# ellipsoidal coordinates

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## 4 matching pages

##### 1: 23.21 Physical Applications
###### §23.21(iii) EllipsoidalCoordinates
Ellipsoidal coordinates $(\xi,\eta,\zeta)$ may be defined as the three roots $\rho$ of the equation …The Laplacian operator $\nabla^{2}$1.5(ii)) is given by
23.21.2 $(\eta-\zeta)(\zeta-\xi)(\xi-\eta)\nabla^{2}=(\zeta-\eta)f(\xi)f^{\prime}(\xi)% \frac{\partial}{\partial\xi}+(\xi-\zeta)f(\eta)f^{\prime}(\eta)\frac{\partial}% {\partial\eta}+(\eta-\xi)f(\zeta)f^{\prime}(\zeta)\frac{\partial}{\partial% \zeta},$
##### 2: 29.18 Mathematical Applications
###### §29.18(ii) EllipsoidalCoordinates
The wave equation (29.18.1), when transformed to ellipsoidal coordinates $\alpha,\beta,\gamma$: …
29.18.10 $u(\alpha,\beta,\gamma)=u_{1}(\alpha)u_{2}(\beta)u_{3}(\gamma),$
##### 3: 30.13 Wave Equation in Prolate Spheroidal Coordinates
The coordinate surfaces $\xi=\mbox{const}.$ are prolate ellipsoids of revolution with foci at $x=y=0$, $z=\pm c$. …
##### 4: 30.14 Wave Equation in Oblate Spheroidal Coordinates
The coordinate surfaces $\xi=\mbox{const}.$ are oblate ellipsoids of revolution with focal circle $z=0$, $x^{2}+y^{2}=c^{2}$. …