Information Technology Reference
In-Depth Information
FIGURE 9.7
Differential areas for two- and three-dimensional problems.
Similarly,
∂
d
x
1
∂η
∂
x
2
∂η
∂
x
3
∂η
r
2
=
η
From vector algebra, the magnitude of the cross-product of two vectors is equal to the area of
the parallelogram formed with these vectors as two sides. Thus,
r
2
|=
g
1
+
g
3
1
/
2
d
g
2
+
dS
=|
r
1
×
ξ
d
η
(9.104)
with
g
1
=
∂
x
2
∂ξ
∂
∂η
−
∂
x
3
x
3
∂ξ
∂
x
2
∂η
=
∂
x
3
∂ξ
∂
∂η
−
∂
x
1
x
1
∂ξ
∂
x
3
∂η
g
2
=
∂
∂
∂η
−
∂
∂
x
1
∂ξ
x
2
x
2
∂ξ
x
1
∂η
g
3
Search WWH ::
Custom Search