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## Homework Statement

Transform the equilibrium equations from cartesian to polar coordinates using x = rcos(theta) and y = rsin(theta):

[tex]\frac{\partial\sigma_{xx}}{\partial{x}} + \frac{\partial\sigma_{xy}}{\partial{y}} = 0[/tex]

[tex]\frac{\partial\sigma_{yx}}{\partial{x}} + \frac{\partial\sigma_{yy}}{\partial{y}} = 0[/tex]

The answer is given as:

[tex]\frac{\partial\sigma_{r}}{\partial{r}} + \frac{1}{r}\frac{\partial\sigma_{r\theta}}{\partial{\theta}} + \frac{\sigma_{r} - \sigma_{\theta}}{r} = 0[/tex]

[tex]\frac{\partial\sigma_{r\theta}}{\partial{r}} + \frac{1}{r}\frac{\partial\sigma_{\theta}}{\partial{\theta}} + \frac{2\sigma_{r\theta}}{r} = 0[/tex]

## The Attempt at a Solution

I've no idea how to proceed. I know how to obtain the result using a free body diagram (which is how we're supposed to solve the problem) but am curious as to how to do it by applying the transformations.

We've covered changing coordinates for integrals in vector calculus but never anything like the above. If anybody can help get me started or point me to some material that'd help me get my head around it, it'd be very much appreciated.

Not sure in which section to post it where to post it but this board seemed as good as any.