Difference between revisions of "User:Tohline/AxisymmetricConfigurations/SolvingPE"

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! style="height: 150px; width: 150px; background-color:lightblue;" |[[User:Tohline/AxisymmetricConfigurations/PoissonEq#Solving_the_.28Multi-dimensional.29_Poisson_Equation_Numerically|Solving the<br /> Poisson Equation]]
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[[User:Tohline/AxisymmetricConfigurations/PoissonEq#Solving_the_.28Multi-dimensional.29_Poisson_Equation_Numerically|Solving the Poisson Equation]]  You have arrived at this page from our [[User:Tohline/H_BookTiledMenu#Axisymmetric_Equilibrium_Structures|''Tiled Menu'']] by clicking on the chapter title that is also referenced in the panel of the following table that is colored light blue.  You may proceed directly to that chapter by clicking (again) on the same chapter title, as it appears in the table.  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" presented in the top panel of the table.
[[User:Tohline/AxisymmetricConfigurations/PoissonEq#Solving_the_.28Multi-dimensional.29_Poisson_Equation_Numerically|Solving the Poisson Equation]]  You have arrived at this page from our [[User:Tohline/H_BookTiledMenu#Axisymmetric_Equilibrium_Structures|''Tiled Menu'']] by clicking on the chapter title that is also referenced in the panel of the following table that is colored light blue.  You may proceed directly to that chapter by clicking (again) on the same chapter title, as it appears in the table.  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" presented in the top panel of the table.

Revision as of 03:56, 29 July 2018

Common Theme: Determining the Gravitational Potential for Axisymmetric Mass Distributions

Whitworth's (1981) Isothermal Free-Energy Surface
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You have arrived at this page from our Tiled Menu by clicking on the chapter title that is also referenced in the panel of the following table that is colored light blue. You may proceed directly to that chapter by clicking (again) on the same chapter title, as it appears in the table. 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" presented in the top panel of the table.


<math>~\Phi(R_*,Z_*)</math>

<math>~=</math>

<math>~ - \frac{G}{\pi} \iint\limits_\mathrm{config} \biggl[ \frac{\mu}{(R_* \varpi)^{1 / 2}} \biggr] K(\mu) \rho(\varpi, z) 2\pi \varpi d\varpi dz \, ,</math>

where,

<math>~\mu^2</math>

<math>~=</math>

<math>~ \biggl[\frac{4R_*\varpi}{(R_* + \varpi)^2 + (Z_* - z)^2} \biggr] \, . </math>

Dyson-Wong Tori
(Thin Ring Approximation)

Solving the
Poisson Equation

Solving the Poisson Equation You have arrived at this page from our Tiled Menu by clicking on the chapter title that is also referenced in the panel of the following table that is colored light blue. You may proceed directly to that chapter by clicking (again) on the same chapter title, as it appears in the table. 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" presented in the top panel of the table.

Using Toroidal Coordinates to Determine the Gravitational Potential

Wong's (1973) Analytic Potential

Trova, Huré & Hersant (2012)

Related Discussions

Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
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Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation

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