Biomedical Engineering Reference
In-Depth Information
6.2.1.2 Exact Formula for Energy Exchange within Segments. The
example just discussed illustrates a simple situation in which only one
minimum and maximum occur over the period of interest. If individual
energy components have several maxima and minima, we must calculate
the sum of the absolute energy changes over the time period. The work, W s ,
done on and by a segment during N sample periods is:
N
W s =
1 |
E s |
J
(6.19)
i
=
Assuming that there are no energy exchanges between any of the three
components (Norman et al., 1976), the work done by the segment during the
N sample periods is:
N
E p + | E kt | + | E kr |
W s
=
J
(6.20)
i
=
1
Therefore, the energy W c conserved within the segment during the time is
W s
W c =
W s
J
(6.21)
The percentage energy conservation, C s , during the time of this event is:
W c
W s ×
C s =
100%
(6.22)
If W s
W s , all three energy components are in phase (they have exactly
the same shape and have their minima and maxima at the same time), and
there is no energy conservation. Conversely, as demonstrated by an ideal
pendulum, if W s =
0, then 100% of the energy is being conserved.
6.2.2 Total Energy of a Multisegment System
As we proceed with the calculation of the total energy of the body, we merely
sum the energies of each of the body segments at each point in time (Bresler
and Berry, 1951; Ralston and Lukin, 1969; Winter et al., 1976). Thus, the
total body energy E b at a given time is:
B
E b =
E si
J
(6.23)
i
=
1
where: E si
=
total energy of i th segment at that point in time
B
=
number of body segments
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