I followed the procedure at the following site,

http://www.astro.utu.fi/~cflynn/Stars/l4.html

and I believe that I've correctly added a centripetal force term to the
derivation of the differential equation for stellar hydrostatic
equilibrium.  That equation relates dP/dr to d_rho/dr, where P is the
hydrostatic pressure, rho is the mass density and r, of course, is the
radial coordinate.  

I added the centripetal force, rho*w^2*r, as a second body force term in
equation (11) on that site, making that equation into

dP/dr=rho(r)*w^2*r*sin(theta)-G*m(r)*rho(r)/r^2,

where w is omega, the rotational frequency of the star, which is allowed to
vary with the latitude on the star, as w=w(theta).

The middle part is pretty much just algebra, and the answer I got was

(1/r^2)*d[(r^2/rho)(dP/dr)]/dr+4*pi*G*rho=[3w^2+2*w*r*dw/dr]*sin(theta).

Actually, you can tell by the presence of a dw/dr term that I allowed w to
vary as a function of both r and theta, but I have no idea whether the is
necessary to understand the physics, so I kept it for completeness and just
in case.

If I were to put in the compressible equation of state for a fluid,
P=K*rho^gamma, my result would be an improved Lane-Emden equation.  I
haven't done that yet, but so far it looks straightforward, and I plan to
do it within the day or two.

In summary, I need to know whether the above equations and derivation look
familiar to the people in this group, and does anybody know if this
particular approach to the problem has ever been taken before.  I have to
know whether I have just reinvented the wheel, so I can start thinking
about whether to get the entire derivation published, rather than just the
first and last equations.  :b