资源描述:
《The Hopping Hoop Revisited.pdf》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、TheHoppingHoopRevisitedAuthor(s):TimothyPritchettSource:TheAmericanMathematicalMonthly,Vol.106,No.7(Aug.-Sep.,1999),pp.609-617Publishedby:MathematicalAssociationofAmericaStableURL:http://www.jstor.org/stable/2589490.Accessed:01/04/201303:07YouruseoftheJSTORarchiveindicatesyouracce
2、ptanceoftheTerms&ConditionsofUse,availableat.http://www.jstor.org/page/info/about/policies/terms.jsp.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddigitalarchive.Weuseinformationtechnologyandtoolstoincre
3、aseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org..MathematicalAssociationofAmericaiscollaboratingwithJSTORtodigitize,preserveandextendaccesstoTheAmericanMathematicalMonthly.http://www.jstor.orgThiscontentdownloadedfrom18
4、3.157.160.23onMon,1Apr201303:07:13AMAllusesubjecttoJSTORTermsandConditionsTheHoppingHoopRevisitedTimothyPritchettInthisMONTHLY,T.Tokieda[1]recentlyprovidedanoveldiscussionofthehoppinghoopproblemdescribedbyLittlewood[2].Unfortunately,theanalysisin[1]isincorrect.Weshowthatifthe"nosl
5、ipping"conditionimposedin[1]and[2]isstrictlyadheredto,thehoopneverbecomesairborne.Essentialfortheobservedhopofthehoopisaphaseinwhichthereisslippageatthepointofcontactofthehoopwiththesupportingsurface.Inordertoexposethisandothersubtletiesnotconsideredin[1],wetreatasomewhatmoregener
6、alproblem.TheviewofLittlewood'shoppinghoopproblempresentedhereisconsciouslydifferentfromthatgivenin[1].InofferingthisalternativewayofthinkingaboutLittlewood'shoppinghoop,wehopetodeepenthereader'sintuitiveunderstandingofpreciselywhythehoophops.Weconsiderherearigidcircularhoopofradi
7、usRandmass(1-A)Mthat,atleastinitially,rollswithoutslippingalongaflatsurface.AnadditionalobjectofmassAMisrigidlyattachedtotherimofthehoop,withthepointofattachmentcoincidingwiththecentroidoftheobject.Here,Misthetotalmassofthecombinedsystemconsistingofthehoopandtheattachedobject.Thep
8、arameterAistheratiooftheobjectmas