3Dconfigurations/RiemannEllipsoids: Difference between revisions
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Excerpt from p. 539 of R. Baker, C. Christenson & H. Orde (2004): | |||
<font color="darkgreen">"Newton first showed that the departure of the figure of the earth from a sphere is due to its rotation. Jacobi showed in 1834 that gravitational equilibrium of a rotating spheroid is consistent with three distinct axes if the angular momentum exceeds a critical value. Direchlet had posed and partially analyzed the conditions for a configuration which is an ellipsoid varying with time, such that the motion in an inertial frame, is linear in the coordinates. His results were edited posthumously by Dedekind in 1860.</font> In his published work dated 1961 — five years before his death — <font color="darkgreen">Riemann took up this problem of Direchlet …"</font> NOTE: | |||
=Riemann (1826 - 1866)= | |||
=See Also= | =See Also= | ||
Revision as of 17:54, 17 June 2021
Background
Excerpt from p. 539 of R. Baker, C. Christenson & H. Orde (2004):
"Newton first showed that the departure of the figure of the earth from a sphere is due to its rotation. Jacobi showed in 1834 that gravitational equilibrium of a rotating spheroid is consistent with three distinct axes if the angular momentum exceeds a critical value. Direchlet had posed and partially analyzed the conditions for a configuration which is an ellipsoid varying with time, such that the motion in an inertial frame, is linear in the coordinates. His results were edited posthumously by Dedekind in 1860. In his published work dated 1961 — five years before his death — Riemann took up this problem of Direchlet …" NOTE:
Riemann (1826 - 1866)
See Also
- Jacobi (1834)
- Dedekind (1860)
- Bernhard Riemann (1876) Gesammelte Mathematische Werke und Wissenschaftlicher, especially Chapter X (p. 168) titled (something along the following line), "A Contribution to Research on Rotating Ellipsoidal Fluids"
- S. Chandrasekhar (1965), ApJ, 142, 890 - 961. The Equilibrum and the Stability of the Riemann Ellipsoids. I. — This work is referenced as Paper XXV in EFE and focuses on S-type Riemann ellipsoids.
- S. Chandrasekhar (1966), ApJ, 145, 842 - 877. The Equilibrum and the Stability of the Riemann Ellipsoids. II. — This work is referenced as Paper XXVIII in EFE and focuses on Riemann ellipsoids of Types I, II and III.
- Chandrasekhar & Lebovitz (1990)
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