拳擊的攻擊方式中，使用次數最多的是持續刺、直拳打擊，其為一種週期性動作，可視為一種震盪器 (oscillator)，作為動力系統去探討其中動作變化的規律。目的：探討持續刺、直拳打擊之模型建立與雙手協調。方法：招募8位菁英拳擊手，在不同頻率下，以持續刺拳與持續刺、直拳打擊牆靶，錄製兩手動作，由Simi motion將拳套上標記點水平面之位移數位化，以動作方向的一維數據計算頻率表現與離散相對相位，並繪製相平面圖與虎克平面圖進行質性觀察，依此進行多元迴歸以建立震盪器模型，並對不同頻率與迴歸公式之解釋量進行比較。此外，將實驗影片製作為數位問卷，招募30位一般人與31位拳擊手判斷影片中動作為間斷或連續，比較兩類觀察者答題一致率後，對間斷或連續答案進行羅吉斯迴歸。結果：相對相位在指定頻率下沒有顯著差異；以質性觀察結果建立之非線性震盪器迴歸模式為：x ̈=截距+c_10 x+c_30 x^3+c_01 x ̇+c_11 xx ̇。迴歸結果發現震盪器模型可描述約2Hz以上之動力；在雙手擊拳時，加上對側手參數進行迴歸可提高部分較低頻率情境之解釋量；知覺測驗部分，兩類參與者之答題一致率沒有差異，羅吉斯迴歸方程之轉折點發生在頻率約2Hz處。結論：持續刺、直拳打擊之動力在高頻時可以震盪器模型進行描述，觀察者亦可分辨高頻之連續擊拳的動力。

In boxing, jab and cross combinations are crucial attacking techniques. These can be thought of as oscillators within a dynamical system. Purpose: To investigate modeling the jab and cross combinations with a nonlinear oscillator and the coordination of the jabs and crosses. Methods: Eight national-level boxing athletes hit the wall pad with continuous jabs and crosses under different frequency conditions. Position data of a marker on the gloves were captured and digitized with Simi motion. The one-dimensional data in the movement direction were used to derive the frequency performance and the discrete relative phase for the jabs and crosses. The nonlinear oscillator models were constructed based on the characteristics of the phase plane plots and Hooke’s plane plots. The models were evaluated under five frequencies. In addition, 30 young adults with no combat sports experience and 31 boxers were recruited to take a digital questionnaire made with the experiment videos and to identify if the actions in the videos were continuous or discrete. The consistencies of the answers were compared between the groups, and the Logistic regression was conducted for the responses on frequencies. Results: There was no significant difference in the relative phase among the given frequencies. The constructed nonlinear oscillator model was: x ̈=intercept+c_10 x+c_30 x^3+c_01 x ̇+c_11 xx ̇. The model had high variance accounted for at frequencies higher than about 2Hz. Adding the term of the other hand to the model in the combination conditions increased the variance accounted for in some low-frequency conditions. There was no difference in the questionnaire answers consistencies between groups. The significant Logistic regression showed the inflection point at about 2Hz. Conclusion: The nonlinear oscillator model captured the dynamics of jab and cross combinations at high frequencies, observers with and without boxing experience could also differentiate the continuous versus discrete dynamics of the punches with frequency.

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