USING METHODS OF NON-LINEAR DYNAMICS TO LOAD-STRESS-TESTS IN A SWIMMING FLUME

Abstract

INTRODUCTION - Sports movements show an exceptional complex structure. In this structure many components exist, which influence themselves in manifold ways. Therefore we consider the human movement a complex dynamical system on the basis of non-linear laws. We take the opinion that it is better to quantify the variability of sports movements by methods of non-linear dynamics than by conventional means on linear basis. METHODS AND RESULTS - For the represented methods in this paper it is enough to choose only one parameter, which de- scribes the system sufficiently. After several years of researches we have found the fundamental quantities for breaststroke with the help of multidimensional regression analysis and factor analysis: the horizontal velocity of hip and the cyclic length. As for the first parameter we could prove a stationary behaviour, we used the horizontal velocity of the hip for our following calculations. By means of experimental time series of this observable it is possible to construct a multidimensional phase-spacediagram. The estimation of the embedding dimension and the time delay was carried out with the Waberproduct analysis (LIEBERT, 1991). With these characteristics the calculations of fractal dimension and the correlation dimension (GRASSBERGER I PROCACCIO, 1983) were realised for separate periods of the total test. The obtained results were com- pared with conventional methods of time series analysis. CONCLUSION - We can assume, that the dimension is a criterion for the variability in the movement performance. Furthermore an optimal value of dimension is expected as a characteristic qualify of an effective movement. REFERENCES LIEBERT, W.: Chaos und Herzdynamik. Verlag Harri Deutsch, FrankfurtIM., 1991 GRASSBERGER, P.; PROCACCIO, I.: Measuring the strength of strange attractors. Physica 9D (1983) 189 - 208