Biomedical Engineering Reference
In-Depth Information
0.4
0.3
0.2
0.1
0.0
0.0
0.2
0.4
0.6
0.8
1.0
FIGURE 7.8
Nonoptimality measure for the constant-force and power-law controls.
the control of Eq. (7.62) with the parameters of Eqs. (7.69) and (7.70);
and
J
1
(u
0
)
denotes the function of Eqs. (7.46) and (7.47) that determines
the minimum deceleration distance of the object for the optimal control of
(7.44) and (7.45).
The definitions of these functions imply that
1
η
(
7
.
57
)
=
3
,
η
(
7
.
62
)
=
0 f
≥
1
.
(7.72)
The graphs of the functions
η
(
7
.
57
)
()
(solid curve) and
η
(
7
.
62
)
()
(dashed
line) for
<
1 are plotted in Fig. 7.8.
REFERENCES
Cheng, Z. Q., Pilkey, W. D., Crandall J. R., Bass, C. R., and Darvish, K., 1999,
Limiting performance of helmets for the prevention of head injury,
Shock and
Vibration
, Vol. 6, pp. 299 - 320.
Gadd, C. W., 1966, Use of a weighted-impulse criterion for estimating injury
hazard, Paper 660793,
Proceedings of the 10th Stapp Car Crash Conference
,
Society of Automotive Engineers. Warrendale, PA, pp. 164 - 174.
Gurdjian, E. S., Hodgsom, V. R., Hardy, W. G., Patrick, L. M., and Lissner, H. R.,
1964, Evaluation of the protective characteristics of helmets in sports,
Journal
of Trauma
, Vol. 4, pp. 273 - 286.
Gurdjian, E. S., Lissner, H. R., Latimer, F. R., Haddad, B. F., and Webster, J.
E., 1953, Quantitative determination of acceleration and intercranial pressure in
experimental head injury,
Neurology
, Vol. 3, pp. 417 - 423.
Gurdjian, E. S., Roberts, V. L., and Thomas, L. M., 1966, Tolerance curve of
acceleration and intercranial pressure and protective index in experimental head
injury,
Journal of Trauma
, Vol. 6, pp. 600 - 604.
Hutchinson, J., Kaiser, M. J., and Lankarani, M. H., 1998, The head injury criterion
(HIC) functional,
Applied Mathematics and Computation
, Vol. 96, pp. 1 - 16.
Lockett, F. J., 1985, Biomechanics justification of empirical head tolerance criteria,
Journal of Biomechanics
, Vol. 18, pp. 217 - 245.
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