A biomechanical model of the craniomandibular complex and cervical spine based on the inverted pendulum

Journal of Medical Engineering and Technology

Volumn 22, Issue 6, 1998, Pages 263-269

  Gillies, G T ^a   Broaddus, W C ^b   Stenger, J M ^c   Taylor, A G ^d  

^a University of Virginia   (United States)

^b VIRGINIA COMMONWEALTH UNIVERSITY SCHOOL OF MEDICINE   (United States)

^c Unviersity of Virginia ^*  (United States)

^d UNIVERSITY OF VIRGINIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BONE; JOINTS (ANATOMY); MATHEMATICAL MODELS; MUSCULOSKELETAL SYSTEM; NEUROMUSCULAR REHABILITATION; OSCILLATORS (ELECTRONIC);

BIOMECHANICAL MODEL; CERVICAL SPINE; CRANIOMANDIBULAR COMPLEX; INVERTED PENDULUM;

BIOMECHANICS;

BIOMECHANICS; CERVICAL SPINE; JOINT MOBILITY; JOINT STABILITY; NECK; REVIEW; TEMPOROMANDIBULAR JOINT;

EID: 0032215420     PISSN: 03091902     EISSN: None     Source Type: Journal    
DOI: 10.3109/03091909809010009     Document Type: Review

References (36)

1. CORBEN, H. C., and STEHLE, P., 1960, The inverted pendulum. In Classical Mechanics, 2nd edition (New York: John Wiley & Sons), pp. 67-69.
2. STOKER, J. J., 1966, Nonlinear vibrations. In Mechanical and Electrical Systems (New York: John Wiley & Sons), pp. 202-213.
3. LANDAU, L. D., and LIFSHITZ, E. M., 1976, Motion in a rapidly oscillating field. In Mechanics, 3rd edition (New York: Pergamon Press), pp. 93-95.
4. KAPITZA, P. L., 1965, Dynamical stability of a pendulum when its point of suspension vibrates. In Collected Papers of P. L. Kapitza, Vol. 2, edited by D. ter Haar (New York: Pergamon Press), pp. 714-725.
5. KAPITZA, P. L., 1965, Pendulum with a vibrating suspension. In Collected Papers of P. L. Kapitza, Vol. 2, edited by D. ter Haar (New York: Pergamon Press), pp. 726-737.
6. PHELPS III, F. M., and HUNTER Jr, J. H., 1965, An analytical solution of the inverted pendulum. American Journal of Physics, 33, 285-295.
7. PHELPS III, F. M., and HUNTER Jr, J. H., 1965, The inverted pendulum. American Journal of Physics, 33, 874.
8. PHELPS III, F. M., and HUNTER Jr, J. H., 1966, Reply to Joshi's comments on a damping term in the equations of motion of the inverted pendulum. American Journal of Physics, 34, 533-535.
9. JOSHI, S. S., 1965, Inverted pendulum with damping. American Journal of Physics, 34, 533.
10. NESS, D. J., 1967, Small oscillations of a stabilized, inverted pendulum. American Journal of Physics, 35, 964-967.
11. KALMUS, H. P., 1970, The inverted pendulum. American Journal of Physics, 38, 874-878.
12. YORKE, E. D., 1978, Square-wave model for a pendulum with oscillating suspension. American Journal of Physics, 46, 285-288.
13. FRIEDMAN, M. H., CAMPANA, J. E., KELNER, L., SEELIGER, E. H., and YERGEY, A. L., 1982, The inverted pendulum: a mechanical analog of the quadrupole mass filter. American Journal of Physics, 50, 924-931.
14. MICHAELIS, M. M., 1985, Stroboscopic study of the inverted pendulum. American Journal of Physics, 53, 1079-1083.
15. MILES, J., 1988, Directly forced oscillations of an inverted pendulum. Physics Letters A, 133, 295-297.
16. BLACKBURN, J. A., VIK, S., and WU, B., 1989, Driven pendulum for studying chaos. Review of Scientific Instruments, 60, 422-425.
17. BLACKBURN, J. A., SMITH, H. J. T., and GROØNBECH-JENSEN, N., 1992, Stability and Hopf bifurcations in an inverted pendulum. American Journal of Physics, 60, 903-908.
18. SMITH, H. J. T., and BLACKBURN, J. A., 1992, Experimental study of an inverted pendulum. American Journal of Physics, 60, 909-911.
19. PINOLI, M., BLAIR, D. G., and JU, L., 1993, Tests on a low-frequency inverted pendulum system. Measurement Science and Technology, 4, 995-999.
20. SAULSON, P. R., STEBBINS, R. T., DUMONT, F. D., and MOCK, S. E., 1994, The inverted pendulum as a probe of anelasticity. Review of Scientific Instruments, 65, 182-191.
21. MURGATROYD, P. N., 1994, The magnetic analogue of the inverted pendulum. American Journal of Physics, 62, 281-282.
22. ACHESON, D. J., 1995, Multiple-nodding oscillations of a driven inverted pendulum. Proceedings of the Royal Society of London A, 448, 89-95.
23. MEIROVIRCH, L., 1970, Methods of Analytical Dynamics (New York: McGraw-Hill), pp. 280-288.
24. JOHANSSON, R., MAGNUSSON, M., and ÅKESSON, M., 1988, Identification of human postural dynamics. IEEE Transactions on Biomedical Engineering, BME-35, 858-869.
25. FURUTA, K., KAJIWARA, H., and KOSUGE, K., 1980, Digital control of a double inverted pendulum on an inclined rail. International Journal of Control, 32, 907-924.
26. LUENBERGER, D. G., 1971, An introduction to observers. IEEE Transactions on Automatic Control, AC-16, 596-602.
27. BROGAN, W. L., 1974, Reconstructing state variables from available outputs. In Modern Control Theory (New York: Quantum Publishers, Inc.), pp. 315-317.
28. HEMAMI, H., WEIMER, F. C., and KOOZEKANANI, S. H., 1973, Some aspects of the inverted pendulum problem for modeling of locomotion systems. IEEE Transactions on Automatic Control, AC-18, 658-661.
29. GUBINA, F., HEMAMI, H., and MCGHEE, R. B., 1974, On the dynamic stability of biped locomotion. IEEE Transactions on Biomedical Engineering, BME-21, 102-108.
30. HEMAMI, H., and GOLLIDAY Jr, C. L., 1977, The inverted pendulum and biped stability. Mathematical Biosciences, 34, 95-110.
31. CHOW, C. K., and JACOBSON, D. H., 1972, Further studies of human locomotion: postural stability and control. Mathematical Biosciences, 15, 93-108.
32. MIZRAHI, J., SOLZI, P., RING, H., and NISELL, R., 1989, Postural stability in stroke patients: vectorial expression of asymmetry, sway activity and relative sequence of reactive forces. Medical and Biological Engineering and Computing, 27, 181-190.
33. GELB, H. (ed.), 1977, Clinical Management of Head, Neck and TMJ Pain and Dysfunction (Philadelphia: W. B. Saunders), p. 80.
34. DAWSON, H. L., 1974, Basic Human Anatomy (New York: Appleton-Century-Crofts), p. 45.
35. NETTER, F. H., 1983, The CIBA Collection of Medical Illustrations, Vol. 1, Part I (West Caldwell, New Jersey: CIBA Pharmaceutical Co.), p. 12.
36. SYMON, K. R., 1971, Mechanics, 3rd edition (Reading, Massachusetts: Addison-Wesley), p. 228.