Visualization of Spherical Harmonics

This is an interactive Java Applet to visualize Spherical Harmonics.
You must enable Java for your browser to use it.

Netscape 6.xx, Mozilla, MS Internet Explorer are recommended browsers. Older versions of Netscape will work, but much slower, because they do not have installed a JIT-compiler.
If you don't see it correctly on your browser, please inform us per Email (include the used browser version and operating system).

Please have some seconds patience for loading the applet. See below the applet for explanation and usage info.

Sorry, your WWW-browser does not support Java Applets.

To use this graphic display, you must Enable Java for your browser

For Netscape select: Edit -> Preferences -> Advanced -> Enable Java.

Short Explanation

This figure shows one specific surface spherical harmonic of degree 'l' and order 'm' of the expansion of a scalar field on the Earth into a series of surface spherical harmonics.
The general term in the double sum over the degree 'l' (l = 1,..,l_max) and order 'm' (m = 0,..,l) is

Y_lm(φ,λ) = P_lm(sin(φ)) × [C_lm cos(m λ) + S_lm sin(m λ)]
where 'φ' is the latitude, 'λ' the longitude and 'P_lm' are the Legendre functions.
Here only the cos-term is displayed, arbitrarily scaled by C_lm = 100. The sine-term is identical with a phase shift of π/2.
The blue lines are the zero-circles of Y_lm.

Usage tips

A full description of functionality is given at the Gravity Field Visualization page.

Most buttons (or the button-labels) have a 'help' option: if you move the mouse cursor over it, a small popup will explain its function.
You can move the Earth in two directions, either with the cursor keys or with mouse dragging (for keyboard actions to work, the main window must have the focus!).
The key-actions are similiar to the Gravity Field-Visualization-Applet.

Troubleshooting

If you experience some odd behaviour of your applet (no reaction to buttons, no image updating, ...) you can inspect what is going wrong, if you have a look at the Java Console of your browser. For Netscape 6.xx you open it with the buttons Tasks -> Tools -> Java Console. There the main actions and errors are logged and you have the possibility to control the Java Virtual Machine (JVM).

One common error, which freezes the applet is eg. the "OutOfMemoryError". It occurs if the pre-allocated memory (usually 64MB) for your JVM is exhausted. This can happen sometimes for maximum resolution grids.
As far as I know (please inform me, if you have better infos) there is no option to enlarge this memory.

If you see this error, you can try to reset the applet, if you start a "garbage collection" by pressing the key 'g' in the Java Console window.
If this fails, you should restart your browser.