Biomedical Engineering Reference
In-Depth Information
can even account for the calcium activation of the muscle. However, a discussion
of these models is beyond the scope of this topic.
4.4
Elastic fibres in three dimensions
The above one-dimensional force extension relation can be generalized to a
fibre/spring having an arbitrary position in three-dimensional space. The locations
of the end points of the spring, say A and B, in the unstretched, initial configura-
tion are denoted by
x
0,A
and
x
0,B
, respectively, see Fig.
4.7
.
The initial length of the spring
0
follows from
0
=|
x
0,
B
−
x
0,
A
|
.
(4.12)
The initial orientation of the spring in space is denoted by the vector
a
0
having
unit length that follows from
x
0,B
−
x
0,A
a
0
=
.
(4.13)
|
x
0,B
−
x
0,A
|
In the stretched, current configuration, the positions of the end points of the spring
are denoted by
x
A
and
x
B
. Therefore the current length
of the spring can be
computed from
=|
x
B
−
x
A
|
,
(4.14)
while the current orientation in space of the spring may be characterized by the
vector
a
of unit length:
x
A
|
x
B
−
x
A
|
x
B
−
a
=
.
(4.15)
a
0
F
A
x
0,B
a
x
0,A
x
A
x
B
F
B
Figure 4.7
Spring in three-dimensional space.
