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====Sheroidal & Spheroidal-Like==== {| class="Chap11B" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px; border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black; " |<b>Incompressible<br />Sequences</b> | ! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[Appendix/Ramblings/MacSphCriticalPoints|Critical Points<br />Along<br />Maclaurin Spheroid<br />Sequence]] | ! style="height: 150px; width: 150px;" |[[Apps/EriguchiHachisu/Models|Eriguchi, Hachisu<br />& Colleagues]] |} <p> </p> {| class="Chap11B" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px; border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black; " |<b>Linear<br />Analysis<br /> of<br />Bar-Mode<br />Instability</b> | ! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[Apps/RotatingPolytropes/BarmodeIncompressible|Bifurcation<br />from<br />Maclaurin<br />Sequence]] | ! style="height: 150px; width: 150px;" |[[Apps/RotatingPolytropes/BarmodeEigenvector|Traditional<br />Analyses]] |} <p> </p> * [https://ui.adsabs.harvard.edu/abs/1949ApJ...109..149C/abstract T. G. Cowling & R. A. Newing (1949)], ApJ, 109, 149: ''The Oscillations of a Rotating Star'' * [https://ui.adsabs.harvard.edu/abs/1965ApJ...141..210C/abstract M. J. Clement (1965)], ApJ, 141, 210: ''The Radial and Non-Radial Oscillations of Slowly Rotating Gaseous Masses'' * [https://ui.adsabs.harvard.edu/abs/1963ApJ...137..777R/abstract P. H. Roberts & K. Stewartson (1963)], ApJ, 137, 777: ''On the Stability of a Maclaurin spheroid of small viscosity'' * [https://ui.adsabs.harvard.edu/abs/1967ApJ...148..825R/abstract C. E. Rosenkilde (1967)], ApJ, 148, 825: ''The tensor virial-theorem including viscous stress and the oscillations of a Maclaurin spheroid'' * [https://ui.adsabs.harvard.edu/abs/1968ApJ...152..267C/abstract S. Chandrasekhar & N. R. Lebovitz (1968)], ApJ, 152, 267: ''The Pulsations and the Dynamical Stability of Gaseous Masses in Uniform Rotation'' * [https://ui.adsabs.harvard.edu/abs/1977ApJ...213..497H/abstract C. Hunter (1977)], ApJ, 213, 497: ''On Secular Stability, Secular Instability, and Points of Bifurcation of Rotating Gaseous Masses'' * [https://ui.adsabs.harvard.edu/abs/1985ApJ...294..474I/abstract J. N. Imamura, J. L. Friedman & R. H. Durisen (1985)], ApJ, 294, 474: ''Secular stability limits for rotating polytropic stars'' <table border="0" align="center" width="100%" cellpadding="1"><tr> <td align="center" width="5%"> </td><td align="left"> <font color="green">The equilibrium models are calculated using the polytrope version (Bodenheimer & Ostriker 1973) of the Ostriker and Mark (1968) self-consistent field (SCF) code … the equilibrium models rotate on cylinders and are completely specified by <math>~n</math>, the total angular momentum, and the specific angular momentum distribution <math>~j(m_\varpi)</math>. Here <math>~m_\varpi</math> is the mass contained within a cylinder of radius <math>~\varpi</math> centered on the rotation axis. The angular momentum distribution is prescribed in several ways: (1) imposing strict uniform rotation; (2) using the same <math>~j(m_\varpi)</math> as that of a uniformly rotating spherical polybrope of index <math>~n^'</math> (see Bodenheimer and Ostriker 1973); and (3) using <math>~j(m_\varpi) \propto m_\varpi</math>, which we refer to as <math>~n^' = L</math>, <math>~L</math> for "linear."</font> </td></tr></table> * [https://ui.adsabs.harvard.edu/abs/1990ApJ...355..226I/abstract J. R. Ipser & L. Lindblom (1990)], ApJ, 355, 226: ''The Oscillations of Rapidly Rotating Newtonian Stellar Models'' * [https://ui.adsabs.harvard.edu/abs/1991ApJ...373..213I/abstract J. R. Ipser & L. Lindblom (1991)], ApJ, 373, 213: ''The Oscillations of Rapidly Rotating Newtonian Stellar Models. II. Dissipative Effects'' * [https://ui.adsabs.harvard.edu/abs/2000ApJ...528..946I/abstract J. N. Imamura, J. L. Friedman & R. H. Durisen (2000)], ApJ, 528, 946: ''Nonaxisymmetric Dynamic Instabilities of Rotating Polytropes. II. Torques, Bars, and Mode Saturation with Applications to Protostars and Fizzlers'' * [https://ui.adsabs.harvard.edu/abs/2003MNRAS.343..619S/abstract M. Shibata, S. Karino, & Y. Eriguchi (2003)], MNRAS, 343, 619 - 626: ''Dynamical bar-mode instability of differentially rotating stars: effects of equations of state and velocity profiles'' * [https://ui.adsabs.harvard.edu/abs/2019ApJ...877....9H/abstract G. P. Horedt (2019)], ApJ, 877, 9: ''On the Instability of Polytropic Maclaurin and Roche ellipsoids'' <p> </p>
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