AxisymmetricConfigurations/SolvingPE

Common Theme: Determining the Gravitational Potential for Axisymmetric Mass Distributions

Solving the Poisson Equation

You have arrived at this page from our Tiled Menu by clicking on the chapter title that is also identified, below, by the light-blue-colored icon. You may proceed directly to that chapter by clicking (again) on that highlighted chapter icon. However, we have brought you to this intermediate page in order to bring to your attention that there are a number of additional chapters that have a strong thematic connection to the chapter you have selected. The common thread is the "Key Equation" titled, Gravitational Potential of an Axisymmetric Mass Distribution, that appears at the top of the following set of chapter synopses.  
 
 
 
 

See Also

• Lord Rayleigh (1917, Proc. Royal Society of London. Series A, 93, 148-154) — On the Dynamics of Revolving Fluids
• P. S. Marcus, W. H. Press, & S. A. Teukolsky (1977, ApJ, 214, 584- 597) — Stablest Shapes for an Axisymmetric Body of Gravitating, Incompressible Fluid (includes torus with non-uniform rotation)

1. Shortly after their equation (3.2), Marcus, Press & Teukolsky make the following statement: "… we know that an equilibrium incompressible configuration must rotate uniformly on cylinders (the famous "Poincaré-Wavre" theorem, cf. Tassoul 1977, &Sect;4.3) …"

• Referring to our accompanying discussion of Type 1 Riemann ellipsoids, it seems that uniform rotation on cylinders is not required. What's going on?