paraboloidal coordinates

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1: 13.28 Physical Applications

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§13.28(i) Exact Solutions of the Wave Equation

►The reduced wave equation

\nabla^{2}w=k^{2}w

in paraboloidal coordinates,

x=2\sqrt{\xi\eta}\cos\phi

y=2\sqrt{\xi\eta}\sin\phi

z=\xi-\eta

, can be solved via separation of variables

w=f_{1}(\xi)f_{2}(\eta)e^{\mathrm{i}p\phi}

, where …

2: 28.32 Mathematical Applications

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§28.32(ii) Paraboloidal Coordinates

►The general paraboloidal coordinate system is linked with Cartesian coordinates via …

3: 12.17 Physical Applications

… ►In a similar manner coordinates of the paraboloid of revolution transform the Helmholtz equation into equations related to the differential equations considered in this chapter. … …