×

zbMATH — the first resource for mathematics

A model of optimal voluntary muscular control. (English) Zbl 0355.92010

MSC:
92B05 General biology and biomathematics
49K15 Optimality conditions for problems involving ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abbott, B. C., Bigland, B., Ritchie, J. M.: The physiological cost of negative work. J. Physiol. 117, 380-390 (1952).
[2] Athans, M., Falb, P. L.: Optimal Control. New York: McGraw-Hill 1966. · Zbl 0196.46303
[3] Ayoub, M. A., Ayoub, M. M., Walkevar, A. G.: A biomechanical model for the upper extremity using optimization techniques. Human Factors 16, 585-594 (1974).
[4] Basmajian, J. V.: Muscles Alive. Their Functions Revealed by Electromyography. Baltimore: Williams and Wilkins 1962.
[5] Beckett, R., Chang, K.: An evaluation of the kinematics of gait by minimum energy, pp. 15-26 in: Biomechanics (Bootzin, D., Muffley, H. C., eds.). New York: Plenum 1969.
[6] Bigland, B., Lippold, O. C. J.: The relation between force, velocity and integrated electrical activity in human muscles. J. Physiol. 123, 214-224 (1954).
[7] Chow, C. K., Jacobson, D. H.: Studies of human locomotion via optimal programming. Math. Biosci. 10, 239-306 (1971). · Zbl 0215.59305 · doi:10.1016/0025-5564(71)90062-9
[8] Close, J. R.: Motor Functions in the Lower Extremities. Analyses by Electronic Instrumentation. Springfield: Ch. C Thomas 1964.
[9] Cohn, D. L.: Optimal systems: I. The vascular system. Bull. Math. Biophys. 16, 59-74 (1954). · doi:10.1007/BF02481813
[10] Halze, H.: Optimization of human motions, pp 138-143 in Medicine and Sport (Cerquilini, S., Venerando, A., Wartenweiler, J., eds.). Vol. 8. Biomechaanics III. Basel: Karger 1973.
[11] Hill, A. V.: The heat of shortening and the dynamic constants of muscle. Proc. Roy. Soc. B 126, 262-274 (1938).
[12] Hill, A. V.: The mechanical efficiency of frog’s muscle. Proc. Roy. Soc. B 127, 434-451 (1939).
[13] Hill, A. V.: The dynamic constants of human muscle. Proc. Roy. Soc. B 128, 262-274 (1940).
[14] Hill, A. V.: Production and absorption of work by muscle. Science 131, 897-903 (1960). · doi:10.1126/science.131.3404.897
[15] Hill, A. V.: The effect of load on the heat of shortening of muscle. Proc. Roy. Soc. B 159, 297-318 (1964a).
[16] Hill, A. V.: The efficiency of mechanical power development during muscular shortening and its relation to load. Proc. Roy. Soc. B 159, 319-324 (1964b).
[17] Hill, A. V., Howarth, J. V.: The reversal of chemical reactions in contracting muscle during an applied stretch. Proc. Roy. Soc. B 151, 169-193 (1959).
[18] Hopf, H. C., Handwerker, H., Hausmanns, J.: Die rasche Willkürbewegung des Menschen. Deutsche Zeitschr. f. Nervenheilkunde 191, 186-209 (1967).
[19] Huxley, A. F., Simmons, R. M.: Proposed mechanism of force generation in striated muscle. Nature 233, 533-538 (1971). · doi:10.1038/233533a0
[20] Joyce, G. C., Rack, P. M. H., Westbury, D. R.: Some mechanical properties of the cat soleus muscle at various stimulus rates. J. Physiol. 197, 23P-25P (1968).
[21] Katz, B.: The relation between force and speed in muscular contraction. J. Physiol. 96, 45-64 (1939).
[22] Leitman, G.: An Introduction to Optimal Control. New York: McGraw-Hill 1966. · Zbl 0167.39003
[23] Matthews, P. B. C.: Mammalian Muscle Receptors and Their Central Actions. Baltimore: Williams and Wilkins 1972.
[24] Merriam, C. W. III.: Optimization Theory and the Design of Feedback Control Systems. New York: McGraw-Hill 1964. · Zbl 0146.13902
[25] Nubar, Y., Contini, R.: A minimal principle in biomechanics. Bull. Math. Biophys. 23, 377-391 (1961). · Zbl 0108.32802 · doi:10.1007/BF02476493
[26] Pfeiffer, A.: Ein kybernetisches Gütemaß für die Koordinierung von Bewegungen. Z. f. Psychol. 171, 395-399 (1965).
[27] Pini, A.: Relazione forza-velocita nel muscolo umano in vivo nel lavoro motore e resistente. Boll. Soc. Ital. Biol. Sper. 41, 1548-1550 (1965).
[28] Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., Mishchenko, E. F.: The Mathematical Theory of Optimal Processes. New York: Interscience 1962. · Zbl 0102.32001
[29] Ralston, H. J.: Recent advances in neuromuscular physiology. Am J. Physical Medicine 36, 94-120 (1957).
[30] Rashevsky, N.: Mathematical Biophysics, 3rd ed., Vol. 2, p. 292. New York: Dover 1960. · JFM 64.1148.01
[31] Rosen, R.: Optimality Principles in Biology. New York: Plenum 1967. · Zbl 0162.51902
[32] Wacholder, K.: Willkürliche Haltung und Bewegung, insbesondere im Lichte elektrophysiologischer Untersuchungen. Ergebnisse der Physiologie 26, 568-775 (1928). · doi:10.1007/BF02741578
[33] Wacholder, K.: Die Arbeitsfähigkeit des Menschen in ihrer Abhängigkeit von der Funktionsweise des Muskel- und Nervensystems, pp. 587-642, in: Handbuch der normalen und pathologischen Physiologie (Bethe, A., et al., eds.), Band 15, 1. Hälfte. 1930.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.