关键词: 网球塔结构, 静力学, 动力学, 力链结构, MATLAB可视化

Abstract: The factors influencing the stability of the “3n+1” style tennis tower，constructed by stacking three tennis balls per layer with one tennis ball on top，are investigated. Under ideal conditions，the presnt study explores the relevant parameters affecting its stability from both statics and dynamics perspectives. It is found that the pressure on the bottom tennis ball is positively correlated with its height，and the static friction coefficient between the tennis balls decreases with increasing pressure. Combining these findings with the results of experiment 1，it is concluded that the energy loss is inversely proportional to the number of layers，suggesting that there is no upper limit to the number of layers in the tennis tower. Taking into account the interference factors，the experiment 2 demonstrates an exponential decrease in the success rate of constructing tennis towers with 2~8 layers. Through analysis of the contact model between tennis balls and the force chain structure，it is determined that the contact force on the bottom tennis ball increases exponentially with the length of the force chain. Ultimately，the maximum height of the tennis tower is determined to be 10 layers.

Key words: tennis tower structure, statics, dynamics, force chain structure, visualization of MATLAB