著者

山本 裕二 横山 慶子 木島 章文 島 弘幸 YAMAMOTO Yuji YOKOYAMA Keiko KIJIMA Akifumi SHIMA Hiroyuki

出版者

名古屋大学総合保健体育科学センター

雑誌

総合保健体育科学 (ISSN:02895412)

巻号頁・発行日

vol.40, no.1, pp.1-14, 2017-06-30

---

This study considered the movements of the defense lines and the ball during a football game as a three-coupled oscillation. Each defense line of two opposing teams oscillated with in-phase synchronization, and the length between each defense line and the ball oscillated with anti-phase synchronization. We introduced a three-coupled oscillation model to understand these synchronizations. First, we considered the case in which three masses, m, and four spring constants, k, were equal in a three-coupled oscillation. We calculated the eigenvectors and eigenvalues based on the equation of motion, and we obtained three modes of oscillation as three angular frequencies in the equation. We obtained key parameters when we defined the initial state of the system, which allowed us to solve the equation of motion for three-coupled oscillation. Next, we considered cases in which three masses and four spring constants differed. To confirm the validity of the three-coupled oscillation model, we calculated the distribution of the relative phase between two outer masses, m1 and m3, as defense lines and the length between two outer masses and the middle mass, m2, as each defense line and the ball. The three-coupled oscillations showed similar distributions of the relative phase. However, the periodogram showed distinct periodicity. Thus, a more sophisticated model is needed to understand the behavior of the defense lines and the ball during football games.