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

Krasovskiy N. N. Teoriya upravleniya dvizheniyem. Lineynyye sistemy [The theory of motion control. Linear Systems], Moskow, 1966 g, 476 p. (rus)

Mironovskiy L. A. Avtomatika i telemekhanika [Automation and telemechanics], 1992, vol. 9, pp. 73–86. (rus)

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/.

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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

No. 2(46) (2015)

Section

Articles

License

Copyright (c) 2015 (Oleksandr Aghyppo) Ажиппо Олександр Юрійович, (Nikolay Balonin) Балонін Микола Олексійович, (Valeriy Druz) Друзь Валерій Анатолійович, (Viktor Suzdal) Суздаль Віктор Семенович

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