable sleep, the calculation runs faster, but odd things happen with the display, depending on what kind of machine you are using. In some cases, the applet blazes along at very high speed, on others the display stops entirely until you reenable sleep. Sometimes it can hang the browser entirely. And because you have now effectively told your computer to spend ALL its brainpower on the applet, getting its attention back can be difficult; there may be a long delay between when you turn sleep back on (by reclicking the sleep button), and when it actually responds. All this is to say that disabling sleep can speed up the orbit calculation immensely, but that it's exact behavior is not guaranteed.
Black Hole:
This turns on the black hole in the center of the galaxy. You can see how it affects the orbits.
Stop:
simply stops the current orbit.
Reset:
Erases the current surface of section. Also, any time a galaxy parameter is changed the surface of section gets erased.