What do you understand by orthogonal curvilinear coordinates ? obtain expression for gradient of a scaler in this coordinate system?

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What do you understand by orthogonal curvilinear coordinates ? obtain expression for gradient of a scaler in this coordinate system?

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What do you understand by orthogonal curvilinear coordinates ? obtain ...

A set of coordinates u = u(x, y, z), v = v(x, y, z) and w = w(x, y, z) where the directions at any point indicated by u, v and w are orthogonal (perpendicular) to each other is referred to as a set of orthogonal curvilinear coordinates.
The gradient is defined by df = ∇f · dx.
We can also express df as, df =(∂f/ ∂uj) duj
or ∇f = (Ej/ hj)( ∂f/ ∂uj)
∇ = (Ej /hj) (∂/ ∂uj)
[since, Eˆj = (∂x/ ∂sj)( ∂sj/ duj), where ∂sj
is the elementary arc length along γj]

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What do you understand by orthogonal curvilinear coordinates ? obtain ...

A scalar system is a directional one i think the curves get cancelled each other by co ordinates sign that could happen

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What do you understand by orthogonal curvilinear coordinates ? obtain expression for gradient of a scaler in this coordinate system?

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