About the Project
NIST

ellipsoidal coordinates

AdvancedHelp

(0.001 seconds)

4 matching pages

1: 29.18 Mathematical Applications
§29.18(ii) Ellipsoidal Coordinates
The wave equation (29.18.1), when transformed to ellipsoidal coordinates α , β , γ : …
29.18.10 u ( α , β , γ ) = u 1 ( α ) u 2 ( β ) u 3 ( γ ) ,
2: 23.21 Physical Applications
§23.21(iii) Ellipsoidal Coordinates
Ellipsoidal coordinates ( ξ , η , ζ ) may be defined as the three roots ρ of the equation …The Laplacian operator 2 1.5(ii)) is given by
23.21.2 ( η - ζ ) ( ζ - ξ ) ( ξ - η ) 2 = ( ζ - η ) f ( ξ ) f ( ξ ) ξ + ( ξ - ζ ) f ( η ) f ( η ) η + ( η - ξ ) f ( ζ ) f ( ζ ) ζ ,
3: 30.13 Wave Equation in Prolate Spheroidal Coordinates
The coordinate surfaces ξ = const . are prolate ellipsoids of revolution with foci at x = y = 0 , z = ± c . …
4: 30.14 Wave Equation in Oblate Spheroidal Coordinates
The coordinate surfaces ξ = const . are oblate ellipsoids of revolution with focal circle z = 0 , x 2 + y 2 = c 2 . …