Editing Apps/RotatingPolytropes (section)

====Focus on Incompressible Configurations====
* [https://ui.adsabs.harvard.edu/abs/1980PThPh..63.1957F/abstract Toshio Fukushima, Yoshiharu Eriguchi, Daiichir Sugimoto &amp; Gennadii S. Bisnovatyi-Kogan (1980)], Progress of Theoretical Physics, 63, 1957: ''Concave Hamburger Equilibrium of Rotating Bodies''
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<font color="green">&hellip; computed the structure of uniformly rotating polytropes with ''small but finite'' values of polytropic index.  In the case of high angular momentum there appeared a concave hamburger-like shape of equilibrium, and the sequence of shapes seemed to continue into a toroid.</font>

<font color="green">&hellip; the Maclaurin spheroid does not represent the incompressible limit of the rotaing [''sic''] polytropic gas because of its restriction of the figure.  The computed sequence of equilibria clarifies the relation between the Maclaurin spheroid and the [[Apps/DysonWongTori#Self-Gravitating.2C_Incompressible_.28Dyson-Wong.29_Tori|Dyson-Wong toroid]].  Moreover it is the sequence of minimum-energy configurations.</font>

TECHNIQUE:  <font color="green">&hellip; method developed by Eriguchi, in which the boundary value problem of gravitational equilibrium is transformed into the Cauchy problem by making the analytic continuation into the complex plane.</font>
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* [https://ui.adsabs.harvard.edu/abs/1981PThPh..65.1870E/abstract Yoshiharu Eriguchi &amp; Daiichiro Sugimoto (1981)], Progress of Theoretical Physics, 65, 1870:  ''Another Equilibrium Sequence of Self-Gravitating and Rotating Incompressible Fluid''
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<font color="green">It has been said that there are only two axisymmetric equilibrium sequences in the case of self-gravitating, uniformly rotating ''incompressible'' fluids &#8212; Maclaurin spheroids and [[Apps/DysonWongTori#Self-Gravitating.2C_Incompressible_.28Dyson-Wong.29_Tori|Dyson-Wong toroids]] &hellip; We have computed &hellip; an intermediate sequence which branches off the spheroids and extends to toroids.</font>

TECHNIQUE:  ''Guess'' the location of the configuration's ''surface'' in the meridional plane then, assuming the density is uniform everywhere inside this surface, determine the corresponding gravitational potential using the integral form of the Poisson equation and a Green's function written in terms of Legendre polynomials. Iterate on this guess until hydrostatic balance is achieved.
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* [https://ui.adsabs.harvard.edu/abs/1982PThPh..67..844E/abstract Y. Eriguchi &amp; I. Hachisu (1982)], Progress of Theoretical Physics, 67, 844:  ''New Equilibrium Sequences Bifurcating from Maclaurin Sequence''
* [https://ui.adsabs.harvard.edu/abs/1982PThPh..67.1068E/abstract Y. Eriguchi, I. Hachisu &amp; D. Sugimoto (1982)], Progress of Theoretical Physics, 67, 1068:  ''Dumb-Bell-Shape Equilibria and Mass-Shedding Pear-Shape of Selfgravitating Incompressible Fluid''
* [https://ui.adsabs.harvard.edu/abs/1984PASJ...36..497H/abstract I. Hachisu &amp; Y. Eriguchi (1984)], PASJapan, 36, 497:  ''Bifurcation points on the Maclaurin sequence''
* [https://ui.adsabs.harvard.edu/abs/1985A%26A...148..289E/abstract Y. Eriguchi &amp; I. Hachisu (1985)], Astronomy &amp; Astrophysics, 148, 289:  ''Maclaurin hamburger sequence''
* [https://ui.adsabs.harvard.edu/abs/1986A%26A...168..130E/abstract Y. Eriguchi, E. Mueller &amp; I. Hachisu (1986)], Astronomy &amp; Astrophysics, 168, 130:  ''Meridional flow in a self-gravitating body.  I. Mechanical flow in a barotropic star with constant specific angular momentum''