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1、Half-BloodHalf-Pipe109AHalf-BloodHalf-Pipe,APerfectPerformanceEnhaoGongXiaoyunWangRongshaLiTsinghuaUniversityBeijing,ChinaAdvisor:JiminZhangAbstractOurbasicmodelhastwoparts:tofindahalf-pipeshapethatcanmaximizeverticalair,andtoadapttheshapetomaximizethepossibletotalangleofrotation.Inanextendedmodel,w
2、eanalyzethesnowboarder’seffectonverticalairandonrotation.Finally,wediscussthefeasibilityandthetradeoffsofbuildingapracticalcourse.Themajorassumptionisthatresistanceincludesthefrictionofsnowplusairdrag,withtheformerproportionaltothenormalforce.Wefindairdragnegligible.Wefirstobtainandsolveadifferential
3、equationforenergylosttofrictionanddragbasedonforceanalysisandenergyconservation.Wecalculateverticalairbyanalyzingprojectilemotion.Wethencalculatetheangularmomentumbeforetheflightanddiscussfactorsinfluencingit.Inanextendedmodel,wetakethesnowboarder’sinfluenceintoaccount.Wecompareanalyticalandnumericalr
4、esultswithreality,usingdefaultparameters;wevalidatethatourmethodiscorrectandrobust.Weanalyzetheeffectsonverticalairofwidth,height,andgradientangleofthehalf-pipe.Wewww.madio.net数学中国findthatawider,steepercoursewithproperdepthandthepathofaskilledsnowboarderarebestforverticalair.Usingageneticalgorithm,w
5、egloballyoptimizethecourseshapetoprovideeitherthegreatestverticalairormaximalpotentialrotation;thereisatradeoff.Implementingahybridscoringsystemastheobjectivefunction,weoptimizethecourseshapetoa“half-blood”shapethatwouldprovidetheeclecticallybestsnowboardperformance.TheUMAPJournal32(2)(2011)109–122
6、.cCopyright2011byCOMAP,Inc.Allrightsreserved.Permissiontomakedigitalorhardcopiesofpartorallofthisworkforpersonalorclassroomuseisgrantedwithoutfeeprovidedthatcopiesarenotmadeordistributedforprofitorcommercialadvantageandthatcopiesbearthisnotice.Abstractingwithcreditispermitted,butcopyrightsforcompone
7、ntsofthisworkownedbyothersthanCOMAPmustbehonored.Tocopyotherwise,torepublish,topostonservers,ortoredistributetolistsrequirespriorpermissionfromCOMAP.110TheUMAPJournal32.2(2011)BackgroundAhalf-pipeisthevenue