Consider the elliptical-cylindrical coordinate system (eta, psi, z), defined by

it was shown that this is an orthogonal coordinate system with scale factors

Determine the dual bases

Burhan Hopper
2020-12-30
Answered

Consider the elliptical-cylindrical coordinate system (eta, psi, z), defined by

it was shown that this is an orthogonal coordinate system with scale factors

Determine the dual bases

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Pohanginah

Answered 2020-12-31
Author has **96** answers

Given that magnitude of gradient along x and y direction is
${h}_{1}={h}_{2}=a{({\text{cosh}}^{2}\text{}\eta -{\mathrm{cos}}^{2}\psi )}^{\frac{1}{2}}.$
and along z direction = h3 =1
Hence delf = vectors in direction of del/magnitude
$=\frac{1}{{(\text{cosh}\eta -{\mathrm{cos}}^{2}\psi )}^{\frac{1}{2}}}\}[\frac{\frac{\partial f}{\partial \eta}}{e1}+\frac{\frac{\partial f}{\partial \mathrm{\setminus}\psi}}{e2}]+e3\frac{\partial f}{\partial z}$

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Change to cylindrical.

spherical:

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