Civil Engineering Reference
In-Depth Information
Z
z
d
z
l
c
z
0
X
x
0
β
x
l
b
x
a
Figure 4.3.
Example 4.2 Rotation,
b
.
dxsin
xabxcos
=
=−=
b
−
z sin
b
l
0
0
zcd
=+
=
zcos
b
+
xsin
b
l
0
0
yy
l
=
0
The equations for
x
,
y
, and
z
can be represented in matrix form as follows:
cos
0
010
0
β
−
sin
β
x
y
z
x
y
z
o
l
=
(4.2)
o
l
sin
β
cos
β
o
l
Example 4.3
Rotation matrix,
g
Derive the gamma,
g
, rotation matrix.
The following variables are represented in Figure 4.4 and are used to
develop
g
. The location of
x
remains unchanged since rotation is occurring
about that axis.
g
= rotation about global
X
axis from the global to the local system
(
y
0
,
z
0
) = global coordinate location
(
y
l
,
z
l
) = local coordinate location
aycos
bzsin
czcos
dysin
=
=
=
=
g
g
g
g
0
0
0
0
