ThreeDimensionalConfigurations/Stability/RiemannEllipsoids

Lebovitz & Lifschitz (1996)

Lebovitz & Lifschitz (1996)

Here we review the work of 📚 N. R. Lebovitz, & A. Lifschitz (1996, ApJ, Vol. 458, pp. 699 - 713) titled, "New Global Instabilities of the Riemann Ellipsoids," and discuss various extensions that have been made to this work. We were prompted to tackle this review by an email received in December 2021 from Howard S. Cohl.  
 
 
 
 
 

Background

In Figure 1, the abscissa is the ratio $b/a$ of semiaxes in the equatorial plane, and the ordinate is the ratio $c/a$ of the vertical semiaxis to the larger of the equatorial semi axes. This diagram shows what 📚 Lebovitz & Lifschitz (1996) — hereafter, LL96 — refer to as "the horn-shaped region of existence of S-type ellipsoids and the Jacobi family;" it underpins all four panels of the LL96 Figure 2.

Figure 1: The Horn-Shaped Region of S-type Ellipsoids

Four example models:

• Riemann Meets COLLADA & Oculus Rift S: (b/a, c/a) = (0.41, 0.385)
• (b/a, c/a) = (0.90, 0.333)
• (b/a, c/a) = (0.74, 0.692)
• (b/a, c/a) = (0.28, 0.256)

See Also

• A library of ellipsoidal harmonics may be available from George Dassios,