Difference between revisions of "User:Tohline/AxisymmetricConfigurations/SolvingPE"
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<table border="1" align="center" cellpadding="10" width="85%"> | <table border="1" align="center" cellpadding="10" width="85%"> | ||
<tr> | |||
<td align="center" colspan="2"> | |||
<table border="0" cellpadding="5" align="center"> | |||
<tr> | |||
<td align="right"> | |||
<math>~\Phi(R_*,Z_*)</math> | |||
</td> | |||
<td align="center"> | |||
<math>~=</math> | |||
</td> | |||
<td align="left"> | |||
<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> | |||
</td> | |||
</tr> | |||
</table> | |||
where, | |||
<table border="0" cellpadding="5" align="center"> | |||
<tr> | |||
<td align="right"> | |||
<math>~\mu^2</math> | |||
</td> | |||
<td align="center"> | |||
<math>~=</math> | |||
</td> | |||
<td align="left"> | |||
<math>~ | |||
\biggl[\frac{4R_*\varpi}{(R_* + \varpi)^2 + (Z_* - z)^2} \biggr] \, . | |||
</math> | |||
</td> | |||
</tr> | |||
</table> | |||
</td> | |||
</tr> | |||
<tr> | <tr> | ||
<td align="center" colspan="2"> | <td align="center" colspan="2"> | ||
Revision as of 03:46, 29 July 2018
Common Theme: Determining the Gravitational Potential for Axisymmetric Mass Distributions
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Dyson-Wong Tori |
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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. |
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Using Toroidal Coordinates to Determine the Gravitational Potential |
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