Finite system optimization sports equipment movements

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.