Gradient, Divergence and Curl in Curvilinear Coordinates

Gradient, Divergence and Curlin Curvilinear CoordinatesAlthough cartesian orthogonal Coordinates are very intuitive and easy to use, it is often foundmore convenient to work with other coordinate systems. Being able to change all variables andexpression involved in a given problem, when a different coordinate system is chosen, is one ofthose skills a physicist, and even more a theoretical physicist, needs to this lecture a general method to express any variable and expression in an arbitrary curvilinearcoordinate system will be introduced and explained. We will be mainly interested to find out gen-eral expressions for the gradient, the Divergence and the curl of scalar and vector fields. Specificapplications to the widely used cylindrical and spherical systems will conclude this The concept of orthogonal Curvilinear coordinatesThe cartesian orthogonal coordinate system is very intuitive and easy to handle.

to yield, eventually, r2’= 1 h uh vh w @ @u h vh w h u @’ @u + @ @v h uh w h v @’ @v + @ @w h uh v h w @’ @w (16) 4 Curl in curvilinear coordinates The curl of a vector eld is another vector eld. Its component along an arbitrary vector n is given by the following expression: [r v] n lim S!0 1 S I v dr (17) where is a curve encircling ...

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  Coordinates, Yield, Curves, Curl, Divergence, Curvilinear, Divergence and curl in curvilinear coordinates, Curl in curvilinear coordinates

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