OrthogonalCurvilinearCoordinates

OrthogonalCurvilinearCoordinates - Div Grad and Curl in...

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Div, Grad and Curl in Orthogonal Curvilinear Coordinates The treatment here is standard, following that in Abraham and Becker, Classical Theory of Electricity and Magnetism. Problems with a particular symmetry, such as cylindrical or spherical, are best attacked using coordinate systems that take full advantage of that symmetry. For example, the Schrödinger equation for the hydrogen atom is best solved using spherical polar coordinates. For this and other differential equation problems, then, we need to find the expressions for differential operators in terms of the appropriate coordinates. We only look at orthogonal coordinate systems, so that locally the three axes (such as r , θ , ϕ ) are a mutually perpendicular set. We denote the curvilinear coordinates by ( u 1 , u 2 , u 3 ). The standard Cartesian coordinates for the same space are as usual ( x , y , z ). Suppose now we take an infinitesimally small cube with edges parallel to the local curvilinear coordinate directions, and therefore with faces satisfying u i
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This note was uploaded on 12/07/2011 for the course PHYSICS 751 taught by Professor Michaelfowler during the Fall '07 term at UVA.

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OrthogonalCurvilinearCoordinates - Div Grad and Curl in...

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