Chandrasekhar Ellipses

Here is my attempt to really make Chandrasekhar's EFE diagrams come to life. I'll start by permitting the reader to construct their own incompressible ellipsoid of arbitrary axis ratio.

Hello to whomever you are! If you were using a browser that understood java, you would see this greating in color! Caption: While the menu is set to "Any," clicking anywhere inside the gray "parameter" rectangle will identify a triaxial ellipsoid having a meridional cross-section of a specific ellipticity (selected axis ratio c/a) and an equatorial cross-section of a specific ellipticity (selected axis ratio b/a). Once a specific choice of the two axis ratios has been made: the (cyan-colored) ellipse to the right of the parameter rectangle will display a meridional cross-section and the (yellow) ellipse below the parameter rectangle will display the equatorial cross-section of your selected ellipsoid; and your selected values of c/a and b/a will be printed on the display line of your browser window.

While the menu is set to "Jacobi" or "Dedekind," clicking anywhere inside the gray "parameter" rectangle will identify a triaxial ellipsoid having the desired equatorial cross-section ellipticity (selected axis ratio b/a), but the ellipticity of the meridional plane cross-section (axis ratio c/a) will automatically be forced to the value that corresponds to a Jacobi (Dedekind) ellipsoid of the selected equatorial ellipticity. Once a specific choice has been made: The (cyan-colored) ellipse to the right of the parameter rectangle will display a meridional plane cross-section and the (yellow) ellipse below the parameter rectangle will display the equatorial plane cross-section of your selected Jacobi (Dedekind) ellipsoid; the values of c/a and b/a that correspond to your chosen Jacobi (Dedekind) ellipsoid will be printed on the display line of your browser window; and the angular velocity (omega) that is associated with the equilibrium properties of your selected Jacobi (Dedekind) ellipsoid will be printed on the display line of your browser window.

While the menu is set to "Jacobi" or "Dedekind," and after a particular ellipsoidal shape has been selected, clicking anywhere outside the gray parameter rectangle (but inside the figure) will initiate a java animation sequence that illustrates how rapidly the selected ellipsoidal figure spins, as viewed from an inertial frame of reference. The clock in the lower right-hand corner of the figure measures time in units of (pGr)-1/2, and the blue number to the right of the equatorial plane cross-section counts the number of times the figure has rotated through 360 degrees. To stop the animation, click a second time anywhere outside the gray parameter rectangle. Clicking a third time in the appropriate region of the figure will reset the clock and reinitiate the animation sequence. The animation must be stopped before another ellipsoidal figure may be selected.