Parabolic Coordinate System Help?

Question

Equations of Transformation.
x = εηcos Φ, y = εηsin Φ, z = 1/2(η^2 - ε^2).

How do I find the Scale factors h(subscript ε), h(subscript η), h(subscript Φ)?

You can use E's n's, or o's for the Greek symbols..

Answer 1

h_ε = sqrt[(∂x/∂ε)² + (∂y/∂ε)² + (∂z/∂ε)²] = sqrt(ε² + η²)
h_η = sqrt[(∂x/∂η)² + (∂y/∂η)² + (∂z/∂η)²] = sqrt(ε² + η²)
h_Φ = sqrt[(∂x/∂Φ)² + (∂y/∂Φ)² + (∂z/∂Φ)²] = εη

Answer 2

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Parabolic Coordinate System Help?
Equations of Transformation.
x = εηcos Φ, y = εηsin Φ, z = 1/2(η^2 - ε^2).

How do I find the Scale factors h(subscript ε), h(subscript η), h(subscript Φ)?

You can use E's n's, or o's for the Greek symbols..