Comment on “Bouncing on a slope” [Am. J. Phys. b 89 b , 143–146 (2021)] 2022 Rod Cross.pdf

该【Comment on “Bouncing on a slope” [Am. J. Phys. b 89 b , 143–146 (2021)] 2022 Rod Cross 】是由【四婆子】上传分享，文档一共【4】页，该文档可以免费在线阅读，需要了解更多关于【Comment on “Bouncing on a slope” [Am. J. Phys. b 89 b , 143–146 (2021)] 2022 Rod Cross 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。Commenton“Bouncingonaslope”[,143–146(2021)]
RodCross
Citation:AmericanJournalofPhysics90,407(2022);doi:
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Commenton“Bouncingonaslope”[,143–146(2021)]
RodCross
SchoolofPhysics,UniversityofSydney,Sydney,Australia
(Received15April2022;accepted19April2022)
/
Ioncereadthatatheoreticalphysicistissomeonewhoimpacts,theangleofincidencetothenormalwasnotequal
willapproximateafour-leggedtableasonewitheitheronetotheangleofreflection,thefrictionforcewasnotnegligi-
ortwolegstosimplifytheproblemandwillthenconcludeble,thedownhillpathdidnotcoincidewiththeuphillpath,
,the
-spinoftheballplayedamajorrole,andthenumberof
eredapointmassprojectilebouncingupanincline,assum-


practicetomakesimplifyingassumptionswhendevelopingTheAmericanJournalofPhysicsshouldcomewitha
aphysicalmodel,
triedtheexperimentusingarealballonarealsurfacebecoincidental.
andfoundthatnoneoftheirassumptionsorconclusions
,,,“Bouncingonaslope,”
werenotequal,,143–146(2021).
ResponsetoRodCross’sLetter
RoubenRostamian
DepartmentofMathematicsandStatistics,UniversityofMaryland,BaltimoreCounty(UMBC),Baltimore,
Maryland21250
(Received19April2022;accepted19April2022)
/
Oneisnevercertainwho,ifanyone,willreadanarticledescribingexplicitlyandpreciselytheassumptionsbuiltinto
:point-massprojectile,noairresistance,no
hasreadourpaperbutalsowasinterestedenoughtoperformenergyloss,
,hisequipmentcertainlydoesnotmeetthose

course!Thepaper’sopeningparagraphsetsthestagebytowhatisdescribedinthatarticleisentirelycoincidental.
(6),June2022#2022PublishedunderanexclusivelicensebyAAPT407
BreakdownofamisinterpretationofNoether’stheorem
)
JosephHenryLaboratories,PrincetonUniversity,Princeton,NJ08544
(Received25April2022;accepted26April2022)
/
ArecentpaperbyLemostitled,1“Breakdownofthecon-systems(aswellasforoneswithnoconstraints),butnotfor
nectionbetweensymmetriesandconservationlawsforsemi-
holonomicsystems,”mayunintentionallyleadthereadertoAccordingtothenarrowbutpopularviewoftheassociation/
supposethatNoether’stheoremsuffersa“breakdown”intheconnectionbetweenconservationlawsandinvariancestated
exampleofamassthatslideswithoutfrictioninsideacylin-intheabovequotefromLemos’spaper,itstitle,“Breakdown

Inclassicalmechanics,Noether’stheorem2isarestate-forsemiholonomicsystems,”,thewordingof
mentofaninsightofLagrangethatiftheLagrangianLofaLemos’spapermayleadreaderstothinkthatNoether’stheo-
systemisinvariantundercoordinateq(thatis,
ofq),thentheCANONICAL(orgeneralized)momentumletteraffirmsthatthefullpowerandvalidityofNoether’s
pq¼***@L=***@q_isaconstantofthemotion(.,aconservedtheorem,foranyandallsystemsdescribablebya
quantity).Unfortunately,thistheoremisoftenmisinter-Lagrangian,isunaffectedbyLemos’sresult.
preted/oversimplifiedtomeanthatiftheLagrangianofa
systemoftotalmassMisindependentofthespatialcoordi-a)Electronicmail:******@,ORCID:0000-0002-3502-7380.
natex,,,221–224(2022).
However,thelinearmomentumisconservedonlyif2See,forexample,’spaper,,.
Poole,Jr.,,ClassicalMechanics,3rded.(AddisonWesley,
px¼***@L=***@x_¼Mx_.
IntheexampleofLemos,theLagrangianisindependentSanFrancisco,2001).Noetherwroteabout“invariance”ratherthan
“symmetry”(mainlyinthecontextofgeneralrelativity),althoughtheterm
ofthehorizontalcoordinatexofthecenterofthecylinder,symmetryisnowpopularlyassociatedwithhertheorem.
butpx¼***@L=***@x_6¼,theterm“action”(used,butnotdefinedin
motioninthisexample,Lemos’spapersuggeststhatthisisaLemos’spaper)canbeconstruedtomean(inthecontextofLemos’spaper)
breakdownofNoether’stheorembecausepxdoesnotequalthe“extended”LagrangianLdefinedinhisEq.(25),whichincludesthe
.
Noether,asaconservedmomentumrelatedtoaninvariance/
symmetrydoesexistinLemos’sexample,exactlyinaccor-ofLemos’sbook,AnalyticalMechanics(.,Cambridge,
2018).
dancewithNoether’“holonomic”and“semiholonomic”
LemoscitedNoether’stheoremintheIntroductiontohis
1,’spaper,,AnalyticalMechanics(World
paper,andimmediatelyafterwardswrote,“Theconserva-Scientific,Singapore,2014).Holonomicsystemshaveconstraintsofthe
ÀÁÈÉ
tionoflinearmomentum,angularmomentum,andenergyformfiðÞfgqj;-dependentcon-
formany-particlesystemsisassociatedwithinvarianceofstraintsoftheformgiqj;q_j;tthatcanbeintegratedtotheholonomic
theactionundertranslations,rotations,andtimedisplace-form,butwhichincludeconstantsthatdependontheinitialconditions.
ments,respectively.”Inthatcontext,readersmightassumeHence,
thatthequotationisNoether’stheorem,althoughitisrathersubsetofholonomicsystemsissometimescalledproper,forwhichcon-
stantsintheconstraintsoftheseholonomicsubsystemsareindependentof
;
“holonomous”¼integral(oko1)laws
showthatthisstatementdoesnotholdforhisexampleofthe(olo1),
4
rollingcylinder,because,asisshowninhistextbook,thisMechanics(Macmillan,NewYork,1899);
statementholdsonlyfor“proper”holonomicmechanicalGermanedition(Barth,Leipzig,1894).
.,,,June2022LetterstotheEditor408
Talking’boutmisinterpretation
)
InstitutodeFısica,UniversidadeFederalFluminense,CampusdaPraiaVermelha,Niteroi24210-340,
RJ,Brazil
(Received26April2022;accepted26April2022)
/
I’mafraidmypaper1hasbeenmisunderstoodbyProfessorconservedcanonicalmomentumisnotthetotallinear
,,contraryto
“breakdownofNoether’stheorem”isneverexpectations,theconservedquantityassociatedwithtrans-
.
supposedbreakdownofNoether’stheoremtothefactthatpxAccordingtoMcDonald,ImisinterpretNoether’stheorem
,Isaybystatingorintimatingthatitprovidesaconnectionbetween
that“Noether’stheoremestablishesthemostgeneralcorre-symmetriesandconservationlawsonlyforstandard
spondencebetweeninvarianceundercontinuoustransforma-
tionsandconstantsofthemotion.”Next,
conservationoflinearmomentum,angularmomentum,andinvarianceandconservationofthetotallinearmomentum
energyareassociatedwith“invarianceundertranslations,foraholonomicsystemwithastandardLagrangianisapar-
rotations,andtimedisplacements,respectively.”TheseticularcaseofNoether’stheorembecause,fortransforma-
resultsare,obviously,particularcasesofNoether’stheoremtionsthatleavetimeunchanged,theinvarianceofthe
becausetranslations,rotations,andtimedisplacementsareLagrangianisequivalenttotheinvarianceoftheaction.

whatsoeverhaveIsuggestedthattheseparticularresultsareholonomicconstraintsistheonlyinstanceofaconnection
Noether’.
LetL¼TÀVbeastandardLagrangian,whereVdoesFinally,McDonaldincorrectlystatesthat“semiholonomic
-systemsareasubsetofholonomicones.”Ifthisweretrue,
nomic,invarianceofboththeLagrangianandthecon-onewouldfacethecontradictionofaresultthatholdsforall
straintsundertranslationsimpliesconservationofthetotalmembersofasetAbutdoesnotholdformembersofasub-
linearmomentum,’sjusttheotherwayaround,holonomicsystems
-areasubsetofsemiholonomicsystems.
dependentintegrableconstraints,whicharesaidtobesemi-IfindMcDonald’scriticismunwarrantedbecauseitrests
holonomic,seemcompletelyequivalenttoholonomiconamisinterpretationofmypaper.
constraintsbecause,intheirintegratedform,theyrestrict
a)Electronicmail:******@,ORCID:0000-0002-2386-1247.
,itcametomeasasurprisethatsemi-1
holonomicconstraintsarenotequivalenttoholonomiccon-,“Breakdownoftheconnectionbetweensymmetriesandcon-
servationlawsforsemiholonomicsystems,”,221–224
straintsasregardstheconnectionbetweensymmetriesand(2022).
,AnalyticalMechanics(.,Cambridge,2018),
.
.,,,June2022LetterstotheEditor409