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Mathematics
Linear and Abstract Algebra
Spherical coordinates via a rotation matrix
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[QUOTE="ShayanJ, post: 5488387, member: 160907"] This is not the usual spherical coordinates. The correct usual ones are: ## x=\rho \sin\theta \cos\phi \\ y=\rho \sin \theta \sin\phi \\ z=\rho \cos\theta ## You don't get the wrong stuff. Its just a convention. Conventions are just arbitrary choices that don't change the results but of course you need to be consistent about them. You can't use one definition of spherical coordinates for some part of the problem and another definition for another part. This is what makes you think this convention gives the wrong stuff. As long as you're consistent, it doesn't matter what definition you use. So you're free to use this definition of spherical coordinates but you need to be careful that anywhere you see spherical coordinates, you should make sure you can make it consistent with this definition you're using. There is nothing wrong with his method. And the reason he gets different results than usual [B]is not his method![/B] His method can be used to find out the definition for the usual convention of spherical coordinates too. What makes he get different results, [B]is just the names he assigns to the angles and the axis he chose from which he measures [/B]## \theta ##. Rename ## \phi \to \theta ## and ## \theta \to \phi ## and measure the new named ## \phi ## from the x-axis instead of the y-axis that he uses. Then do the calculations as he explains and you'll get the usual definition of the spherical coordinates. [/QUOTE]
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Spherical coordinates via a rotation matrix
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