Finite system optimization sports equipment movements

Authors

  • (Oleksandr Aghyppo) Ажиппо Олександр Юрійович Kharkiv State Academy of Physical Culture, Ukraine https://orcid.org/0000-0001-7489-7605
  • (Nikolay Balonin) Балонін Микола Олексійович State University of Airspace Instrumentation, Russian Federation
  • (Valeriy Druz) Друзь Валерій Анатолійович Kharkiv State Academy of Physical Culture, https://orcid.org/0000-0002-4628-6791
  • (Viktor Suzdal) Суздаль Віктор Семенович Institute for Scintillation Materials NAS of Ukraine,

DOI:

https://doi.org/10.15391/snsv.2015-2.001

Keywords:

the movement technique in sports, the finite time systems, Eigen-functions, the optimization, the mathematical modeling

Abstract

Purpose: to provide mathematical theory coordinated with physical experiments, and gave the general orientation in the optimization technique of movements in sport. Material and Methods: theory of systems, matrix theory, Internet resources and mathematical environment MATLAB. Results: for simple dynamic blocks – first order inertial block, integrator and double integrator shown that the input signal in the form of the Eigen-function a maximum gain in amplitude when it passes through the block and the quadratic norm of the output signal is determined by the maximum Hankel singular value. Conclusions: proposed to use a mathematical theory of finite time systems in the optimization techniques of movement in sport. The numerical experiments have shown the existence for linear dynamic systems of real Eigen-functions – does not distort the system inputs are considered in reverse time.

References

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Glover К. All optimal Hankel-norm approximations of linear multivariables systems // Intern. J. Control. – 1984. – V. 39, № 6. – P. 1115–1193.

Mironovskiy L. A., Balonin N. A. Avtomatika i telemekhanika [Automation and telemechanics], 1999, vol. 11, p. 3–18. (rus)

Balonin N. A., Mironovskiy L. A. Avtomatika i telemekhanika [Automation and telemechanics], 2002, № 6, p. 3–22. (rus)

Balonin N. A. Finite time interval dynamic system, available at. – Access mode : http://mathscinet.ru/systems/finitetime/.

Published

2015-04-30

How to Cite

Ажиппо Олександр Юрійович (Oleksandr A., Балонін Микола Олексійович (Nikolay B., Друзь Валерій Анатолійович (Valeriy D., & Суздаль Віктор Семенович (Viktor S. (2015). Finite system optimization sports equipment movements. Slobozhanskyi Herald of Science and Sport, (2(46), 11–18. https://doi.org/10.15391/snsv.2015-2.001

Issue

Section

Articles