同心鼓问题的数学模型

Mathematical Model of Concentric Drum Problem

摘要: 为了研究“同心鼓运动”的最佳协作策略，本文分别对排球的下落、碰撞、上升进行受力分析，建立了协作策略优化模型。通过求解微分方程及利用遍历搜索，得到该策略下每个人的发力时机、大小及竖直面与绳子的夹角，进一步探讨实际情况下遇到鼓面倾斜问题该如何调整，建立了同心鼓倾斜修正模型并给出调整策略。

Abstract: In order to study the best cooperation strategy of “concentric drum movement”, this paper analyzes the force of falling, collision and rising of volleyball, and establishes the optimization model of cooperation strategy. By solving differential equations and using ergodic search, the timing and size of each person’s exertion and the angle between vertical plane and rope under this strategy are obtained. Further discussion is made on how to adjust the problem of drum tilt in actual situation. A correction model of concentric drum tilt is established and an adjustment strategy is given.