A dynamical analysis of tennis: concepts and data

This research reported here draws on self-organization theories and dynamical system models to investigate the collective behaviour of tennis players. In tennis, the unceasing to-and-fro displacements of a player about a "home" reference position, located in the middle of the baseline, are akin to those of an oscillator, and the reciprocal attending of both players establishes an informational linkage. Thus, theoretically, the displacement of the two players can be analysed as a system formed by two coupled non-linear oscillators. In such a system, relative phase has been shown to be an adept measure of the temporal synchronization between the oscillators. We hypothesized that relative phase is a relevant collective variable to characterize the relative motion of tennis players. Four players were videotaped and their displacements analysed. The results revealed just two stable patterns of synchronization, in-phase and anti-phase, as the players moved in the same or opposite directions, respectively. Moreover, relative phase showed two types of evolution within trials: either it remained stable at in-phase or anti-phase, or it exhibited transitions between these two modes. In accordance with our hypothesis, the results identified relative phase as a pertinent collective variable to represent both invariance and change in the relative displacements of tennis players. Such a finding opens new avenues for investigating dual sports.     

A dynamical analysis of tennis: Concepts and data

This research reported here draws on self-organization theories and dynamical system models to investigate the collective behaviour of tennis players. In tennis, the unceasing to-and-fro displacements of a player about a “home” reference position, located in the middle of the baseline, are akin to those of an oscillator, and the reciprocal attending of both players establishes an informational linkage. Thus, theoretically, the displacement of the two players can be analysed as a system formed by two coupled non-linear oscillators. In such a system, relative phase has been shown to be an adept measure of the temporal synchronization between the oscillators. We hypothesized that relative phase is a relevant collective variable to characterize the relative motion of tennis players. Four players were videotaped and their displacements analysed. The results revealed just two stable patterns of synchronization, in-phase and anti-phase, as the players moved in the same or opposite directions, respectively. Moreover, relative phase showed two types of evolution within trials: either it remained stable at in-phase or anti-phase, or it exhibited transitions between these two modes. In accordance with our hypothesis, the results identified relative phase as a pertinent collective variable to represent both invariance and change in the relative displacements of tennis players. Such a finding opens new avenues for investigating dual sports.     

足球送别曲

这是我第二次给贵刊投稿,恐怕也是五年内的最后一次。还有280天,我将走上战场,在高考到来之际,我为《当代体育》的所有读者献上自己真诚的祝愿,受国安球迷给北京队的口号：“赢也爱你,输也爱你,不拼不爱你”启发,我用我的座右铭“成亦在我,败亦在我,不拼不是我”和大家共勉,祝愿在2010年考学的莘莘学子们都能圆梦!