Mathematical modelling in sports

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I am an applied mathematics student and I am looking to think of an idea for mathematical modeling in sports. I need to use a differential equation to do this. I was wondering if anyone here had some ideas that I could possibly use to create a differential equation from and then model it, thanks!

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Here is a couple of old and not very old papers that you maight find useful:

  • Keller J. B. A theory of competitive running. Physics today. 1973. p. 43.
  • Keller J. B. Optimal velocity in a race. American Mathematical Monthly. 1974. p. 474-480.
  • Reardon J. Optimal pacing for running 400-and 800-m track races. American Journal of Physics. 2013. V.81(6). p. 428-435
  • Morton R. H. A mathematical and computer simulation model of the running athlete. Bulletin of the Australian Mathematical Society. 1985. V.32, June. p. 469-472.
  • Morton R. H. On a model of human bioenergetics. European journal of applied physiology and occupational physiology. 1985. V. 54(3). p. 285-90.
  • Aftalion A., Bonnans J. F. Optimization of running strategies based on anaerobic energy and variations of velocity. SIAM Journal on Applied Mathematics. 2014. V. 74, № 5. p. 1615-1636.
  • Aftalion A., Fiorini C. A two-runners model: optimization of running strategies according to the physiological parameters. arXiv preprint arXiv:1508.00523. 2015.

Hope this helps.