Switch the divergence coordinate system

oronanschel · Nov 2, 2011

Homework Statement

i have the divergence in the (x,y,z) Cartesian as [tex]\frac{dA_x}{dx}+\frac{dA_y}{dy}+\frac{dA_z}{dz}[/tex]

and the assignment is to transfer it to cylindrical system [tex](r,{\phi},z)[/tex], by any way i choose.

Homework Equations

tried with the chain rule, but i am doing something wrong, though
i get the gradient in the cylindrical system

HallsofIvy · Nov 2, 2011

It is impossible to tell you what, if anything, you are doing wrong if we cannot see what you did!

oronanschel · Nov 3, 2011

look at 1 then 2

then there is 1+2

in the left side there are some derivatives , and variables
transformation to explain

Handwritten derivation of the divergence in cylindrical coordinates: top line del dot A = (d/dx, d/dy, d/dz)(Ax, Ay, Az) = dAx/dx + dAy/dy + dAz/dz; below, the chain rule expansion of dAx/dx, dAy/dy and dAz/dz in terms of r, theta and z, with the relations x = r cos theta, y = r sin theta, z = z, r = sqrt(x^2 + y^2), theta = arctan(y/x).

Handwritten derivation converting a divergence expression from Cartesian to polar coordinates, with partial derivatives of r and theta with respect to x and y, unit vector relations, and step-labelled equations marked 1, 2 and 1+2.

Handwritten derivation in cylindrical coordinates: partial derivatives of A with respect to r, theta and z expanded using unit vectors r-hat, theta-hat and z-hat, with terms grouped and an inequality to the divergence formula at the bottom.

Switch the divergence coordinate system

Homework Statement

Homework Equations

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