Difference between revisions of "User:Tohline/2DStructure/ToroidalCoordinateIntegrationLimits"

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(→‎Preamble: Insert my schematic image of Apollonian circles)
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==Preamble==
==Preamble==
Some useful figures:
*
* [https://upload.wikimedia.org/wikipedia/commons/b/b2/Apollonian_circles.svg]


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Revision as of 01:41, 9 November 2015

Toroidal-Coordinate Integration Limits

In support of our accompanying discussion of the gravitational potential of a uniform-density circular torus, here we explain in detail what limits of integration must be specified in order to accurately determine the volume — and, hence also the total mass — of such a torus using toroidal coordinates.


Whitworth's (1981) Isothermal Free-Energy Surface
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Preamble

Apollonian Circles (schematic)

(see also Wikipedia's Apollonian Circles)
Figure 2 Figure 3

Apollonian Circles

Diagram of Torus and Toroidal Coordinates

Diagram of Torus and xi_2-constant Toroidal Coordinate curve

See Also

 

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