美国数学建模优秀论文0

《美国数学建模优秀论文0》由会员上传分享，免费在线阅读，更多相关内容在应用文档-天天文库。

1、Team#6336Page14of14ModelforseekingsweetspotAbstractUsinganenergyanalyzingapproach,asimplemodelisraisedforfindingthe“sweetspot”andanalyzingitsparametricproperty.Tosimplifytheproblem,thebathitbyahighspeedballisstudiedasacantilever.Bysetupitsdynamicmodelandenergyformula,findi

2、ngthesweetspotreducedtofindingthespotwhichminimizetheenergytransferringbetweentheballandthebat.Numericalmethodsaregiventosolvethedynamicalequationandcomputethetotalenergythebatreceived.Usingourmodelandalgorithms,wecaneasilycalculatethepositionofthe“sweetspot”andanalyzeitsv

3、ariationwiththeparameterssuchasthegeometricalparametersandphysicsconstants.Ourcalculationshowsthattheenergytransferredintothebatisminimizedattheposition22inchesfromthehandleofthebat,whichmeansthemaximumpowertransferredtotheball.Themodelisinexcellentagreementwithexperimenta

4、ldata.Bychangingtheparameterssuchascrosssection,radiusandmomentofinertiainthemodel,wealsoanalyzedthecorkingbat,andanalyzedtheinfluenceofcorking.Wefindthatcorkingisslightenoughtoignore.BecauseofthedifferenceofdensityandYoungmodulusindifferentmaterials,theenergytransferredto

5、thebatwillbechanged.Finallybymakingafigurewhichisusedtocomparethesolutionsweget,youcaneasilyfindthataluminumbatsarebetterthanthewoodbats.MaybethisiswhyMajorLeagueBaseballprohibitsmetalbats.Keywords:Sweetspot,energy,numericmethod14Team#6336Page14of14Contents1.Introduction……

6、………………………………………………………………31.1Problemwiththesweetspotandourmodel’sgoal………….............31.2ModelAssumption……………………………………………………...…32.ModelfortheBall-BatCollision………………………………………………42.1ball-batcollision……………………………………………….…………..42.2Energyconvert……………………………………………………………42.3Vibrat

7、ionofthebat……………………………………...…………….…..52.4Thenumericalresultsandanalysis……..………………………...……..63.TheCorkingeffect…………………………………………………………….74.Materialinfluence……………………………………………………………..914Team#6336Page14of145.Summary………………………………………………………………………106.References……………………………………………………..

8、…………….107.Appendix……………………………………………………………………...111.Introduction1.1Problemwiththesweetspot