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=Common Theme: Determining the Gravitational Potential for Axisymmetric Mass Distributions=

You have arrived at this page from our [[H_BookTiledMenu#Axisymmetric_Equilibrium_Structures|''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.

==Chapter Synopses==

===Part I===
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<table border="1" align="center" cellpadding="10" width="85%">
<tr>
<th align="center">Related Chapters (Part I)</th>
</tr>
<tr>
<td align="left" colspan="2">
{| class="Chap22A" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black"
|-
! style="height: 150px; width: 150px; background-color:whiteF;" |[[Apps/DysonWongTori#Thin_Ring_Approximation|Dyson-Wong<br /> Tori]]<br />(Thin Ring Approximation)
|}
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</td>
</tr>
<tr>
<td align="left" colspan="2">
{| class="Chap22B" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black"
|-
! style="height: 150px; width: 150px;" |[[AxisymmetricConfigurations/PoissonEq#Solving_the_.28Multi-dimensional.29_Poisson_Equation_Numerically|Solving the<br /> Poisson Equation]]
|}
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</td>
</tr>
</table>

===Part II===

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<table border="1" align="center" cellpadding="10" width="85%">
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<th align="center">Related Chapter (Part II)</th>
</tr>
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<td align="left" colspan="2">
{| class="Chap22C" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black"
|-
! style="height: 150px; width: 150px; background-color:#D0FFFF;" |[[2DStructure/ToroidalCoordinates#Using_Toroidal_Coordinates_to_Determine_the_Gravitational_Potential|Attempt at<br />Simplification<br /><br /><font color="green" size="+2">&hearts;</font>]]
|}
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</td>
</tr>
</table>

===Part III===
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<table border="1" align="center" cellpadding="10" width="85%">
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<th align="center">Related Chapters (Part III)</th>
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<td align="left" colspan="2">
{| class="Chap22D" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black"
|-
! style="height: 150px; width: 150px; background-color:whiteF;" |[[2DStructure/ToroidalGreenFunction#Using_Toroidal_Coordinates_to_Determine_the_Gravitational_Potential|Using<br /> Toroidal Coordinates<br /> to Determine the<br /> Gravitational<br /> Potential]]
|}
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{| class="Chap22E" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black"
|-
! style="height: 150px; width: 150px; background-color:whiteF;" |[[Apps/Wong1973Potential#Wong.27s_.281973.29_Analytic_Potential|Wong's <br />(1973) <br >Analytic Potential]]
|}
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</table>

=Related Discussions=
<ul>
<li>Common Theme:
<ul>
<li>
Menu Tile:  [[AxisymmetricConfigurations/SolvingPE|Solving the (Axisymmetric) Poisson Equation]]
   <math>\Rightarrow</math>     Points principally to: [[AxisymmetricConfigurations/PoissonEq|AxisymmetricConfigurations/PoissonEq]]
</li>
<li>
Menu Tile:  [[2DStructure/UsingTC|Using Toroidal Coordinates to Determine the Gravitational Potential]]
   <math>\Rightarrow</math>     Points principally to: [[2DStructure/ToroidalGreenFunction|2DStructure/ToroidalGreenFunction]]
</li>
<li>
Menu Tile:  [[2DStructure/TCsimplification|Attempt at Simplification]]
   <math>\Rightarrow</math>     Points principally to: [[2DStructure/ToroidalCoordinates|2DStructure/ToroidalCoordinates]]
</li>
<li>
Menu Tile:  [[Apps/WongAP|Wong's Analytic Potential (1973)]]
   <math>\Rightarrow</math>     Points principally to: [[Apps/Wong1973Potential|Apps/Wong1973Potential]]
</li>
<li>
Menu Tile:  [[Apps/DWT|Dyson-Wong Tori]] (Thin Ring Approximation)
   <math>\Rightarrow</math>     Points principally to: [[Apps/DysonWongTori|Apps/DysonWongTori]]
</li>
</ul>
</li>
<li>
(Apollonian Circles) [[2DStructure/ToroidalCoordinateIntegrationLimits|Toroidal-Coordinates Integration Limits]]
</li>
<li>
[[Appendix/Ramblings/ToroidalCoordinates#Toroidal_Configurations_and_Related_Coordinate_Systems|Determining the Relationships between Toroidal Coordinates and other Coordinate Systems]]
</li>
</ul>

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2DStructure/TCsimplification - Revision history