2010年美国数学建模竞赛获奖论文-英文版VIP专享

For office use onlyT1 ________________T2 ________________T3 ________________T4 ________________Team Control Number8038Problem ChosenAFor office use onlyF1 ________________F2 ________________F3 ________________F4 ________________Team #8038 February 23, 2025SummaryBaseball is a popular bat-and-ball game involving both athletics and wisdom. There are strict restrictions on the material, size and manufacture of the bat. It is vital important to transfer the maximum energy to the ball in order to give it the fastest batted speed during the hitting process. Firstly, this paper locates the center-of-percussion (COP) and the viberational node based on the single pendulum theory and the analysis of bat vibration. With the help of the synthesizing optimization approach, a mathematical model is developed to execute the optimized positioning for the “sweet spot”, and the best hitting spot turns out not to be at the end of the bat. Secondly, based on the basic model hypothesis, taking the physical and material attributes of the bat as parameters, the moment of inertia and the highest batted ball speed (BBS) of the “sweet spot” are evaluated using different parameter values, which enables a quantified comparison to be made on the performance of different bats. Thus finally explained why Major League Baseball prohibits “corking” and metal bats.In problem I, taking the COP and the viberational node as two decisive factors of the “sweet zone”, models are developed respectively to study the hitting effect from the angle of energy conversion. Because the different “sweet spots” decided by COP and the viberational node reflect different form of energy conversion, the “space-distance” concept is introduced and the “Techniq...