User:Tohline/Appendix/Mathematics/ToroidalSynopsis01

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Synopsis of Toroidal Coordinate Approach

Whitworth's (1981) Isothermal Free-Energy Surface
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Here we attempt to bring together — in as succinct a manner as possible — our approach and C.-Y. Wong's (1973) approach to determining the gravitational potential of an axisymmetric, uniform-density torus that has a major radius, <math>~R</math>, and a minor, cross-sectional radius, <math>~d</math>. The relevant toroidal coordinate system is one based on an anchor ring of major radius,

<math>~a^2 \equiv R^2 - d^2 \, .</math>

See Also

Whitworth's (1981) Isothermal Free-Energy Surface

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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