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ID:49735684
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页数:14页
时间:2020-03-04
《美国数学建模优秀论文.doc》由会员上传分享,免费在线阅读,更多相关内容在工程资料-天天文库。
1、ModelforseekingsweetspotAbstractUsinganenergyanalyzingapproach,asimplemodelisraisedforfindingthe"sweetspot"andanalyzingitsparametricproperty.Tosimplifytheproblem,thebathitbyahighspeedballisstudiedasacantilever.Bysetupitsdynamicmodelandenergyformula,findingthesweetspotreducedtofindingthespotw
2、hichminimizetheenergytransferringbetweentheballandthebat.Numericalmethodsaregiventosolvethedynamicalequationandcomputethetotalenergythebatreceived・Usingourmodelandalgorithms,wecaneasilycalculatethepositionofthe"sweetspot"andanalyzeitsvariationwiththeparameterssuchasthegeometricalparametersan
3、dphysicsconstants.Ourcalculationshowsthattheenergytransferredintothebatisminimizedattheposition22inchesfromthehandleofthebat,whichmeansthemaximumpowertransferredtotheball.Themodelisinexcellentagreementwithexperimentaldata.Bychangingtheparameterssuchascrosssection,radiusandmomentofinertiainth
4、emodel,wealsoanalyzedthecorkingbat,andanalyzedtheinfluenceofcorking.Wefindthatcorkingisslightenoughtoignore.BecauseofthedifferenceofdensityandYoungmodulusindifferentmaterials,theenergytransferredtothebatwillbechanged.Finallybymakingafigurewhichisusedtocomparethesolutionsweget,youcaneasilyfin
5、dthataluminumbatsarebetterthanthewoodbats.MaybethisiswhyMajorLeagueBaseballprohibitsmetalbats.Keywords:Sweetspot,energy,numericmethodContents1.Introduction3ProblemwiththesweetspotandourmodePsgoal3ModelAssumption32.ModelfortheBall-BatCollision42.1ball-batcollision42.2Energyconvert42.3Vibratio
6、nofthebat52.4Thenumericalresultsandanalysis63.TheCorkingeffect74.Materialinfluenee95・Summary106・References107.Appendix11!•IntroductionProblemwiththesweetspotandourmodePsgoalThereisaspotonthefatpartofabaseballbatwheremaximumpoweristransferredtotheballwhenhit.Opposetotheexplanationbasedontorqu
7、e,itisnotattheendofthebatknowingfromexperience.Fromourmodel,wecanexplainwhythesweetspotisnotattheendofthebatandaccuratelydeterminethelocationofthesweetspot.Someplayersbelievethathollowingoutacylinderintheheadofthebatandfillingitwithcorkorrubberenha
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