Biomedical Engineering Reference
In-Depth Information
y
y
F
y
e
y
d
y
e
y
d
x
e
x
F
x
e
x
z
z
x
x
Figure 2.18
Application of the corkscrew rule.
F
d
P
d
n
d
t
e
y
e
x
e
z
Figure 2.19
The moment of a force acting at point Q with respect to point P.
d
t
, parallel to the line of action. Then, we can write for the moment
M
of vector
F
with respect to point P:
M
=
d
×
F
=
(
d
n
+
d
t
)
×
F
=
d
n
×
F
.
(2.66)
The definition in Eq. (
2.63
) also assures that the resulting moment is the zero
vector if the point P is located on the line-of-action of the force vector (in that
case
d
n
=
0).
In the general three-dimensional case, see Fig.
2.16
, the procedure to determine
the moment of the force
F
with respect to the point P is comparable. The column
representations of the vectors
d
and
F
in this case are given by
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
d
x
d
y
d
z
F
x
F
y
F
z
∼
=
,
∼
=
,
(2.67)
and the resulting column representation of the moment follows from Eq. (
1.35
):
⎡
⎣
⎤
⎦
d
y
F
z
−
d
z
F
y
∼
=
d
z
F
x
−
d
x
F
z
.
(2.68)
d
x
F
y
−
d
y
F
x
