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Minimum-time running: a numerical approach

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Języki publikacji
EN
Abstrakty
EN
The article deals with the minimum-time running problem. The time of covering a given distance is minimized. The Hill-Keller model of running employed is based on Newton's second law and the equation of power balance. The problem is formulated in optimal control. The unknown function is the runner's velocity that varies with the distance. The problem is solved applying the direct Chebyshev's pseudospectral method.
Rocznik
Strony
83--86
Opis fizyczny
Bibliogr. 16 poz., rys.
Twórcy
autor
autor
Bibliografia
  • [1] BEHNCKE H., Optimization models for the force and energy in competitive sports, Mathematical Methods in the Applied Sciences, 1987, Vol. 9, 298–311.
  • [2] COOPER R.A., A force/energy optimization model for wheelchair athletic, IEEE Transactions on Systems, Man, Cybernetics, 1990, Vol. 20, 444–449.
  • [3] FAHROO F., ROSS M., Direct trajectory optimization by Chebyshev pseudospectral method, Journal of Guidance, Control, and Dynamics, 2002, Vol. 25, 160–166.
  • [4] KELLER J.B., A theory of competitive running, Physics Today, 1973, Vol. 26, 42–47.
  • [5] KELLER J.B., Optimal velocity in a race, American Mathematical Monthly, 1974, Vol. 81, 474–480.
  • [6] MAROŃSKI R., ŁUCJANEK W., Optymalizacja trajektorii samolotu w locie na zadaną odległość, The Archive of Mechanical Engineering, 1979, Vol. XXVI, 239–256.
  • [7] MAROŃSKI R., Simple algorithm for computation of optimal velocity in running and swimming, Book of Abstracts of the XV ISB Congress “Biomechanics’95”, 1995, Jyväskylä, Finland, 588–589.
  • [8] MAROŃSKI R., Minimum-time running and swimming: an optimal control approach, Journal of Biomechanics, 1996, Vol. 29, 245–249.
  • [9] PANASZ P., MAROŃSKI R., Commercial airplane trajectory optimization by a Chebyshev pseudospectral method, The Archive of Mechanical Engineering, 2005, Vol. LII, 5–19.
  • [10] PINCH E.R., Optimal control and calculus of variations, Oxford University Press, Oxford, 1993.
  • [11] PRITCHARD W.G., Mathematical models of running, SIAM Review, 1993, Vol. 35, 359–378.
  • [12] ROBERTS S.M., SHIPMAN J.S., Two-Point Boundary Value Problems: Shooting Methods, Elsevier, New York, 1972.
  • [13] ROGOWSKI K., MAROŃSKI R., Driving techniques for minimizing fuel consumption during record vehicle competition, The Archive of Mechanical Engineering, 2009, Vol. LVI, 27–35.
  • [14] SANDERSON B., MARTINDALE W., Toward optimizing rowing technique, Medicine and Science in Sports and Exercise, 1986, Vol. 18, 454–468.
  • [15] TÖZEREN A., Human Body Dynamics, Springer, New York, 2000, p. 243.
  • [16] WOODSIDE W., The optimal strategy for running the race, Mathematical and Computer Modelling, 1991, Vol. 15, 1–12.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPBB-0002-0019
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