Finite Dynamic Models in Sports
Abstract
Introduction: The classical theory of linear dynamical systems is largely focused on an infinite or semi-infinite interval. This applies to the frequency response functions, the Laplace transform, stability analysis, and other areas where a lot of useful results were obtained. However, in practice this approach is only applicable to dynamic systems whose running time is significantly longer than their eigen processes. On the other hand, real systems often operate on finite intervals of time commensurate with the time of their eigen processes. Such systems cover dynamic processes in sports. Purpose: The goal is to show the effectiveness of sport models based on discrete frequency characteristics of linear dynamic systems with finite time intervals, illustrating this by the examples of elementary dynamic units of the first and second orders. Results: It is shown that, unlike the continuous frequency characteristics, the discrete ones take in consideration the finite time interval of athlete movements. A definition is given for discrete frequency characteristics of finite-time linear dynamic systems. A mathematical model is described for a double integrator in comparison with the graph of lifting a barbell. It is shown that the points of discrete frequency characteristics are located on the continuous frequency response. Practical relevance: The discrete frequency characteristics complement the classic continuous frequency response, being consistent with them in amplitudes and acting as a clarifying characteristics, taking into account an important practical factor which is the finite time of real processes. The corresponding software for mathematical Internet sites has been developed.Published
2016-06-01
How to Cite
Balonin, N., Sergeev, M., & Suzdal, V. (2016). Finite Dynamic Models in Sports. Information and Control Systems, (3), 34-37. https://doi.org/10.15217/issn1684-8853.2016.3.34
Issue
Section
System and process modeling