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Optimization models for the force and energy in competitive sports. (English) Zbl 0626.49009
A general optimal control model for running and swimming is developed, whose principal parameters are the energy reserves, the breathing rate and the force. This model is then applied to the world records in these disciplines. It describes the data very well and the parameters employed have values, which agree closely with those obtained by other means.

MSC:
49J99 Existence theories in calculus of variations and optimal control
92Cxx Physiological, cellular and medical topics
93C15 Control/observation systems governed by ordinary differential equations
49K15 Optimality conditions for problems involving ordinary differential equations
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[1] Ballreich, Weg und Zeitmerkmale von Sprintbewegungen (1969)
[2] Baumann , W. Kinematic and dynamic characteristics of the sprint start. Biomechanics VB 194 199 Int. series on Biomechanics Univ. Park
[3] Behncke , H. A Mathematical Model for Competitive Running. Proc 9th Symposium über Operations Research · Zbl 0617.73104
[4] Cavagna, Mechanical Efficiency in Level Walking and Running, J. of Phys. 268 pp 467– (1977)
[5] Counsilman , J. E. Schwimmen. Frankfurt 1972
[6] Davies, Wind Resistance and Assistance in Running, Medic. Sport 13 pp 199– (1981)
[7] Filipov, On certain Questions in optimal control, SIAM J. Control 2 pp 76– (1962)
[8] Keller, A Theory on Competitive Running, Physics Today 26 pp 43– (1973) · doi:10.1063/1.3128231
[9] Keul, Muskelstoffwechsel (1969)
[10] Margaria , R. Biomechanics and energetics of muscular exercise. Oxford 1976
[11] Mathews, The Physiological Basis of Physical Education and Athletics (1976)
[12] Neustadt, Optimization (1976)
[13] Di Prampero, Energetics of Swimming in man, J. Appl. Phys. 37 pp 1– (1974)
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