# User:Tohline/Appendix/Ramblings/ConcentricEllipsodalCoordinates

(Difference between revisions)
 Revision as of 07:49, 26 October 2020 (view source)Tohline (Talk | contribs) (Created page with ' =Concentric Ellipsoidal (T6) Coordinates= {{LSU_HBook_header}} ==Back…')← Older edit Revision as of 08:01, 26 October 2020 (view source)Tohline (Talk | contribs) (→Concentric Ellipsoidal (T6) Coordinates)Newer edit → Line 6: Line 6: ==Background== ==Background== - Building on our [[User:Tohline/Appendix/Ramblings/DirectionCosines|general introduction to ''Direction Cosines'']] in the context of orthogonal curvilinear coordinate systems, here we detail the properties of [https://en.wikipedia.org/wiki/Elliptic_cylindrical_coordinates Elliptic Cylinder Coordinates].  First, we present this coordinate system in the manner described by [[[User:Tohline/Appendix/References#MF53|MF53]]]; second, we provide an alternate presentation, obtained from Wikipedia; then, third, we investigate whether or not a related coordinate system based on ''concentric'' (rather than ''confocal'') elliptic surfaces can be satisfactorily described. + Building on our [[User:Tohline/Appendix/Ramblings/DirectionCosines|general introduction to ''Direction Cosines'']] in the context of orthogonal curvilinear coordinate systems, and on our previous development of [[User:Tohline/Appendix/Ramblings/T3Integrals|T3]] (concentric oblate-spheroidal) and [[User:Tohline/Appendix/Ramblings/EllipticCylinderCoordinates#T5_Coordinates|T5]] (concentric elliptic) coordinate systems, here we explore the creation of a concentric ellipsoidal (T6) coordinate system.  This is motivated by our [[User:Tohline/ThreeDimensionalConfigurations/Challenges#Trial_.232|desire to construct a fully analytically prescribable model of a nonuniform-density ellipsoidal configuration that is an analog to Riemann S-Type ellipsoids]]. - + =See Also= =See Also=

# Concentric Ellipsoidal (T6) Coordinates

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## Background

Building on our general introduction to Direction Cosines in the context of orthogonal curvilinear coordinate systems, and on our previous development of T3 (concentric oblate-spheroidal) and T5 (concentric elliptic) coordinate systems, here we explore the creation of a concentric ellipsoidal (T6) coordinate system. This is motivated by our desire to construct a fully analytically prescribable model of a nonuniform-density ellipsoidal configuration that is an analog to Riemann S-Type ellipsoids.