Present a clear discussion of the equilibrium structure of nonrotating
polytropes having polytropic indices in the range 0 < n < ¥. The emphasis should be on models for which
there is no known analytical solution to the
Lane-Emden equation.
The presentation should be in an HTML format,
similar to
the presentation that already has been made for
"Spherical, n = 1 Polytropes."
To complete this project, it will be necessary to write a numerical
algorithm that will effectively solve the
Lane-Emden equation for arbitrary values of the polytropic index, n.
Rather than looking through the literature for a numerical technique that
will accurately integrate a nonlinear, second-order, ordinary differential
equation and applying it to the Lane-Emden equation directly, however,
I recommend that you adopt the
Self-Consistent Field Technique. Before sitting down to write an SCF algorithm based
on my
outline of the technique, I recommend that you try to implement the technique
*analytically* to derive the solution for Maclaurin Spheroids,
as described in the
accompanying homework problem.

As a check of your results, you should at least compare your numerically
derived model structures for n = 1 and n = 5 polytropes to the analytically
known results. You may wish to present a summary table of model properties
like the one I've presented in the accompanying discussion of
polytrope properties.