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Whitworth's (1981) Isothermal Free-Energy Surface
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Key Parallel References

The following seven references serve as excellent supplemental printed texts to this Wiki-based H_Book because the fundamental physics and astrophysics concepts that are covered in these texts have significant overlap with the concepts we are discussing. The degree to which these references provide discussions that are parallel to ours is illustrated in our accompanying key equations appendix.

  • [BT87] Binney, J. & Tremaine, S. 1987, Galactic Dynamics (Princeton, NJ: Princeton University Press)
  • [BLRY07] Bodenheimer, P., Laughlin, G. P., Różyczka, M. & Yorke, H. W. 2007, Numerical Methods in Astrophysics An Introduction (New York: Taylor & Francis)
  • [C67] Chandrasekhar, S. 1967 (originally, 1939), An Introduction to the Study of Stellar Structure (New York: Dover)
  • [H87] Huang, K. 1987 (originally 1963), Statistical Mechanics (New York: John Wiley & Sons)
  • [KW94] Kippenhahn, R. & Weigert, A. 1994, Stellar Structure and Evolution (New York: Springer-Verlag)
  • [LL75] Laundau, L. D. & Lifshitz, E. M. 1975 (originally, 1959), Fluid Mechanics (New York: Pergamon Press)
  • [P00] Padmanabhan, T. 2000, Theoretical Astrophysics. Volume I: Astrophysical Processes (Cambridge: Cambridge University Press); and Padmanabhan, T. 2001, Theoretical Astrophysics. Volume II: Stars and Stellar Systems (Cambridge: Cambridge University Press)
  • [ST83] Shapiro, S. L. & Teukolsky, S. A. 1983, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (New York: John Wiley & Sons); republished in 2004 by WILEY-VCH Verlag GmbH & Co. KGaA

Other References

  • [CRC] Selby, Samuel M. 1971, CRC Standard Mathematical Tables (Cleveland, Ohio: The Chemical Rubber Co.)
  • [EFE] Chandrasekhar, S. 1987 (originally, 1969), Ellipsoidal Figures of Equilibrium (New York: Dover)
  • [HK94] Hansen, C. J. & Kawaler, S. D. 1994, Stellar Interiors: Physical Principles, Structure, and Evolution (New York: Springer-Verlag)
  • [MF53] Morse, Philip M. & Feshbach, H. 1953, Methods of Theoretical Physics: Parts I and II (New York: McGraw-Hill Book Company)
  • [Shu92] Shu, Frank H. 1992, The Physics of Astrophysics, Volume II: Gas Dynamics (Mill Valey, California: University Science Books)
  • [T78] Tassoul, Jean-Louis 1978, Theory of Rotating Stars (Princeton, NJ: Princeton Univ. Press)

Appendix of EFE

The presentation of the subject in this book (Ellipsoidal Figures of Equilibrium) is based on the following papers:


  • [Publication I] S. Chandrasekhar (1960), J. Mathematical Analysis and Applications, 1, 240: The virial theorem in hydromagnetics
  • [Publication II] N. R. Lebovitz (1961), ApJ, 134, 500: The virial tensor and its application to self-gravitating fluids
  • [Publication III] S. Chandrasekhar (1961), ApJ, 134, 662: A Theorem on rotating polytropes

Spheroidal & Ellipsoidal Sequences

Binary Systems

  • [Publication XIX] S. Chandrasekhar (1963), ApJ, 138, 1182: The equilibrium and stability of the Roche ellipsoids
  • [Publication XX] N. R. Lebovitz (1963), ApJ, 138, 1214: On the principle of the exchange of stabilities. I. The Roche ellipsoids
  • [Publication XXI] S. Chandrasekhar (1964), ApJ, 140, 599: The equilibrium and the stability of the Darwin ellipsoids
  • [Publication XXXI] S. Chandrasekhar (1969), Publications of the Ramanujan Institute, 1, 213 - 222: The effect of viscous dissipation on the stability of the Roche ellipsoid
  • [Publication XXXIX] M. L. Aizenman (1968), ApJ, 153, 511: The equilibrium and the stability of the Roche-Riemann ellipsoids
  • [Publication XL] S. Chandrasekhar (1969), ApJ, 157, 1419: The stability of the congruent Darwin ellipsoids

Effects of General Relativity

  • [Publication XXVI] S. Chandrasekhar (1965), ApJ, 142, 1513: The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies. I. The Maclaurin spheroids and the virial theorem
  • [Publication XXX] S. Chandrasekhar (1967), ApJ, 147, 334: The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies. II. The deformed figures of the Maclaurin spheroids
  • [Publication XXXI] S. Chandrasekhar (1967), ApJ, 147, 383: Virial relations for uniformly rotating fluid masses in general relativity
  • [Publication XXXII] S. Chandrasekhar (1967), ApJ, 148, 621: The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies. III. The deformed figures of the Jacobi ellipsoids


  • [Publication VI] S. Chandrasekhar (1962), Proc. 4th U. S. Nat. Congress of Applied Mechanics, pp. 9 - 14: An approach to the theory of the equilibrium and the stability of rotating masses via the virial theorem and its extensions
  • [Publication XII] S. Chandrasekhar & N. R. Lebovitz (1962), ApJ, 136, 1105: On the occurrence of multiple frequencies and beats in the β Canis Majoris stars
  • [Publication XVII] S. Chandrasekhar & N. R. Lebovitz (1963), ApJ, 138, 185: Non-radial oscillations and the convective instability of gaseous masses
  • [Publication XVIII] S. Chandrasekhar & P. H. Roberts (1963), ApJ, 138, 801: The ellipticity of a slowly rotating configuration
  • [Publication XXII] S. Chandrasekhar (1964), Lectures in Theoretical Physics, Vol. VI, Boulder 1963 (Boulder: University of Colorado Press), pp. 1 - 72: The higher order virial equations and their applications to the equilibrium and stability of rotating configurations
  • [Publication XXVII] N. R. Lebovitz (1965), lecture notes. Inst. Ap., Cointe-Sclessin, Belgium, p. 29: The Riemann ellipsoids
  • [Publication XXXIII] S. Chandrasekhar (1967), Communications on Pure and Applied Mathematics, 20, 251: Ellipsoidal figures of equilibrium — an historical account
  • [Publication XXXIV] N. R. Lebovitz (1967), Annual Review of Astronomy and Astrophysics, 5, 465: Rotating fluid masses

See Also


Whitworth's (1981) Isothermal Free-Energy Surface

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