Erparuftcxrfi HatttaoHarbHHI yHxBepc[rer

nu. JI.H.fvvrurera

L.N.Gumilyov Eurasian National

University

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no o6pa3oBarerrbnofi nporpaMMe <8D05304 - (Dugurca>>

(nanpan.neune noAroroBKlr (8D053- @nrnqecttne rr xlrMlqecrlte HayKrr>)t

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llporpanrnra Bcrynrrrenbnoro oK3aMeHa no Qnrnrce Ans floc'ryflarcqrrx B

AoKTopaHrypy no o6paronare.nssoft rporpaMme dD05304 - @ncrKa)

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o6pasoearelruofi nporpaunae <8D05304 - @usl4Ka>) cocraBJIeHbI no cJIeAyoIqI'IM

Alrcur4nrrrHaM o6rqefi I,I Teoperl,Iqecxoft Qusuxu:

l. Mexanura2. Monexy.nrpHat QLI3rKa3. 3rexrpn.recrBo I,I MarHerI43M.

4. Onrnxa.5. Aronrsaq v s.LepHas $raaurca.6. 3rerrpo4llHaMllKa.7. Kealrroeaq MexaHuKa.

Mexanlrna.{urialrnra varepuansHofi ToqKI,I flocryrlarerl'Horo I'I BpauarenrHoro aBItxeHHc.

O6o6ruenHr,re cKopocru u KoopjtrHarbr. Cro6ru flyaccosa. Mexanr,rqecrue rore6aHI.rc I,I BoJrHbt

e crr,;routnofi cperle. ,{uuxeuuc B lclruepuuanbHbtx cllcreMax orcqera. 3atcour'I Aunatruxu A,'Iq

Her4Hepur4a,'rbHr,rx cr4c'reM. flpeobpa:oaaxufl lutu.r,es pr llopesqa. .Il,anauura rBepAoro rena.

Movenrrr HHeprrsrr! cHJrbr 14 HMlyJlbca. Vr,rrt 3filepa. YpaeHeuur 3ftlepa. Bgauruoaeficrs e

rer. 3axouu Kennepa u BceMupHoro rtroreHlrt. Kocur'tqecrue cKopocrl4. flpunqunHatl\{eHbrrrero jreiicrsu.{. flpl.rveplt cro npHMeHeuuq B pa3n}rrlubrx pa3gelax tpustlxtt. Ypaanenue

f alrH:rsrorra. Knueuat ura Il .qnIIaMI,IKa rBepaoro rena. MoMeHT I'IHepIlI4H! MoMeHT llMnym'ca'MoMeHr urJrbr. 'l'eopeua fiofircrtca-llltefiuepa. Ocuonulte 3aKoHbr rlgpo4unauuru. I4x

dru:nuecruii cMrrc:t. Bsleoa ypaBl{c}Itf, }iepHy:r.nu pI ero creAcrBr'It. ,,{aelenue B )I(rrAl(ocrtx rr

ralax. YpanHerrue HenpepbrBIIocrl'r.

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cocrosHr.r.s r.{Aealbrroro ra:a. Hrortpoqecc . A,qlra6arnr,rfi a nolurponurtfi npoqecclt'Pacnpele..rrenue Maxceer,'la no cKopocrtM I{ SHeprIrtM TerlJroBoro .4BrrxeHl'lt. Han6olee

BepoqrHaJr cKopocrb MoJreKyJr. Cpeqtl.rr apu$veruvecrar cKopocrb' Cpe4nu KBa'4paruqHat

cKopocrb )tone1y"-r. 9uc-uo c'reneHefi cgo6OAst MoneKyJIbI. 3axog pannouepHoro pacnpeAeneHn.fi

f Hepf ur4 rro creneHrM cso6oqst MoneKyn. Teuoeuxocrs I'IAeaJI6Hr,rx ra3oo. Teuoeurocru C, u

C,,. Ouruuecxufi cvr,rc:r Qopnynn Mafiepa. @a:osoe flpocrpaHcrBo. Murpocxonu'recrae u

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l4x npzuenenne Inr pacqera rerrJroBbrx Anurarelefi. Pealrnrte ra:rt. Bnyrpennts Jl{eprv.s

peatbHofo rara. ?ifrferr fefi-Jlnccara H Axoynr-ToMcona. Cxuxeuue fa3oB. flpouecclrrrepeHoca B ra3ax. 3axos (Dnxa. 3aroH Oypre. Ooprrlyna Hr,rcrona. YpaeHeuue BaH-4ep-

Baa.lrca. I4:orepr.ru Bau-4ep-Baa-;tt'ca. Kpuruuecxue lapaMerpbl' Hepaeencrno Klay:Nyca.?Hrponnr. Ou:uqecruii ct\'t btcn :tHTportau. BeporrHocru H 3HTponuc. Ceoficrea xlt,4Kocreft.

Iloeepxuocrnoc HarrxeHrre. CMaquBaHae. ,{arneUne 11oA l,rcKpr4BneHHofi loBepxHocrr,rc.

Kaln:r:rxpulre t{BJreur{q. Oa:osbte nepexoa},1 flepBoro poAa. ypaBHeHue Klafinepona-K:ray:uyca. Tpoilrra.r rouxa.,II,uarpavMa cocrotHllt.

l)"rexrpn.recrno ll MarHerll3v[ellNeHue 3aptxeHHbrx qacTr.III B 3IeKTp[rIeCKnX I{ MafHIiTHLTX IIOJI'X. flone

.qBHxyuefocr 3apq.{a. IlnnonbHbtii t.l My,'lbThnoI6HbII MoMeHTbt cHcTeMr'I 3aptAoB Bo BHerrrHeM

fiOne. fIocTOrHHOe MaIHLtTHOe nOnC. MaIHIITHHfi MOMeHT. MargUrgOe ttone O6I'eMHIIX I'I

noBepxHocTIIbIX roKoB. TeH30p 3JteKrpoMarHltrHOfo tto,'1f,. flpeo6pasonanut JIopeHIIa &[q nontI4Htipnanrtr 11o.]rq. M].nbrurror bH bre pa3.qoxeHrrr rroreHlrr{a,roB gJreKTpoMarHllrHoro nors. floreToqerrHbrx, o6beMHbrx tloBepxHocTHbtx tl nuHeftHbIX 3aptAOB B o.4HOpoAHOfi cpeAe. TeopeMa

faycca. Merog roH<fopMHoro oro6paxeHv,r. flpunuun cynepno3lllll4H. flolrpuraqur3neKTpoMarHH'rHr,rx BoJlH. O6uIne CsoficrBa. I{aCTHbIe CJIyqaI'I JIpIHeiiHOfi Ir KpyroBgfi

noxsprr3arlrrr4. Bo,rsa c snnxnTl'lqecKofi [oJUlpI'I3alI]Iefi. ,{z$$epeuuua'r6Hble ypaBHeHI4t

MafHllTocrarr{Kpt I4 3aKoH Anrnepa. Bexropnrril floreHql{a.[ I{ MarHIlrHa, vHAyKIII4t KpvroBoro

Br4TKa TOKa. MaltnrHOe 11OnC OI paHHqeHHOTO paCnpeAeJIeHHt TOKOB. TOpVOfaOe I'I3nyqeHLe.

I4:",ryueuue tpr.l KyJoHoBcKoM B3afiMo,qeicrBr.I]i. KBaApynoJII'Hoe I4 MarH]rrHo-Ar4rrojrbHoe

r.{3iryreHrre. Ilo.renur.ra-qLr JlnenapAa-Buxepra. Cnerrpa:DHoe pa3JroxeHl'le 3alra3AblBtuourux

noTeHuxaIoB. !nnolsHoe u3nyqeHHe. ,{uno,lsuoe r{3JIyqeHfie IIpH CTOJIKHOBeHI,ItX. MaTHI4THO9

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pa3nnr{Hoii xon$lrrypaqlrn. ?<ft!err Xo:ua. I4:lyveuue 6rtcrpo4utxylqnxcs 3apqAoB'

Marul,Irnue MoMeHTbr aroMoB: op6r4'rar'lbHbrfi MOMeHT, CII,IHOBOii MOMeHr, IIOnHbIii MOMeHT.

lopvorHoe H3-t) qeHHe B penrr14BHarcKoM cnyqae. flpoooAHuxu n rneKTpHrrecKoM IIone. )Heprl4t

3reKmHqecKofo no.ttt. Pa6ola no nepeMeuleHl'rlo 3apsAa B cHCTeMbI 3aptaoB Bo BHe[rHeM rro]re'

MoJe;ur lo-r.spn3yeMocrl Morexyn. Sueprur 3rexTpltqec(oro tloJlt B ax3reKTp]rKtx. TeopeMa

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\1OMCHT. AeilCTByIOUtre Ha OfpaHl{qeHlt6e pagnpeAeneHl-Ie ToKa Bo BHemHeM MaIHITTHOM none.

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pat:1luHsrfi floreHqr{a,\. gerupcxvcpustfi noreHllna,'I 3neKTpoMarHI'ITHoro noJls. VpaoueHlln

,:lBr4lffeH6r 3aprla B no:re. Ilo-n.rp1llauut flpx orpaxeHurl E rlorHoe BHyTpeHHee orplDKeHI'Ie.

BoirHr,r s lrpoBoarllqei cpe,qe. flpocrarr MoAeJIb fipoBoAl.lMocrx.

OrIrrlKahurep$epenuu.a csera. Mero,'IbI ronorpa$uqecxofi sanucu I'l Boc[po[3Be.ueHuq

n3o6paxeHHii. ,{nofiHoe nyqenpenoMneHrle cBeTa r ecrecrBeHHuur onrltqecKilt aKTIrRHocrb

Mareprjz|-'IoB. ,{a$paxqti' crera. .{r.rtfpaxrlur <Dpayuro$epa. lr'r$paxuxq @penen. Cnupa;rl

Kopnrc- .{ucnepcllt cBera. ?rerrpottnar reopufl arrcfiepcul{ cBera. florlouenlre cnera. 3$$errflonlepa. tr4:ryvenue Banulora-gepeHKoBa. MoneKyntpHr,le crleKrpbr. Tunst cnr:u uexgyaroMaMlt B MoneKyne- Bparqare:rsune, ro:re6arerlHo-spaularenbHbte crIeKTprJ. 3nexrpouno-xorc6ateltnsre cneKTpLI.

Alortraq u flaepnas r[lnuraKarerrsar u o6oloqeqsaq MoAenI{ tapa. Yponnu 3Hepruu 1l BoJIHoBbIe $ynrquu

CocToqrrHfi IHcKperHorO cneKTpa. C,ryvafiuOe BbIpoxAeHIIe. Cnus g,relteurapHblx qaCTIlq.

CnuHOssre o11eparopbr r{ clLIHoBbIe $yHxquu. Koutrlyraquouuble cooTHoIIIeHI4e. Teopur a,uQa-

pacfla,{a B KBa3r{KJraccr{qecrou npu6;ruNeHulr. AroM BoaopoAa. Cnerrp arolra Boaopoaa'

MoAe,rr aroMa c rorrKlz 3peHnq onsllon PereptfopAa L nocryJraron 6opa. Aroll soaopoaa e

1oc'rorHHoM 3,,'reKrpr4t{ecKoNl noae, :tf@ercr lllrapxa. OcuonuHe cnoficrsa t4ep. 3gepr1l cBt3l'r

aloMHoro r,apa. .flgepnrre cu:tu. Cucreva aBlx HyKnoIroB.

),rerrpoauHamuraYpaeuelrlre Maxcsejrra B HHTefpalJrr,Hofi r.r AuooepeHqnanrnoft $opt'le u lfi cMbIcJr.

VpaeneHue HenpepbrBHocrr.r. 3;rerrpovarHurHbre BoJrHrI. Mouoxpouaruvec(tuI IIJIocKIUI BOJIHa.

IlO,rrpU:aqur rlJlOcKttX 3neKTpOMarHI,ITHblX BOnH. Pen.t1l4ggcrCl(at KOBapIIaHTHOCTb ypaanenui

3jle1Tpogr.rHaMuxu. Ilorenlluarrr,r SneKTpoMarHurHolo florl. Kaln6ponovHar I4HBapI'IaHTHocrb.

Vpannenru Maxcee,UIa e uurerpa,rrHoii $opue. TeuSOp eJIeKTpOMaTHI'IrHOro nOJI' npOI'I3BOnbHO

gurxyrqaana" raprga. tr4unylbc 3-[eKTpOMarHt THOIO nO:rx. lar:renae cBeTa. Peurenue

ypaarreur-rfr Maxcsejl,la MeroAoM 3ncKrpOALIHaMI,IqecKLIx noTeHIII4alor. Yparnenur !a,ra:u6epa.CsO6OAnsre Ir cBr3aHHbte rapsAst. VCpeAneHHble ypaBgeHl4f, noJlt AJrt cficreMbl cBO6OAHblx H

cBr3aHHbrx 3apraoB. vpaeuenur Marcne:ua-JlopeHr1a,4nr Mr.tKpocKonltqecKofo nolrt

lJcKTpoHHofi Teopt4Ir. MoHoxpoMaruqecKar{ fi pelr,rbHiul 3JreKTpoMulrHI,lrHhIe BoJlHbI. Oasonat }I

rpynngBaf, CKOpOCTH. 3agava paCCernnl. KgaHrOgO - MexaHuqegKaq [OCTaHOBka 14 [pIlHUI't[r'I

peureHur. Ann-r .rryaa H ceqeHl4e pacce'.ji.u'.. onraqecKas TeopeMa' Paccessue

3lIeKTpOr\larHI.tTH6IX BojIII C Meulbtt\t14 qaCTOTaMIr. PaCCeggue gJIeKTpOMafHI'ITHbX BonH C

6o;rtruuun qacroTarvru. cnerrpa,rtuoe pa3noxeH e SreKrpoMarHI,ITHOro I,I3nyqeHuc B

y.;ll, l'papex.[TI{BI4cTcKoM c.ilyqae-

Ksanronaq MexaHrrKaHa6lrcAaeur,re rlu:uuecrue Be,'ruqr4Hbl u,rngefinue caMoconptlKeHHble oflepaTopbl.

clo6crseHHrre $ynxqr.ru I,l co6crBeHHr,re 3HaqeHr.rr Ir,rHeitHbIX ctMOCOIIptXdHHbrX ofiepaTopoB.

Paler.rrue Bo BpeMeHr.t cpeaHux 3Har{eHr4fi <furnvecrr,rx BenurII4H. Ypaouenr.re Spentfecra.

Teopeua 3peuQecra. Boruoeat $ynr<uur u flpltHqtln cyfleprro3ltlpu' Oneparop fauu;rlrosa'Vpanncnze lllpegr.iirrepa. Ceoiicrsa cI'IMMerpuL pelxeHl4fi oaHoMepuoro ypaBHeal'rt

Il]paitrnaapu c qerHbrN,l noreHuHa,loM. Marelraruqecrr.rfi anfiapaT KBaHTOBOn MexaHHKH.

Kovtryrarlur oI]eparopoB u e€ r!urr.r.recKnfi cMblcn. coorsonenue HeolpeAeJleHHocrei

l'efi:eH6epra. Oneparop r4Mnynbca. Co6crsenHHe 3uaqeHltt z co6crseHuHe rpymqltu.Kooprunarnoe Il r{MnynbcHoe llpercraBJleulrt soruonoft OyrrruI,tl,t. Oneparop flpol'I3Bo.4Hofi

Surzvecxoii BennqllHl,l no BpeMeHH. 3aroHur coxpaHeHut. flnorHocrb noroKa BepotrHocrl'l.VpanueHue He[pepbrBHocrl4 n rcsaHtogoi MexaHxKe. Vpanueuur lllpe4lrrepa B crallloHapHoMc-rr-vqae H ero pemeHurr. Craunonapnue cocroqHHt. O6rqr.re csoficrsa crarlnoHapuLrx cocrocHufiojlHo\repHoro .iIBlrxeHnq. KsaHroBbIii rapMoHH.Iecrufi ocqul,rrrop n 4erapronofi z c$epruecxoficrrcreMax KooprnHar. Bo,tHoel,te Qyuxuur.r n crIeKTp 3ueprlM- Cnuu. Ypannenut lnpara nK-'rcfina-|op.lona. ux ceoilctga u cBq3b. Oneparopsl poxaeHl,Is u yHrftlrox(eHvt. Orpaxeune unpoxoxreHue qacrrrrbr qepe3 oaHoMepHuft notenuualrHrtfi 6aprep. Oneparop MoMeHTa

r.rMnyxbca. Peureuue ypanuenafi na co6crneHuste 3HaqeHI4t. CSepnvecrue tpyurquu.llosrluarcuuii lt rroHlD(alolu]tfi oneparopst. Marpnuua.r reoplrt MoMeHra. Marpuunarrfopuy-,rraponr<a rsaHrosofi MexaHltKl.L PaCuet varpnvHbtx 3.rIeMeHToB. 3aAa'ra AByx ren.

lerNenue B rreHrpiurbHoM lore. O6ulue cBoicrBa. Klaccu(furaqua cocrotHl4ft Ar.tcKperHoro

cneKrpa. Ypannenue .fxt pa]lniutbHoii sorHosoft Qpmquu. Ypanneulte flay:ru. [ruNeHue:aprxenHoi qacruubr B MarHHrHoM none. MarpHIIbI clllHa 1/2. Ceoficrsa varpr'rq flaylu.Bo,rHogat rfynxuun qaorllllbl co cIrI'tHoM 112. Ypotuu Jlan4ay. Cloxenue MoMeHroB B

xsaHrogofi MexaHuKe. KorS$uqneHrrr Kle6ua-fopaaua. flocrpoenue BoJrHoBbrx $1'nxqufi c

OIIPCACJIEHI{I'IM CYMMAPHbIM CTIHHOM AJI' ABYX qACTI4II CO CNIIH:MH %. KNATUTIACCU.{CCTOE

npu6:ruNeuae. BoruoeHe QyurcUuu It ycnoBllt cuII4BKI4. Vcnonur [puMeHI4MOCTl.I

KBa3r4xJraccfiqecxoro npu6:ruNenut. [Ipaeulo KBaHToBaHIIt Eopa-3oruueprf e.nr4a. flputr,Iep

Haxo)fiAeHHq 3HepreTltrrecKoro cneKTpa c noMo[lbrc [paBHna KBaHToeaHI4s. Kga314r,'Iacc}l'recruft

xorQ$uqueHr npoxo)I{aeHut 'tepe3 noreullltarbHbli 6apbep. Bepo.rrnocr.u aepexoaa u3

cocroc6[{ Ar4cKperHoro cneKTpa B cocrotl{}It lrenpep6lBnofo cneKTpa no,[ aeftcrefievnepl.rOluqecKoro Bo3MyuIeHHt. MoveHr HMnynbga. LS- tl jj- Csqgr. O6N,IeHHoe B3auMoAencTBHe

n Knanrosofi MexaHuKe. flapa- n op'rorc,ruft. flpunqnn ToxAecTBeggocru. Ctarucrrlxa Oepnalt-

lupaxa u Bo:e-3itsurrefiHa. Broplrvnoe r(BaHToBaHrde. @epur.rousr, o[epaTopbr yHHqToxeHte IlpoxJeHuq, KoMr{}TaUHoHHble coorrtolleH}it. 3rfQerr 3eevasa (npocrofi u cnoxnslfi). MerO4

Purqa. flpuveneHrre BapuaquoHHoro MeTOAa r npu6rulxeunhlM pacrleTaM. Bepo.rrHoCrlrrepexola Me)(AJi cocTocrlrrtMH aHcKpeTHofo cne(Tpa floa Br[qHueM Bo3M),'UIeHHfl,

teilc rB) touero KoHeqHoe BpeMt. C,ryvafi HecrauuoHapHblx uorvyueHnfi' Teopnr

crarllroHapHbrx no:nyrUeuufi A,tq COCrocHLtfi AIICKpSTHOT6 c[eKTpa c BbtpoXAeHueM. flpurraepu.

Teopar crauuoHapHbrx Bo3v)ruenu :\trs cocTo.f,Hufi agcKperHoro cnel$pa 6er aupoxaeunr.flpuvepsr. BopHoecxoe lpn6,ruNeune B 3aaaqe paccesqqrg.. Ycrosuq [pr.rMeHuMOCTIl

6opuoecxoro npn6,ruNeuux. Ilpe.lellnsre cJIyqaI4 MeAJIeHHux u 6rrcrplx qacrnq. tlacrzqa g

epuoAr.rirecKoM nole. Btrpoxgeuue ypoeHeft sHeprllv. PaslOxenue nolHonofi tbynxqufl saAaqu

paCCerHHr rro cocrosHl.lrM s OIIpeAeneHHbIM MOM9HTOM. (Da:Onas Teoput paccetHur' (Da-gsl H

Marpuqa paccerH1tt. Merog caltocornagOBaHHoro nOJt XapTpIr-OoKa. CTaTucTI4qeCK[[ MSTOA

Touaca-@epvu.

3aneAynutufi Ka$eApofio6uefi n reoperrqecKofi Qll3nKu P /tf r'-( MuPsarYnoe P'