Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part III: Theory in the case of vertical angular frequency and in the general spin‐case

Abstract

Last, but not least, the general case of angular frequency is to be treated. A rough qualitative discussion of the solutions is gven as well as-if the equations are viewed as a three-dimensional dynamical system-the unique stable equilibrium, which depends on the spin. This equilibrium turns out to be globally attractive, which can be proved by the construction of a suitable Ljapunov function. Then, the ball flight system can be transformed into a fourth-order scalar differential equation.

Effect of altitude on football performance

“…Although most of the focus in the medical literature is on the physiological effect of altitude on performance, the physical effects of altitude (Fuchs 1991(Fuchs , 1995 may actually be equally or even more important, especially for sports for which success depends substantially on a high degree of technical skill with a ball, as opposed to aerobic power and endurance. In the United States, it has been often discussed that altitude resident teams in Denver, Colorado at 1609 m have much better home records than they do away records.…”