Biomedical Engineering Reference
In-Depth Information
e
z
M
3
M
2
e
y
M
1
e
x
Figure 2.23
Moment vectors identified by means of scalars.
e
z
M
3
M
2
e
y
M
1
e
x
Figure 2.24
Moment vectors identified by means of vectors and having a single arrowhead.
M
1
=
M
1
e
x
,
M
2
=−
M
2
e
y
,
M
3
=
M
3
e
z
. (2.70)
Notice that the moment vector
M
2
is pointing into the negative
y
-direction. Alter-
natively, if in the figure the moment vectors are drawn with a single arrowhead, as
in Fig.
2.24
, they denote actual vectors and are identified with vector symbols.
Exercises
2.1
The vector bases
{
e
1
,
e
2
,
e
3
}
and
{
1
,
2
,
3
}
are orthonormal. The following
relations exist:
2
√
2
2
√
2
1
1
1
=
e
1
+
e
2
2
√
2
2
√
2
1
1
2
=−
e
1
+
e
2
e
3
.
The force vector
F
is defined with respect to basis
3
=
{
e
1
,
e
2
,
e
3
}
according to:
F
=
e
3
.
(a) Determine the decomposition of
F
with respect to basis
2
e
1
+
3
e
2
−
4
{
1
,
2
,
3
}
.
