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

Burhan Hopper 2020-12-30 Answered

Consider the elliptical-cylindrical coordinate system (eta, psi, z), defined by x=a cosh ηcosψ,y=asinh ηsinψ;z=z, η GE 0,0 LE ψLE 2π, zR.In PS6
it was shown that this is an orthogonal coordinate system with scale factors h1=h2=a(cosh2 ηcos2ψ)12.
Determine the dual bases (E1,E2,E3),(η,ηψ,z).Showt:^f=a1a(cosh2eatcossψ)12[fηe1+fψe2+fze3,fwhere(e1,e2,e3) denotes the unit coordinate basis.

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Expert Answer

Pohanginah
Answered 2020-12-31 Author has 96 answers
Given that magnitude of gradient along x and y direction is h1=h2=a(cosh2 ηcos2ψ)12. and along z direction = h3 =1 Hence delf = vectors in direction of del/magnitude =1(coshηcos2ψ)12}[fηe1+fψe2]+e3fz
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