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§ 105*. MOMEHT HHEPU.HH TEJIA OTHOCHTEJibHO |
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H (10), TO OKOH'IaTeJibHOITOJIY'IHM |
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It= lxcas2a+JY cos2 ~+Jz cos2 y-21xy cos a cos~- |
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(12) |
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3a,ll.a11a 121. |
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272
K KOHil,aM oCTep:>KHH, TO HH DOJIO>KeHHe Il,eliTpa Mace, liH MOMeHT HHepil,HH
J z He H3MeHHTCH, HO CTaHeT He paBHbiM HYJIIO Il,eHTpo6e>KHbiH MOMeHT HHepunn J yz H ocb Oz He 6y,ZJ;er rJiaBHoii:; B pesyJihTare npn spameHiut B03HHKHYT ,ZJ;OllOJIHHTeJibHble 6oKOBble ,ZJ;aBJieHHH Ha ITO,ZJ;WHITHHKH ( OCb 6y,ZJ;eT «6HTb»).
fJJasa XXII
TEOPEMA 0 )J.BH)I(EHIUi U.EHTPA MACC CHCTEMbl
§ 106. ,li.H«<»«<»EPEHU.HAJlbHbiE YPABHEHH.sl ,IJ.BH)I(EHHSI CHCTEMbl
PaccMoTpHM CHCTeMy, cocTOHli1.YIO H3 n MaTepnaJihHbiX TO'leK. Bhl-
.n.eJIHM KaKyiO-HH6y,ZJ;b TO'IKYCHCTeMbl C MaCCOH mk. 0603Ha'IHMpaBHO- ,ZJ;eHCTBYIOIII.YIO Bcex npHJIO>KeHHbiX K TO'lKeBHelliHHX CHJI (H aKTHBHbiX, H peaKII.Hil CBHseil) qepes Fk_, a paBHO,ZJ;eilcTBYIOli1.YIO scex BHyTpeHHHX
CHJI - qepes Ft EcJIH TO'lKa HMeeT npH 3TOM ycKopeHHe ~. TO no OCHOBHOMY 3aKoHy JJ:HHaMHKH mkak=F'k+Fk'·
AHaJiorH'lHbliipesyJibTaT IIOJIY'IHMJJ:JI.SI JII06oii TO'IKH.CJie,ZJ;oBaTeJih·
HO, ,li.JI.SI BCeii CHCTeMbl 6yJJ:eT
m1a1 = Ff_ +F"t, |
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m2~=~+F~. |
( 13) |
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miin=F'h+ FA. |
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YpaBHeHHH (13) npe.n:cTaBJIHIOT co6oii au¢¢epeHlfUll;AbH.t:t£ ypaene-
HUfl aeu:JJCeHUfl cucme.Mbl8 eeKmOpHOU cpop.Me (B HHX ii,.=v-;; = f~t). Bxo.n:H-
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flpoeKTHpyH paBeHCTBa (13) Ha KaKHe-mr6yJJ:b KOOpJJ:HHaTHbie OCH, DOJIY'IHMJJ:HcM>epeHil,HaJihHble ypaBHeHH.SI JJ:BH>KeHH.SI CHCTeMbl B npoeK• Il,H.SIX Ha 3TH OCH.
floJIHoe peweHHe OCHOBHOll sa.n:aqH JI:HHaMHKH JJ:JIH CHCTeMbl 6y,ZJ;eT COCTOHTb B TOM, 'IT06bl, SHaH sa.n:aHHble CHJibl H HaJIO>KeHHhle CBH3H,
npOHHTerpHpOBaTb COOTBeTCTBYIOIII.He .n:mtxpepeHI1,HaJibHhle ypaBHeHH.SI H onpe,ZJ;eJIHTb B pesyJihTaTe 3aKOH ,ZJ;BH>KeHHH Ka>KJJ:OH H3 TO'leKCHCTeMbl H peaKII.HH cs.Siseil. C.n:eJiaTb 3TO aHaJIHTH'leCKHy,ZJ;aeTCH JIHWh B oT.n:eJihHbiX CJiy'laHX,Kor.n:a 'IHCJIOTO'leKCHCTeMbl HeBeJIHKO, HJIH >Ke HHTerpH-
py.SI ypaBHeHH.SI 'IHCJieHHO C ITOMOII1,b!O 3BM.
O.n:HaKo npn peweHHH MHornx KOHKpeTHhlX sa,ZJ;a'l Heo6xo.n:HMOCTb
HaXO.IJ:HTb 3aKOH .IJ:BH>KeHH.SI Ka)KJJ:OH H3 TO'leKCHCTeMbl He B03HHKaeT, a 6biBaeT .IJ:OCTaTO'lHOHaUTH KaKHe-TO XapaKTepHCTHKH, onpe.n:eJIHIOIIl,He ,ZJ;BH>KeHHe sceil cncTeMhl B u.eJioM. HanpnMep, 'IT06blycTaHOBHTb, KaK
.IJ.BH>KeTC.SI ITO,ZJ; ,ZJ;eHCTBHeM npHJIO>KeHHbiX CHJI KpHBOlliHITHO-llOJI3YHHbiH MexaHH3M (eM. pnc. 158 B §57), .n:ocTaTO'lHOonpe,ZJ;eJIHTb saKOH Bpaiil,e-
273
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(13) Herrocpe.n:cTBeHHo He rrpHMeHHIOT, a rrpnMeHHIOT .n:pyrne, pa3pa6oTaHHble B JJ:HHaMHKe MeTOJJ:bi. K HX qncJiy OTHOCHTCH MeTOJJ:bl, KOTOpbie JJ:aiOT lliHpOKO HCITOJib3yeMhie B HH:>KeHepHOH rrpaKTHKe
auHa.MuKu cucmeMbl, rroJiyqaeMhie KaK cJie.n:cTBH.H ypaBHeHnil (13);
3TH TeopeMhi H 6y.n:yT paCCMOTpeHhl B .n:aHHOH H B Tpex ITOCJieJJ:YIOW.HX rJiaBax.
Ho rrpe.n:sapHTeJihHO peWHM OJJ:HY 3a.n:aqy, rroKa3biBaiOW.YIO, qTo
HCKOMbiH pe3yJibTaT MO:>KHO HHor.n:a 3¢<PeKTHBHO HaXOJJ:HTb H Herrocpe]!,-
CTBeHHO, HCITOJib3YH |
,!l,IIqxpepeHuHaJihHhle |
ypaBHeHHH |
ABH:>KeHHSl |
CH- |
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3al(a'la 122. L( H H aM H 'Ie C K H ii r a C H T e JJ b |
K 0 JJ e 6 |
a H H ii:. YKperr- |
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JJeHHbiH Ha rrpy>KHHe rpy3 |
J COBeprnaeT BbiHY>K)I.eHHble KOJJe6aHHll IIO!( )l.eHCTBHeM B03- |
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Mym;aJOm;eii: eHJJbl Q, |
IIpOeKUHll KOTOpoii |
0x=Q0 sin pt |
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(eM. § 96). |
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Orrpel(eJJHTb, rrpH |
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3TH KOJJe6aHHll, IlpHKpeiiHB K rpygy 1 Ha |
rrpy>KilHe |
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3<fJ<fJHUHeHTOM >KeeTKOeTH c 2 rpy3 2 Maecoii |
m2 (pHC. |
283), |
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P erne H H e. Byl(eM orrpel(eJJHTb |
IIOJJO>KeHHll |
rpy- |
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30B KOOpl(HHaTaMH X1 H X2, |
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MeHHH eTaTH'IeeKOfO paBHOBeCHll rpy30B, |
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X ITO BepTHKaJJH BBepx. TOrl(a eHJJbl Tli>KeCTH ypaBHOBeCl!T· |
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Cll eHJJaMH yrrpyroCTH |
FlcT=c1AlcT H |
F2cT=c2A2cT |
H H3 |
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ypaBHeJIHt!: )I.BHMeHHll |
HeKJJJO'IaTCll |
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B § 94 3a)l.a- |
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'IY112), a Y'IHTbJBaeMwe rrpH |
l(BH>KeHHH |
CHJJhl yrrpyro- |
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CTH 6y)l.yT IIpOIIOpUHOHaJJbHbl YiJ.JJHHeHHHM, KOTOpble IIOJJy- |
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'laiOTrrpy>KHHbl IIpH eMem;eHHl!X rpy30B OT IIOJJOMeHHH eTa- |
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TH'IeeKQfO paBHOBeCHll. 3TH |
YiJ.JIHHeHHll |
6y)l.yT COOTBeT- |
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~~ CTBeHHO paBHbl A1=xi H A2 =x2-x1 H Ha rpys 2 6y-
PHc. 283 |
l(eT l(eiicTBOBaTb eHJJa ynpyrocTH p--;_ (F 2 x= -c2A.2), a Ha |
rpy3 1 - eHJJbl "F;=-~. fi (fu=-c1A.1) H Q. B pe3YJJbTaTe IIOJJy'IHMeJJel(yJOm;He )I.H<fJ<PepeHuHaJJbHble ypaBHCHHll l(BH>KeHHll rpy30B:
m;xl = - c1x1 +c2(x2-xl) +Q0 sin pt, |
m2x2 =- c2 (x2- x1). |
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4To6w KOJJe6aHHll rpysa |
1 racHJJHeb, )I.OJJ>KHO 6biTb x1=0. Tor,!la |
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c2x2 +Q 0 sin pt=O H m.:X2 =-c2x2. |
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Hs rrepsoro ypaBHeHHll x |
= - (Q /c ) sin pt H x~=p2 |
(Q /c |
) sin pt. B pesyJJbTaTe rro):t- |
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0 |
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2 |
cTaHOBKa BO BTOpoe ypaBHCHHe IIOeJJe eOKpam;ermli )l.aeT m2p2 = c2.
3TO H 6y,!\eT HCKOMbiM yCJJOBHCM rarneHHll, B KOTOpOM O)lHOH H3 BCJIH'IHHm2 HJIH c2 MO>KHO 3MaBaTbCll rrpoH3BOJJbHO. KoHe'IHO,MeJJaTeJJbHO, 'IT06blMacea m2 6hiJJa MCHbrne, HO IIpH MaJJOH m2 H 3a)laHHOM p 6y)l.eT MaJJO H c2, a 3TO IIpHBe,!leT K He>KeJJaTeJJbHOMY yBeJJH'ICHHIO aMIIJIHTY.!\hl Q0/c2· KOJJe6aHHH rpy3a 2.
§ 107. TEOPEMA 0 )J.BH)l(EHHH I.J,EHTPA MACC
B pH.n;e CJiyqaeB AJIH orrpe.n:eJieHHH xapaKTepa ABH:>KeHII.H cHcTeMbi (oco6eHHO TBep,[(OrO TeJia) Tpe6yeTCfl 3HaTb 3aKOH ABHIKCHHH ee ueHTpa MaCe. lJT06bl HaHTH 3TOT 3aKOH, o6paTIIMCfl K ypaBHeHHHM JJ:BmKeHHH CHCTeMbi (13) H CJIQ)KHM noqJieHHO HX JieBhle H rrpaBbie '13CTH. Tor.n:a rroJiyqHM
( 14)
flpeo6pasyeM JieByiO qacTb paBeHcTBa. Hs cpopMyJlhl (1').D.JIH pa)l;uycaBeKTopa ueHTpa Mace HMeeM
~ mkrk=Mrc·
BepH oT o6eux tiacTeii: 3Toro paBeHCTBa BTopy10 npoHsBO)l;HYIO no speMeHH H 3aMe"laH, 'ITOnpOH3BO)l;HaH OT CYMMbi paBHa cyMMe npOH3BO).I,- HblX1 HaH)l;eM
HJIH
( 15)
r)l;e ac- ycKopeHHe ueHTpa Mace CHCT€Mbl. TaK KaK no CBOHCTBY BHYT·
peHHHX CHJI CHCT€Mbl ~f1=0, noJiy"'HM OKOH"laTeJibHO H3 paBeHCTBa
(14), Y"'TH (15),
( 16)
YpaBHeHHe(16)HBbrpa)KaeT TeopeMy o ,ZJ;BH)KeHHH ueH- T p a M a C C C H C T e M bl: npOU38eOeHue .MaCCbl CUCtne.Mbl Ha ljCKOpeHUe ee qeHmpa .Mace paeHo zeo.Mempu~cKoii cyM.Me ecex oet1cmeytof4UX Ha cucme.My BHeumux cuA. CpaBHHBaH ypaBHeHue (16) c ypaBHeHHeM )l;BH)KeHHH MaTepHaJibHOH TO"'KH [§ 74, cpopMyJia (2)], npH.D.eM K ).l.pyroMy Bblpa)KeHHIO TeopeMbl: qeHmp .Mace cucme.Mbl iJeu:JtCemcR KaK .MamepUaAbHaJl mof{Ka, Macca Komopotl paeHa .Macce ecet1 cucme.Mbt u K Komopotl npuAo:JtCeHbt ece eHeumue cuAbt, oetlcmeytoll{Ue Ha cucmeMy.
flpoeKTHpyH o6e "laCTH paBeHCTBa (16) Ha KOOp)l;HHaTHbie OCH, ITO· JIY"'HM:
(16')
3TH ypaBHeHHH npe).I.CTaBJIHIOT C060H iJucfJr/JepeHu,uaAbHbte ypaeHeHUJl 08U:J!CeHUJl l{fHmpa Mace B rrpoeKIJ.HHX Ha OCH ,ZJ;eKapTOBOH CHCTeMbi KOOp- ,Zl;HHaT.
3Ha"leHHe .lJ.OKa3aHHOH TeopeMhl COCTOHT B CJie)l;yiOIII.eM.
1. TeopeMa )l;aeT o6ocHoBaHue MeTo)l,aM )l;HHaMHKH TO"'KH.Hs ypasueuuti (16')BH)l;HO, "'TOpetueHUJl, Komopbte Mbt noAyt.taeM, pacc.MampueaR iJaHHoe meAo KaK MamepuaAbHYto mot.tKy, onpeiJeARtom 3aKoH iJsu:JtCeHUJl U,eHmpa MQCC amoeO meAa,
B qacTHOCTH, ecJiu TeJio ).I.BH)KeTCH nocTyrraTeJibHO, TO ero ,ZJ;BH)KeHHe rroJIHOCThiO onpe)l;eJIHeTCH )l;BIJ)KeHueM ueHTpa Mace. TaKHM o6pasoM, nocmynameAbHO iJeu:JtCyU{eecR meAo MO:JtCHO scezaa paccMampueamb leaK
.MamepuaAbHYIO moliKY c .Maccotl, paeHoii .Macce meAa. B ocTaJihHblX CJiyqaHx TeJIO MO)KHO paCCMaTpHBaTh KaK MaTepHaJibHYIO TO"'KY Jlllillb TOr)l;a, KOf)l;a npaKTll"leCKH .lJ.JIH onpe)l;eJieHHH nOJIOJKeHIIH TeJia .lJ.OCTaTO"'HO3HaTb llOJIO)K€HHe ero UeHTpa Mace H ,ZJ;OnyCTHMO no ycJIOBHHM pewaeMOH 3a.ll.a"'H He npHHHMaTh BO BHHMaHHe Bpal.ij.aTeJihHYIO qacTb ).l,B H)K€H!U! TeJia.
275
fnasa XXIII
TEOPEMA Oli U3MEHEHIUI KOJIUIIECTBA ,!J.BU)I(EHU}I
CHCTEMbl
§ 110. KOJIH4ECTBO ,!J.BH)I(EHHSI CHCTEMbl
KoAuttecmeoM oeu:JJCeHufl cucmeMbt 6yoeM Ha3bteamb eeKmOpHyto eeAuttuHy Q, paeHyto ~eOMemputteCKOU cyMMe (~AaBHOMY eeKmopy) KOAUttecme
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oeu:JJCeHUfl ecex motteK |
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miif |
m2iit |
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Q=~mkvk. |
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floJib3YHCh 3THM orrpe.n:eJie- |
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v0 |
HHeM, |
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MOlll.hiO |
KOTopoH: |
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Jierqe BbiqHCJIHTb BeJilllHIHY Q, |
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a TaK)Ke YHCHHTb |
ee |
CMblCJI. |
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288 |
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l1s paBeHCTBa (1 ') |
CJie.n:yeT, qTo |
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~mit;;;= Mrc. |
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Bep.SI OT o6eux qacTeM: rrpoH3BOJJ:HYIO no speMeHH, rroJiyqnM |
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drk |
Md~ |
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·-'·/nit dT = |
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HJIH |
~mkvk = Mvc. |
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0TCIOJJ:a HaXOJJ:HM, qTO
(19)
280
T. e. KOAUI#!CmBO 08U;){CC1iUfl cucmeMbl pa81i0 npOU38COC1iU10 MUCCbl BCCU cucmeMbl Ha cKopocmb ee l{CHmpa Mace. 3THM pe3yJihTaToM oco6eHHO YJl.06Ho noJih3oBaThCH nprr BhrqrrcJieHHH KoJIHqeCTB Jl.BH)KeHHH TBep}l.biX TeJI.
113 <j)opMyJihi (19) BH)l.HO, qTQ eCJIH TeJIO (HJIH CHCTeMa) }l.BH)KeTCfl TaK, qTQ rreHTp Mace OCTaeTCfl HellO}l.BH:lKHbiM, TO KOJIHqecTBO }l.BH)KeHHfl TeJia paBHo HyJiro. HanprrMep, KoJirrqecTBo .IJ.BH:lKeHH5I TeJia, spaiiiarorrrerocH BoKpyr Heno}l.BH)KHOH ocrr, npoXOJl.HIIIefi qepe3 ero rreHTp Mace, 6y)l.eT paBHo HyJiro.
EcJIH :lKe .IJ.BH)KeHHe TeJia HBJIHeTcH CJIO)KHblM, TO BeJIHqHHa Q He 6y}l.eT 3aBHCeTb OT ero spaiiiaTeJihHoro }l.BH)KeHHH BOKpyr rreHTpa Mace. HanpHMep, )l.JIH KaTHIIIerocH KoJieca Q=Mvc, He3aBHCHMO OT Toro, KaK spaiiiaeTCH KoJieco BoKpyr ero rreHTpa Mace C.
TaKHM o6pa3oM, KOJirrqecTBo }l.BH:lKeHHH MO)KHO paccMaTpHBaTh KaK xapaKTepHCTHKY fiOCTynaTeJibHOrO }l.BH)KeHHfl CHCTeMbi (TeJia), a npH CJIO)KHOM }l.BH:lKeHHHKaK XapaKTepHCTHKY nocTynaTeJibHOH qacTH }l.BH)KeHHfl BMeCTe C rreHTpOM Mace.
§ 111. TEOPEMA OS H3MEHEHHH I(OJIHliECTBA ,ll.BH)I(EHHSI
PaccMoTpHM cncTeMy, cocT05lUJ.YID H3 n MaTepHaJihHhlX TO'leK. Co- CTaBHM }l.Jifl ;:nofi CHCTeMbi Jl.H¢<PepeHIIHaJihHble ypaBHeHHfl }l.BII)KeHIIfl
(13) II CJIO:lKHM IIX noqJieHHO. Tor}l.a noJiyqiiM
~mkak= ~Fk+ ~Ft.
nocJie}l.Hflfl cyMMa no CBOHCTBY BHyTpeHHHX CHJI paBHa HYJIIO. KpoMe Toro,
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0KOHqaTeJibHO HaXO)l.IIM |
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YpaBHeHIIe |
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Bhrpa:lKaeT |
T e o p e My |
o 6 |
H 3 Me H e H II II |
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K 0 JI H q |
e C T B a |
}]. B II :lK e H II 5I C H C T e M bl B |
}l. H <lJ <lJ e p e H- |
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ll II a JI h |
H o fi |
<P o p M e: |
npouseooflafl |
no |
epeMeHu om KOAUtLecmea |
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OBU;JfCCiillfl cucme.Mbl paeHa eeOMempuiieCKOU cyMMC ecex aeacmeyJOwpx Ha cucmeMy BHeutHux cuA. B
dd~x= ~Fkx• d;t = ~FkY• d~z = ~Fkz· |
(20') |
Haii}l.eM ,n.pyroe Bblpa)KeHIIe TeopeMbi. nycTb B MOMeHT BpeMeHH
f=O KOJIIIqecTBO )l.BII)KeHIIfl CHCTeMbl paBHO Q0 , a B MOMeHT f1 |
CTaHOBIITCfl |
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paBHhiM |
1 • Tor}l.a, YMHO)Kafl o6e qacTH paBeHcTBa |
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t,
Q1-cJ:= ~ ~ Fkdt
0
281
HJlH
(21)
TaK KaK llHTerpaJihi, CTOfllll,lle cnpaBa, ,D.a!OT llMfiYJibCbi BHeiiiHHX CllJI. YpaBHeHHe (21) Bbrpa:lKaeT Teo p eM y o 6 n 3M e He H n n KOJillqeCTBa .li:Bll:lKeHllfl CllCTeMbi B llHTerpaJib- H 0 H <lJ 0 p M e: U3.MCfleliUC KOAU4£Cm8a 08UiJICC1iUfl CUCme.Mbl3a liCKOmopbtfi npo.MeiJ/CymoK 8pe.MeHu paeHo cy.M.Me u.MnyAbC08, iJeiicmeyrowpx Ha
cucme.My 8HeutHux cuA 3a mom iJ/Ce npo.MeiJ/CymoK epe.MeHu.
B npoeKu;HHX Ha KOOpJI.HHaTHble ocn 6y,n:eT:
QI.x-Qox=~Skn Qiy-Qoy=~Sky• Qlz-Qoz=~Skz· (21')
Y Ka)KeM Ha CBf!3b Me:lK.D.Y )J.OKa3aHHOH TeopeMOH ll TeopeMOH 0 )J.BII- )KeiJ.llll u;eHTpa Mace. TaK KaK Q=Mvc. To, no)l.CTaBJIHH 3TO 3HaqeHHe s paseHcTso (20) n yqnThiBaH, qTo dvcldt=ac, noJiyqnM Mac=~.Ft T. e. ypaBHeHne (16).
CJie}l.oBaTeJihHO, TeopeMa o ,n:BH)KeHHH u;eHTpa Mace n TeopeMa o6 ll3MeHeHllll KOJillqeCTBa ,n:BH:lKeHHfl eneTeMbi npe,D.CTaBJif!IOT C060ii:, no cyiii;ecTBy, .n.se pa3Hble ¢opMbi o,n.Ho.ll n Toil :lKe TeopeMhi. B Tex cJiyqaHX, KOr,n:a ll3yqaeTef! )J.Bll:lKeHHe TBep,n:oro TeJia (llJill CllCTeMbi TeJI), MO)KHO B paBHOH Mepe llOJib30BaTbef! JII060H H3 3TllX <lJopM, npnqeM ypaBHeHHeM (16) o6blqHo noJib30BaTheH YJI.06Hee. .llJIH HenpepbiBHoii :lKe cpe}l.bi ()KllJl.KOeTb, ra3) np n peiiieHHll 3a,n:aq o6hJqHo noJio3yiOTef! TeopeMoii o6 ll3MeHeHHll KOJinqeeTBa ,n:BH)KeHHH cneTeMhi. Ba)KHble npnJIO)KeHHH 3Ta TeopeMa H>vieeT TaK:lKe B Teopnn y.n:apa (eM. rJI. XXXI) n npn nsyqeHnn peaKTHBHoro JI.BH:lKeHHH (eM. § 114).
OpaKTHqeeKafl I.J;eHHOeTb TeopeMbi eoeTOllT B TOM, qTO OHa fi03BOJif!eT HeKJIIOqllTb ll3 paCCMOTpeHllfl Hanepe,D. Hell3BeCTHb!e BHyTpeHHlle CllJibi (HanpHMep, eHJibl )J.aBJieHI:Ifl ,n.pyr Ha ,n.pyra qaCTlll.l; :lKll}l.KOCTH),
§ 112. 3AI(OH COXPAHEHH51 I(OJIUliECTBA )J,BU)I(EHM51
l13 TeopeMhl 06 ll3'vleHeHllllKOJIHqecTBa .li:Bll)KeHHfl ClleTeMbl MO)KHQ IJOJiyqHTb eJie,n:yiOlll,lle Ba)KHb!e CJie)l.CTBllfl.
1. OycTb cyMMa Beex BHeiiiHHX cnJI, ,n.eiicTByiOlli,HX Ha cHcTeMy, pas-
Ha HYJIIO:
~Fk=O.
Tor}l.a H3 ypaBHeHHH (20) cJie}l.yeT, qTo npH 3TOM Q=const. TaKHM o6pa3oM, ecAu cyMMa 8cex 8HeutHux cuA, iJeiicm8YfOU{UX Ha cucme.My, paeHa HYAfO, mo eeKmop KOAu4£cm8a iJ8UiJICCHUfl cucme.Mbl 6yiJem nocmoflHefl no .MOOYAfO U HanpaeAeHUfO.
2. 0yCTb BHeiiiHlle CllJibl, }l.eHCTBYIOIII;lle Ha CHCTeMy, TaKOBhi, qTo cyMMa nx npoeKu;Hfi Ha KaKyiO-Hn6y,n.h och (HanpnMep, Ox) pasHa Hymo:
~F.kx=O.
Tor}l.a H3 ypaBHeHnii (20) cJie}l.yeT, qTo npn 3TOM Q..,=const. TaKnM o6pa3oM, ecAu cy.MMa npoeKlfUtl ecex iJeucmeyroU{uX 8HCutHux cuA Ha
,282
fJiasa XXIV
TEOPEMA OS H3MEHEHHH MOMEHTA
I(OJIHIJECTB ~BH)I(EHH$1 CHCTEMbl
§ 115. rJIABHbJA MOMEHT f(OJIHlfECTB ABH)J(EHH.si CHCTEMbl
DoHHTHe o MOMeHTe KOJIIIqecTBa ,n;BII)KeHHH ,n;JIH o.n;Hofi MaTeprraJibHofr TOqKH Ob!JIO BBe,n;eHO B § 85. TAa81ibtM MOMelirnOM KOAUiiCCrnB 08UiJ/CeHUfl (HJIII Kll/iemutteCKUM .MO.MCHmOM) CUCmCMbl OmHOCUrnCAbliO aaHHOcO t{Ciirnpa 0 Ha3btBaemcRBeAuiiuHa K 0 , paeHwt aeoMempuqecKOii cyMMe MoMeHmoe IWAuiiecme aeuiJ/CeHUfl ecex motLeK cucmeMbt omHocumeAbHO amoao t{CHmpa *:
(30)
Ana.1ornq11o onpe.n;eJIHIOTCH MOMeHTbi KOJIIItJeCTB )l;BII)KeHrrH cncTeMhi QTHOCHTeJibHO KOOp)l;HHaTHhiX OCeu:
Kx='Smx(mkV,.), Ky='Smy(mkvk), K.. ="Smz(mk'V;.). (31)
Dpii 3TOM Kx, Ky, Kz npe.n;cTaBJI5IlOT co6ofl o.n;HospeMeHHO npoeKUHH BeKTopa Ka Ha KOOPJl.IIHaTHhre ocH.
B § 110 ohiJio OTMeqeRo, qTo KOJIHqecTBO }l.BmKeHHH ciicTeMhl MO)KHO
paccMaTpHBaTh KaK xapaKTeprrCTHKY ee IIOCTynaTeJihHOfO }l.BIJ:)KeHIIH. 113 IIOCJie.n;yroruero oy}l.eT Bli)l;HO, qTQ eAaBiiblU MOMeHm KOAUiieCrne OBU-
iJ/CeliUfl ( KUHemuiiecKuii MOMeHm) cucmeMbl MOiJ/Cem paccMampueambcfl
KaK |
xapaKmepucmuKa ee |
epalt{ameAbHOeO aeuiJ/CeHUfl. |
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B |
K II H e T II q e c K II fi |
M oM e H T |
B p a ru a ro ru e roc H T e JI a. |
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KaqecTBe |
Ba)KHOro |
KOHKpeTHoro |
npiiMepa |
Hafi.neM 3HaqeHrrH |
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Ku KIf II Kx )l;J15I TeJia, |
sparuaroruerocH |
BOKpyr |
Heno,n;BII)KHOH ocrr z |
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(prrc. 295). |
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KpaTKOCTH aeJIH'IHHYKo Ha3hiBaJOT KHHeTHtieCRHM MoMeHTOM HJIH |
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"' 4ame lVI!! |
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npOCTO MOMeHTOM |
KOJIHtieCTII ]\Bll:/1\eHHH CHCTeMbl, |
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290