where
is the ath partial derivative in curvilinear coordinates, Ac a vector and êc a basis vector.
because that resolves to (after many headaches, deriving the derivatives of basis vectors and general cursing):
where ha would be the Lamé-coefficients of the specific basis. This is the expression for the gradient of a vector-field, not a scalar field, which should not come as a surprise of course, since (Acêc) is a vector.
Should not come as a surprise. Surprised the hell out of me, though.
Apparently I have nearly managed to forget everything I ever learned about vector and tensor calculus - so I know what I will be doing the next couple of days...
Edit: Formulas generated via the excellent Texify webpage. If you can't see any, then Texify is dead or down - sorry about that!
Edit the second: Put in the formulas as images, so everybody can see them, even if Texify is acting up - thanks Stephanie for pointing that out!.
Catchy title, you wild man, you. Nothing gets a girl all excited like curvilinear coordinates.
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I couldn't see the formulas, but, let's face it, I haven't done math like that in decades. If I saw it, I would only be humiliated.
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ReplyDeleteI know Stephanie - something I'll try at the next party for sure! Nothing beats 'May I do vector calculus on your curvilinear coordinate system' for a pick-up line ;)
ReplyDeleteBtw, I fixed the formulas, if you want to bask in the glory that is the gradient of a vector-field.
Not that I'm not fond of you, Boris, but I really don't.
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