Advertisement

Competitive Running on a Hilly Track

  • Elena Andreeva
  • Horst Behncke
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 124)

Abstract

In [4] J.B. Keller treated the problem of competitive running by means of variational calculus. This simple model was improved and put on a more realistic basis in [1]. Both results, however, predict a slowing down in the last phase of a run, which is particularly pronounced in the model of Keller. While this is true for sprints and on the average for longer distance runs, the final sprint in many races seems to belie these conclusions. Two factors are most likely responsible for this effect. The first are psychological influences. Since this is difficult to model mathematically, we shall concentrate here on the physiological factor, glycolysis.

Keywords

Power Constraint Pyruvic Acid Breathing Rate Terminal Constraint Competitive Running 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Behncke, H.: Optimization models for the force and energy in competitive sports. Math. Meth. Appl. Sci. 9 298–311 (1987).MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Behncke, H.: A mathematical model for the force and energetics in competitive running. J. Math. Biol. 31 853–878 (1993).zbMATHCrossRefGoogle Scholar
  3. [3]
    Bryson, A.E; Ho, Y.C.: Applied Optimal Control. Hemisphere Publishing Co. Washington, New York London, 1975.Google Scholar
  4. [4]
    Keller, J.B.: A Theory of Competitive running. Phys. Today 26 43–47 (1973).CrossRefGoogle Scholar
  5. [5]
    Margaria, R.: Biomechanics and energetics of muscular exercise. Oxford Univ. Press., Oxford (1976).Google Scholar
  6. [6]
    Neustadt, L.: Optimization. Princeton Univ. Press, Princeton (1976).zbMATHGoogle Scholar
  7. [7]
    Reid, W. T.: Sturmian Theory for ordinary differential equations. Springer Verlag New York, Heidelberg, Berlin 1980.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Elena Andreeva
    • 1
  • Horst Behncke
    • 2
  1. 1.Department of MathematicsTver State UniversityTverRussia
  2. 2.FB Mathematik/InformatikUniversität OsnabrückOsnabrückGermany

Personalised recommendations