Apps/EriguchiHachisu/Models
Eriguchi, Hachisu, and their various Colleagues
Following the completion of their respective doctoral dissertations, Yoshiharu Eriguchi and Izumi Hachisu embarked upon an extremely fertile research collaboration which, especially over the decade of the 1980s, transformed the international astrophysics community's understanding of the structure and stability of rotating, selfgravitating fluid configurations. Others — including myself (J.E.T.) — were drawn into, and benefitted significantly from participation in, various ones of these collaborative research efforts. In what follows, we list and summarize the key results from a significant number of these "Eriguchi and Hachisu" collaborative publications.
Our list is broken into two broad topical categories: Principally Uniformly Rotating, Incompressible Configurations (polytropic index, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n=0} ) and Principally Differentially Rotating, Compressible Configurations (polytropic index, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n>0} ). The efforts by both Eriguchi and Hachisu to extend our understanding of incompressible configurations beyond the Maclaurin spheroid sequence and the Jacobi/Dedekind sequence — more broadly, Riemann Stype ellipsoids — is summarized in HE84c.
Kickoff
Eriguchi78
Y. Eriguchi (1978)
Hydrostatic Equilibria of Rotating Polytropes
Publications of the Astronomical Society of Japan, Vol. 30, pp. 507  518
(p. 515): "This paper is based on the author's dissertation, submitted to the University of Tokyo, in partial fulfillment of the requirements for the doctorate."
Hachisu82
📚 Hachisu (1982)
Gravothermal and Gravogyro Catastrophes of Rotating and SelfGravitating Gaseous Disks
Publications of the Astronomical Society of Japan, Vol. 34, pp. 313  335
(p. 333): "This paper is based on the author's dissertation, submitted to the University of Tokyo, in partial fulfillment of the requirements for the doctorate."
Principally Uniformly Rotating, Incompressible Configurations
ES81
Concave Hamburger: OneRing (incompressible case)
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c, below.
Another Equilibrium Sequence of SelfGravitating and Rotating Incompressible Fluid
Progress of Theoretical Physics, Vol. 65, No. 6, pp. 1870  1875
NOTE: Results from an independent effort to construct models along this identical sequence appear in … 


HES82
Concave Hamburger: OneRing (compressible, as well as, incompressible case)
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c, below.
Rapidly Rotating Polytropes and Concave Hamburger Equilibrium
Progress of Theoretical Physics, Vol. 68, No. 1, pp. 191  205
NOTE: In this HES82 publication, the authors point out (with attending explanation) that some of the modeling results published earlier by 📚 Fukushima, Eriguchi, Sugimoto, & BisnovatyiKogan (1980) are demonstratively wrong.
EH82
Triangle: Square: Ammonite and TwoRing (pt. 1)
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c
New Equilibrium Sequences Bifurcating from Maclaurin Sequence
Progress of Theoretical Physics, Vol. 67, No. 3, pp. 844  851
NOTE: Color images copied from our separate discussion of binary masstransfer simulations. 
NOTE: Results from an independent effort to construct models along this identical "tworing" sequence appear in …
M. Ansorg A. Kleinächter, & R. Meinel (2003)
Uniformly Rotating Axisymmetric Fluid Configurations Bifurcating from Highly Flattened Maclaurin Spheroids
Monthly Notices of the Royal Astronomical Society, Vol. 339, Issue 2, pp. 515  523
n/a  See the curve labeled "(3)" in Figure 2 (p. 517) of AKM2003 
See Table 4 (p. 520) of AKM2003 
See Figure 8 (p. 521) of AKM2003 
EHS82
DumbBell: PearShaped
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c, below.
DumbBellShape Equilibria and MassShedding PearShape
of Selfgravitating Incompressible Fluid
Progress of Theoretical Physics, Vol. 67, No. 4, pp. 1068  1075
EH83a
TwoRing (pt. 2)
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c, below.
Two Kinds of Axially Symmetric Equilibrium Sequences of SelfGravitating and Rotating Incompressible Fluid
— TwoRing Sequence and CoreRing Sequence —
Progress of Theoretical Physics, Vol. 69, No. 4, pp. 1131  1136


EH83b
MultiBody
… as categorized in 📚 Hachisu & Eriguchi (1984c); also see HE84c, below.
Gravitational Equilibrium of a MultiBody Fluid System
Progress of Theoretical Physics, Vol. 70, No. 6, pp. 1534  1541
HE84c
Summary
Fission Sequence and Equilibrium Models of Rigidity [sic] Rotating Polytropes
in Double Stars, Physical Properties and Generic Relations; Proceedings of IAU Colloquium No. 80 held at Lambing, Java, June 37, 1983
Editors: Bambang Hidayat, Zdenek Kopal, Jurgen Rahe; Dordrecht, D. Reidel Publishing Co.
Astrophysics & Space Science, Vol. 99, pp. 71  74
Also see our separate discussion of the Fission Hypothesis 
HE84
Bifurcation Points on the Maclaurin Sequence
Publications of the Astronomical Society of Japan, Vol. 36, No. 3, pp. 497  503
HE83
Bifurcations and Phase Transitions of SelfGravitating and Uniformly Rotating Fluid
Monthly Notices of the Royal Astronomical Society, Vol. 204, pp. 583  589
EH85
Differentially Rotating, "Maclaurin Toroid" Sequence
… extending the work of 📚 Marcus, Press, & Teukolsky (1977).
Maclaurin Hamburger Sequence
Astronomy and Astrophysics, Vol. 148, pp. 289  292
Principally Differentially Rotating, Compressible Configurations
Hachisu86a
A Versatile Method for Obtaining Structures of Rapidly Rotating Stars
The Astrophysical Journal Supplement Series, Vol. 61, pp. 479  507
Models having Uniform Rotation — §II.c, Eq. (11), p. 481 

Models having Uniform Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v_\varphi} — §II.c, Eq. (12), p. 481 



Models having jconstant rotation — §II.c, Eq. (13), p. 481 
See Also
 Properties of Maclaurin Spheroids
 Excerpts from Maclaurin's (1742) A Treatise of Fluxions
 Properties of Homogeneous Ellipsoids
Appendices:  VisTrailsEquations  VisTrailsVariables  References  Ramblings  VisTrailsImages  myphys.lsu  ADS  