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simplethinker
snjwffl
Active Member
Joined: 25 Jul 2006
Posts: 700
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 Posted: 27 May 2008 12:52:21 am Post subject: |
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I'm not sure how high into mathematics people here have gotten, but I've posted this in a couple of math forums and didn't get a single response, and since UTI is sort of a math forum (calculators do math, at least they're supposed to) I'm posting it here:
I'm reading a book on tensor calculus and since there are few practice problems I've been trying to solve problems from basic vector calculus using tensors.
What I thought would be one of the easiest things to do was to calculate divergence in some common coordinate systems (contract over the covariant derivative relative to the Christoffel symbols), but what I end up with doesn't match up with what it should be. The formula for the covariant derivative at Mathworld and Wikipedia both match what my book says and what I've been doing. I've derived the same contracted Christoffel symbols of the second kind (three different ways) as mathworld and wikipedia so I don't think that's the problem.
On mathworld's page on cylindrical coordinates they divide by the scale factor in the very last step deriving the formula for divergence, and on Wikipedia's page on curvilinear coordinates they do the same thing, but I'm not sure why since there's no mention of it in their definitions of the covariant derivative. At first I thought that they multiplied a covariant tensor field by the metric tensor to turn it into a contravariant field so it could be contracted over, but in cylindrical coordinates that didn't work for me either.
This is really starting to bug me, and I'd appreciate any hep anyone can give me.  |
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