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Posts Found in a Bathtub
Jun. 29th, 2006
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Jun. 29th, 2006
letters!
Jun
.
29th
,
2006
08:29 am
A neat proof of Lame's formula for the Laplacian.
Let u be a compactly supported test function.
The x
i
are orthogonal, so
∂x
a
/
&partξ
i
∂x
b
/
∂ξ
i
is g
aa
if a = b, and zero otherwise. Also, the Jacobian is √(g
11
g
22
g
33
) = √g.
So,
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