基于力学模型的同心鼓动态调整策略

Dynamic Adjustment Strategy of Concentric Drum Based on Mechanical Model

本文是对2019年全国大学生数学建模竞赛B题的解答和进一步研究.本文对排球撞击鼓面过程进行受力分析,并建立受力模型,给出了进行同心鼓游戏的最优策略.该策略结合实际情况,确定了队员的站位策略,拉力组合策略,及在球偏离竖直平面时的动态调整策略.在问题一中,在不产生人为失误的情况下,以人在同等体能下,能连续颠起更多的球为优化目标;通过受力分析,给出队员站位策略.在问题二中,考虑队员失误的情况,利用题目给定的数据集,计算不同情况下队员失误产生的鼓面倾斜角.在问题三中,结合现实情况下失误的情况,对问题一的策略进行调整,给出具有容错性的动态调整策略.在问题四中,给出在球偏移竖直方向时,为使球回到竖直方向的颠球策略.

A further study on the Problem B of 2019 China Undergraduate Mathematical Contest in Modeling is presented.The force analysis of the volleyball impact on the drumhead process is carried out,the force model is established and the optimal strategy for the concentric drum game is given.The strategy combines the actual situation to determine the team's position strategy,the pull combination strategy,and the dynamic adjustment strategy when the ball deviates from the vertical plane.In Question 1,the target is continuously erect more balls.By doing force analysis,the team position strategy is obtained.In Question 2,considering the player's mistakes,using the data set given by the title,the drum angle of the player's mistakes in different situations is calculated.In Question 3,combined with the situation of mistakes in the real situation,the strategy of Question 1 is adjusted,and a dynamic adjustment strategy with fault tolerance is given.In the fourth question,a ball-turning strategy is given to return the ball to the vertical direction when the ball is offset in the vertical direction.