Civil Engineering Reference
In-Depth Information
where the length of vector
u
is given by
2
2
2
(2.12)
u
u
u
u
x
y
z
v
T
u
u
c
Figure 1.4
Projection of vector
Derivatives of vectors
The derivatives of the displacement vector may be written as
w
-½
u
w
u
w
u
-½
-½
x
x
x
°°
°°
°°
w
y
w
x
w
z
°°
°°
°°
w
u
°°
w
u
w
u
w
u
°°
w
u
w
u
°°
°°
(2.13)
y
y
y
u
;
u
;
u
®¾
®¾
®¾
,
x
,
y
,
z
w
x
w
x
w
y
w
y
w
z
w
z
°°
°°
°°
°°
w
u
°°
°°
w
u
w
u
z
z
z
°°
°°
°°
w
x
w
z
w
y
¯¿
°
¯¿
¯¿
In indicial notation we simply write
w
u
i
(2.14)
u
i
,
j
w
x
j
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