美国数学建模优秀论文.doc

Team #6336 Page 1 of 13 1 M odel for seeking sweet spot Abstract Using an energy analyzing approach, a simple model is raised for finding the “ sweet spot ” and analyzing its parametric property. To simplify the problem, the bat hitbya high speed ball is studied asa cantilever . By set up its dynamic model and energy formula, finding the sweet spot reduced to finding the spot which minimize the energy transferring between the ball and the bat. Numerical methods are given to solve the dynamical equation pute the total energy the bat received. Using our model and algorithms, we can easily calculate the position of the “ sweet spot ” and analyze its variation with the parameters such as the geometrical parameters and physics constants. Our calculation shows that the energy transf erred into the bat is minimized at the position 22 inches from the handle of the bat, which means the maximum power transferred to the ball. The model is in excellent agreement with experimental data . By changing the parameters such as cross section, radius and moment of inertia in the model, we also analyzed the corking bat, and analyzed the influence of corking. We find that corking is slight enough to ignore. Because of the difference of density and Young modulus in different materials, the energy transferred to the bat will be changed. Finally by making a figure which is used pare the solutions we get, you can easily find that aluminum bats are better than the wood bats. Maybe this is why Major League Baseball prohibits metal bats . Keywords: Sweet spot, energy, numeric method Team #6336 Page 2 of 13 2 Contents 1. Introduction …………………………………………………………………… 3 Problem with the sweet spot and our model ’s goal …………... .. .... .... 3 Model Assumption ……………………………………………………...…3 2. Model for the Ball-Bat Collision ……………………………………………… 4 ball-bat collision ………………………………………………. …………..4 Energy convert …………………………………………………………… 4 Vibration of the bat ……………………………………... …………….…..5 Then