(формат)Тарг

P1<{P2/sina,

tPYHKL{UU ( UAU 83JltnblM CO 3/WKO.M MUI-IYC llactnHbt.M npOU3800Hbl.M om notneH(,{UaJlbfWU Emepzuu) no coomeemctnBYIOU{U.M o6o6u,eHHbt.M KoopiJuHama.M.

llpHMep 3, Bee CUJlbl, ,n,eiiCTBYIOUJ.Ue Ha CUCTeMy, U306pa>&eHHYIO Ha puc. 3671 norenu;uaJibHbi. EcJiu npu sroM nanpaBUTb Koop,n,unarnyiD ocb Az BepruKaJibHO BBepx1 lrO llO <jxlpMyJiaM (64), (64') M3 § 127 Hail:,n,eM AJ!ll BCeii CUCTeMbl

IT=- (PI/2) cos cp-p (b0+x) cos cp+cx2/2,

I'Jleo6o6rneHHbie KOop.n.unaTbl q1=cp, q2=x. Tor.n.a
arr	.	an
Q1 = - acp-=-	[Pl!2+ p (b0 +x)l Sill cp,	Q2 = - - = p cos cp- ex,
		ax
~TO C0BTI3JI,aet C pesyJibTaTa~IJ.I, llOJiytJeHHbiMU		B npi!Mepe 2.
§ 144. YCJIOBH.SI	PABHOBECHSI CHCTEMbl
8 0606W.EHHbiX	KOOP,!J,HHATAX

CorJiacHo npuHuimy B03MO}!{Hhrx nepeMerueHuii Heo6xo,n;HMhlM H ,ll;OCTaTO'IHbiM ycJIOBlleM paBHOBeCHH MeXaHHt:IeCKOH CllCTeMhl HBJIHeTCH paBeHcTBO HYJIIO cyMMbi 3JieMeHTapHbiX pa6oT scex aKTHBHhlX ciiJI

(II CHJI TpeHHH ecJIII OHH COBepruaiOT pa6oTy) Ha JIIOOOM B03M0}KHOM nepeMerueHIIH cucTeMhr, T. e. ycJioBHe 2!6Ak=0. B o6o6rueHHbiX Koop,n;H· HaTaX 3TO yCJIOBHe, COrJiaCHO paBeHCTBy (112), ,n;aeT

Q16q1 +Q2<'>qz+ • • •+Qs<'>qs=O.

(116)

TaK KaK Bee BeJIH'IHHhi6q1, 6q2 , ••• , <'>qs Me}K.n;y co6oii He3aBHCHMhi, lfO paBeHCTBO (116) l'.fO}KeTBhiiiOJIHHTbCH TOr,zl,a H TOJibKO TOr,n;a, Kor,n;a

I{a}K)J.blll H3	K034J¢HUHeHTOB npn	6qb l'Jq z, , , , , 6q s B OT,ll;eJibHOCTH pa-
BeH HYJIIO,	T. e.
		(117)
B caMOM .n;e.'le, ecJIH .n;orrycnrTb,		qTo o,n;Ha 113 3THX BeJinqHH, HanpHMep

Ql> He paBHa HYJIIO, TO Bcer.n;a MO}KHO COOOIUHTh CHCTeMe TaKoe B03MO}K· Hoe rrepeMerueHHe, npH KOTOpOM 8qt"=f=.0, a 8q2 =6q3 =. , .=6q8 =0, II Mhl

npH)J.eM K npOTHBOpe'llliOC yCJIOBHeM (116).

TaKHM o6pa30M, OAR paBHoeecuR .Mexwtu<tecTwii cucme.Mbt Heo6xoou.Mo U OOCmamO'iHO, 'itnOObl Bee o6o6Uilfltibte CUAbl, C00tn6emcm6y/OU{Ue Bbt6paHHbl.M OAR cucme.Mbt o6o6u,eHHbtM Koopowtama.M, 6btAU paBHbtHYfiiO. lfUCJIO yc1106UU pa81i08eCUfl (117) pa6HO, KaK BH)l.HM, 'IHCJiyOOOOIUeHHbiX

Koop.n;uHaT, T. e.	ttucAy cmeneHeu	ceo6oobt cucme.Mbt.
lb cpaBHeHHH	MeTO)J.a Bhl'IHCJieHHH OOOOJJJ.eHHbiX CHJI (eM. § 143) II
CTIOC06a perueHHH	3a)l.a'I, KOTOpbiM	IIOJib30BaJIHCb B § 140, Bll)l.HO, 'ITO

110 cyruecTBY npH perneHHH 3a.n;aq C IIOMOIUbiO IIpHHUHIIa B03MO}!{HbiX nepeMei!J.eHHH Mbl Bhl'IHCJIHJIHCOOTBeTCTBYIOIIJ.He OOOOIIJ.eHHbie CHJihl, a 3a•

TeM npHpaBHHBaJIH HX HYJIIO.

PaccMoTpHM erue .n;sa npuMepa.

]. YC.'IOBHeMpaBIIOBeCUli CHCTeMbl, H306paJKeHHOH Ha puc. 366, 6y,n,er Q1=0 HJlll P1=fP21sin a. nocKOJibKy npn BbltJHcJJennn Qi 6b!JIO npmil!To, qro FTp=fN=Fnp, TO ycJioBne Q1=0 .n.aer nau6oJiblllee snatJenne P1 , npn KoropoM rpys A ne orrycKaeTcll, rr. e. orrpe.n.eJil!eT rrpe.n.e.'lbnoenoJioJKenue paBHOBeCHll (eM, § 25), CucreMa 15y.ll.eT B paaHOBecnn u npn

375

§ 145. YPABHEHHSI JIArPAH)l(A

lho6bi Haii:TII ypaBHeHHH ,Il,BIIA<eHIISI MeXaHII'-leCI<OH CHCTeMhi B OOOUIII.eHHh!X KOOp,li,HHaTaX, o6paTII~1CH K OOII.I.eMy ypaBHeHH!O )J.IIHaMHKH

(102), KOTopoe ,ll,aeT

(120)

llJIH o6u.r.HoCTII He 6y,ll,eM npe,ll,noJiaraTh, '-ITO Bee HaJio:lKeHHhle Ha

CliCTeMy CBH3H SIBJIHIOTCH H,ll,e8JibHbiMII. TI03TOMy B nepByiO CYMMY MO-

ryT	BXO,li,IITb	KaK pa60Thl 8KT!IBHbiX CHJI, T8K H, HanpHMep, pa60Thl
CIIJI	TpeHIISI.
TiyCTh CHCTeMa IIMeeT S CTeneHeH CBOOO,ll,bi If ee IIOJIO}I{eHIIe onpe,ll,e-
JISieTCH o6o6rueHHhiMH Koop,li,IIHaTaMII (104). Tor,r1,a no ¢opMyne			(112)
		~<'3Al< = Ql <'3ql +Q2 <'3qz+ · · · +Qs <'3qs.	(121)
0'-leBII~HO,		'-ITOCOBeprneHHO TaK me, KaK 3TO Ob!JIO C,ll,eJiaHO B § 143
)l.JIH	ciiJI F10	MO:lKHO rrpeo6pa3oBaTh K o6o6rueHHhiM KOOp,li,IIHaTaM
sneMeHTapHyiO pa6oTy ciiJI IIHepuHII F~. Tipii noM nony'-IHM
		~oA~ = Q¥ <'3q1 +Q~ <'3q2 + ... +Q~' oqs,	(121 ')

r,n;e Q~, Q;, ..., Q~- o6o6U{eHHbte CUJlbl UHepi{UU, KOTOpbie COfJiaCHO <iJopMyJiaM (109, (Ill) 6y,ll,yT:

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- 1	= ~ (_i_ (z: mkv:)]-_!_ ('			1:	mkv:) =_?_(aT )-aT
Q"						dt aq1 iJq '
	dt aq'1	2	iJql		2

r)J.e T=Z:mkv:12- KIIHeTuqecKaH 3HepriiH ciicTeMhl.

AHaJioriiqHble Bhrpa}KeHIIH noJiyqaTCH )J.JIH scex OCTaJibHbiX o6o6-

IIJ,eHHbiX CHJI IIHepuiiii. B	pe3yJihTaTe paBeHCTBa (123) )J.a)J.yT OKOHqa.
TeJibHO	(aT)		aT		)
d		-		Ql,
dt	a(h		aql =		I
d(aT)		-	aT
dt	aqz		Oq~=	Qz,	}	(127)
............
d	(aT)		aT		I
dt	- .	-a-=Qs.			J
	aqs		qs
YpaBHeHIIH (127) H npe)J.CTaBJIHIOT co6oii					aucpcpepeHI{UaJliJHbte ypas-

HeHUfl oeu:J/CeHUR cucme.MblO o6o6Uif!HHbtX Koopounamax uAu ypasnenuflX

Jlazpafl:J/Ca *. 4IICJIO 3TIIX ypaBHeHHl'i:, K8K BH)J.IIM, paBHO qncJiy CTeneHeii: CBOOO)J.bl CIICTeMbl.

YpasHeHIIH JiarpaH}Ka )J.BIOT e)J.HHblii II npiiroM )J.OCTaToqHo npocToii

MeTo,n; perneHHH 3a,n;aq )J.IIHaMHKII. Ba}I{Hoe npeHMyiiJ,ecrso 3THX ypaBHe-

HHii COCTOHT B TOM, qTO HX Bli)J. II qifCJIO He 38BHCHT HH OT KOJIJiqecrsa

TeJI (IIJIII ToqeK), BXO.D;Hlll,IIX B paCCMaTpiiBaeMyiO CHCTeMy, HII OT TOfO, KaK 3TH TeJia )J.BII}KYTCH; onpe.rr.eJIHeTCH qJICJIO ypaBHeHHH JlarpaH}Ka TOJihKO tiiiCJIOM cTeneHeii cso6o,ll,bl CHcTeMhr. KpoMe Toro, npH II.II.eaJibHhiX CBH3HX B npaBbie qaCTll ypaBHeHHH (127) BXO.II.HT 0006IIJ,eHHbie aKTHBHbie CliJibi, ll, CJle.II.OBaTeJibHO, 3TH ypaBHeHHH TI03BOJIHIOT 3apaHee

IICKJIIQqHTb ll3 paCCMOTpeHHH Bee Harrepe,n; HeH3BeCTHble peaKI.J.llll CBH3eH.

OcHOBHaH 3a)l.aqa .II.IIHaMHKII B o6o6rueHHhrx Koop,n;IIHarax cocToiir B TOM, qroohr, 3HaH o6o6rueHHble CHJibi Qb Q2, ... , Q8 II naqaJihHbre YCJIOBHH, HaUTH 38KOH )J.BII}KeHHH CliCTeMbi B BH)J.e (107), T. e. orrpe.rr.eJIHTb o6o6rueHHhre Koop.n;IIHaTbl q11 q2 , ••• , Qs KaK ¢YHKI.J.HH speMeHH. TaK KaK KIIHeTIIqecKaH 3HeprHH T 38BHCHT OT OOOOII.J.eHHbiX CKOpOcTeii qi,

TO rrpu ,n;uqxpepeHUllpOBaHHH nepBbiX tiJieHOB ypaBHeHIIH (127) no t

B JleBbiX lJ3CT5lX 3THX ypaBHeHHH llOHBHTCH BTOpbie npOII3BO)l.Hhie TIO speMeHII q~ OT IICKOMbiX Koop.rr.uHaT. CJie)J.OBaTeJihHO, ypasHeHHH JlarpaH}Ka npe.n;cTaBJIHIOT co6oii: o6biKHOBeHHbre .n;uqxpepeHuiiaJihHhre ypas-

HeHIIH		BTOporO		nopH)l.Ka	OTHOCIITeJihHO	OOOOlll,eHHbiX KOOp)J.IIHaT q11
Qz, ·	•	.,	Qs·
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CHCTeMy			CliJibl TIOTeHII.HaJibHbie, TO, llCITOJib3YH c}lopMyJibl (115), MO}KHO

* YpaBHeHHH JiarpamKa MoryT rrpuMeHHTbCH )l.JIH usy'leHHHt~BJHKeHHH JiroObiX MeXaHH'leCKHXCHCTeM C reoMeTpH'leCKHMH(TOlJHee C rOJIOHOMHb!MH) CBll3l!MH. ,UJill H3Y· lJeHHll )J.BHJKeHHll HerOJIOHOMHblX CHCTeM (CM. § 137) iiCll0Jlb3YIOTCH ,npyrne ypaBHeHiill 1

KOTOpble B ,llaHHOM Kypce He paCCMaTpHBaiOTCH,

378

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3

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5

PA3JI,EJ1

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r JI a B a

1. 0CHOBHble IIOHSITH51

ll HCXO)I,Hble IIOJIOlKeHHI!

CTaTHKH

9

§ I.

A6coJIJOTHO TBepiJ:Oe TeJio; cnJia. 3a,aa'ln cTanum

9

§ 2.

HcXOIJ:Hble noJioJKeHHH cTaTHKU ..

II

§ 3. CBH3f! a nx peaKUHH

•

• . .

.

•

•

• .

15

r J] a B a. II.

CJiolKeHne CIIJI. CncTe~la CXO)I,Rlli,HXCR

CHJI

18

§ 4.

feOMeTpH'leCKHHCll0C06 CJ!OJKeHHH CHJI. PaBHO.'I,eiiCTBYIO!l\351CXO!l_H-

18

Il~llXCif CHJI; pa3.'IOJKeHHeCHJI

• • . .

. . • . •

. • • • . . . • .

§ 5.

ITpoeKUHH cHJibi ua ocb 11 Ha nJiocKOCTb. AHaJIHTHLJecKnii cnoco6 sa-

20

,n_annH H C.'IOJKellrrH CllJI . . .

. .

• .

§ 6.

PaBHOBecne CHCTeMhl CXO!l_Hll\HXCH Cll•1 . . . .

,

•

23

§ 7.

PemeHne

33J13'l CTaTHKII . . .

• . .

•

•

• •

• . .

25

r JI a B a

III.

MoMeHT CHJ!bl OTHOCIITCJibHO U.CHTpa. napa CIIJI

31

§

8.

MoMCHT CHJli:>l OTHOCIITeJibHO UeHTpa (H,1H TO'lKH)

31

§

9.

f1apa CHJI. MOMC!lT

napbl . . . .

. • . . . . .

33

§ 10*. TeopeMbr o6 3KBHBaJieHT!!OCTH

n

o

c.10JKeHuH nap

35

r JI a B a

IV. npHB€.1\CHHe CHCT€Mbl CHJI K IJ.€HTPY· YcJ!OB!tR paBHOBeCHR

37

§ 11.

TeopeMa

o rrapaJI.'leJibHOM rrepeHoce

cHJibl • • . . • • • •

37

§ 12.

ITpnBeJ(eHne

cncTe~Ibi

CHJI

K

)l:aHHoMy

ueHTPY

.

• . .

.

•

• .

38

§ 13. YcJIOBHH paBIIOBeCHH CHCTeMbl CHJI. TeopeMa 0 MOMCHTe paBHO,'l,eikT-

40

BYIO!l\efi

• .

. • .

.

• . .

f JI a B

a

V.

0JIOCKaR

CHCTeMa

CHJI •

•

•

•

•

• . • • .

. • • • •

41

§ 14.

AJire6paH'lCCKHe MOMeHTbi

cHJihi

n

rrapbi . . . • • • .

41

§ 15,

f1pHBC!l_€I!He llJIOCKOH CHCT€Mbl CHJI K npOCTeifmeMy BHJ(y

44

§ 16,

PaBHOBCCHe II.'lOCKOHCHCTCMbl CHJI. C.!Jy'laH napaJIJieJibllbJX CHJI

46

§ 17.

Pewenne sa,n_a'l •

• . . .

•

.

•

•

. .

. .

•

.

• . .

•

•

• •

48

§ 18.

PaanosecHe cncTeM

TeJI •

•

.

• .

• .

• . .

•

• . •

• .

• .

53

§ 19*. CraTHlJeCKH

onpe,n_eJIHMbie

n

cTaTH'leCKH neonpe,n_eJIHMbie cncTeMui

56

T€JI (KOHCTPYKUHH) . . . .

• .

•

•

§ 20*. Onpe,n_eJieHne BHyrpermnx ycnJinfr

57

§ 21 *. Pacnpe,n_eJieHHhle

crrJibi . . .

58

§ 22~. PaclJeT

rrJiocKnx

cpepM • .

61

r J] a B a

VI.

TpeHne

• . •

• . . .

64

§ 23.

3aKOHbl TpeiiHH CKOJibJKeHHH • . .

64

§ 24.

PeaKUHH rnepoxollaTbiX Cllf!3eiL Yro.lJ rpeHIIlT

66

§ 25.

Pasnoaecne

npn

Ha.lJHlJHH

rpfHHH

• •

66

§ 26*. TpeHne

HHTH o un.nHHIJ:PWieCK)'!O nosepxHOCTb

69

§ 27*. TpeHne

Ka'leHHH . . . .

•

•

•

•

.

•

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71

412

r

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a B a

VII.

npocrpaHCTBeHHall CHCTCMa CIW . .

• . . . . . .

.

.

.

•

72

§ 28.

Mm.IeHr CH.'lbiOTHOcnreJILHO ocll. Bwmc.'ICHHer.~annoro

ncr;ro;Ja

11

!'.~a!IHOI'O MOMCI!Ta

C!lCTe:.\Ll

CH.'l , , .

. .

, . . . ,

.

.

.

.

72

§ 29*, TipHBe)l:eHHe ITjJOCTpilHCTE7,Hl!Ot'\C!KTCMLI C!W .~<

lljJO~Tciilll('!\!y

"!:,'\)'

77

§ JO.

PaBnosec11e r:po!l3BOJibliOll upu..: 1pancr;:;emiOH cucH·~r'>r c<~Jr. C:1) _

'lai{ napa.~!le.TbHhix crw ..

79

J]

a R a

VIII.

L(eHTP 1lllKeCTI-! ...

80

§ell.

lJ,CHTp

napa.~.1e.1b!lb!X

Cll.'l ,

86

§ 32.

CIIJIOBOe no.1e. UeHrp

T51lKCCTH

rv p~oro TC'.'la

83

"C)Co

]\oop,n_HH3Tbl [[efl'i'iJOBT51ll,C'CI 1<

C,"(liOflOJ,Jlh!X TC.~

89

::-; 00.

§ 34.

Cnoco6hi orrpe)l:eJieHIJ51 rwop~1,r:n nenrpon TrDKecnl re.'I

90

§ 3.3.

I~cHrpLI T51,KCCTtl HerwropLIX o.:u;opo;.\HbiX

TUI . . . .

93

P/\.3D:EJ1

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K11IIE.'.iATI1KA T04KH 11 TBEP.J,Of'O TEJ1A

r J] a B a

I X.

KI'!He~:nmn TO'lKH . . . .

93

~ 3G.

Bse.n_eHHe B KI!HeMaTHKY . . . .

9S

§ 37.

Cnoco6Lr sa;pHH51 IJ:BmKe!ln51 10'1,(!1.

96

§ 38.

BeKrop

cKopoc·IH ro'lKH . . . . . .

99

§ 29.

BeKTop

ychopermR TO'lrm . . . . .

100

§ 40.

Onpel(e.~em~e o:opocTH 11 yrKopeHnH

TO'lKH Epn

J:oop;umaTHOM

102

§ 11.

cnoco6e sal(aHH51 .L!BHiKeHIHI . . . .

.

•

•

• •

• •

Pewenne

3a.'l,a'lJ(!IHeMarHKH Hl'!KH . . . . .

. . . . . • •

103

§ 42.

OCH ecTeC1:1t:HHOro 1pcxrpaHHIIKJ. LincJIOIJOe 3I.bYtiiHc o:Kopocm

107

§ 43.

KacareJit..HOe n nopMaJib!lOe ycrwpenHH TO'!KH . .

103

§ 44.

HeKoropbre qacTHLre c.rryqan l(BmKeiiHfl

TO'IKH . . .

110

§ 45.

fpacpl!KH

IJ:BHZ\€HIIll, CEO]lOCTII II ycKO]l€1!!15! TO'll;il

112

§ 43.

PerneHlle

3d,1il'I . . . . . . . . . . . . . . . . .

114

§ 47·". Cr~opocTb

u ycKopeH!Ic TO'lKI!B no.151pHLrx KoO]lflH!JaTax

116

r J] a B a

X.

nocrynaTeJibHOe II spauwTeJibHOe )l.BlllKCHHII

T!lfjl;l,OfO Te.~a

117

§ 48.

Tiocrynare:rb!J02 J(BHJKeHJie . . . . . . . . . . . . . . . .

117

§ 49.

BpalllaTe.%H02 1J:3InKeHHe T!lep,'l;oroTeJia BOKpyr CCII. Yr.'IO!l:JHcr-.o-

IJ9

pocrb II

yrJI0:30€ yCKOpCHHe • . . . .

. • , . .

§50. PaBHm!epHoc H paBHOnepeMeHHoe BJlallleHHfl .....

,

•

!:2!

r J]

§51. CKopocTH Ii yctwpeunH TO'iCKHpalL(alO.t(crocH re.1a

. . .

•

122

all a

XI.

flJJOCKOnapaJIJICJ!bHOe )I,B!IlK€HIIe

TBep,!i.OfO re.la

.

• . .

127

§ 5J.

YpaBHeHI\51 n.lOCKorrapanJie.%!1oro ,ll,BH}KeHI\51 (AiliDKeHH51 n.Toc-

Koii <jmryph').Pa3/IO£K€HIIe !1-BWKCHHH

!13 ITOCT}TJJ re.1bHO€

II

Bpa-

I 27

lllaTeJibHOe . . . . . . . . . . . . . . . . . . . . . . . . . .

§53'". Onpe,n_e,leHn~ rpaeKropu!{ Tu'!ei( rr.'IOCKOHqmrypbr

. . .

. .

• .

129

§54.

Onpe,n_eJielH\C CKO]lJC1eH TOI.\eK n.'IOCKOM<tmrypbl .

, , , , .. ,

130

§55.

TeopeMa o·npoeKUa51x cKopoCTeii ll:IlYX TOlJeK re:w . . . . . . .

·131

§56.. Onpe.n_e.1enne cKopoCTei'iTOI.\eK n.1o::Kolr qmrypLr c no:~IOU\blO MfHO-

132

BeHnoro UeHTpa CKOpOCTeH. TI0!!51THe 0 UCIIT]JOII)l:3X

§57.

PeweHHe

sa)l:aY . • . . . . . . . . . .

• • . . . . .

136

§58*. Onpe,n_c.'lenHc ycKopeHHH ro•reK n.1ocKoii qmrypLI • . . • . . .

140

r .'!

§59'. Mrnosennbll! ue!ITp ycKopeunii

• • . . . . . . . . . . . . . .

145

a B a

XI I$. ,li.BHlKCHHe TBep)l,oro teJia BOK;Jyr HCflO)I,BHlKHOK T<l'lKIIII )I,BH-

14 7

lKeHHe CBOOO)I,HOfO TBCp)J.OfO TeJia • ,

. ,

, , , , , •

§ 60.

)lBf!iKerme

T!lep~OIO TCJI3, I1Mel0lll<:f0 0!1-HY Hel!Oj!,B!lfi(H)'IOTOlJI(Y

147

§ 61.

KHHeMaTH'JecrweypaBHeHHH 3i'wepa . . • • • • . . . . . . •

149

§ 62.

CKopocm 11 ycrwpean51 To'leKre:ra . . . . . . . .

150

~ 63.

06lllHl!

c.'Iy•wii.'J:BH)KeHH!lcsoCio~Horo TBep.n_oro re.1a

153

r JI a B a

X II I. CJIOlKHOe )I,BHlKeHHe TO'iKH .

• . . . . . . . .

!55

§ 6i.

0THOCHTe,1bHOe, nepeHOCHOe H a6cOJHOTHOe !l-BH:lli.eUH51

155

§ 65.

TeopeMa

o

c.1o:lli.eHna CKopocrefi

•

• •

• • •

• . .

156

413

§ 66.

TeopeMa o CJIO)Kemm ycKopeH!ril (reopeMa KopnoJinca)

160

§ 67.

Pewemre 3a,IIa'l • •

•

•

•

• • • • •

•

•

164

r J] a B a

X IV-~<.

CJJOlKHOe

)I,BlllK€HII€

TBep)l,oro

TCJJa

169

~ 68.

CJJoJKenne rroCTynaTC.~bllb!X iJ:B!llKenm1 •

•

•

• .

169

§ 69.

CJioJKenne npallleHnlr nor,pyr .r~nyx napa.~.~eJJhHhiX oceri

169

§ 70.

L~nJIHHIJ:pn'lecKne sy6'1aTb!enepe~J:a4H

. •

•

• . .

.

•

•

172

§ 71.

C.~oJKenne npall\CHHH BOKpyr nepeceKaKLmnxcH ocef1

•

• . • • . •

174

§ 72.

C.~O)!{€JH!e nocrynareJibHOI o

n

npam:JTC.1bHoro /IBHlKeHai'r. Bmrro-

176

noe IJ:BHlK€HHC • , , ,

•••

,

•

,

,

,

•

,

,

,

••••

,

•

•

•

PA3/J:EJI

TPETYrc:J"

.ll!IHAAI.HKI\. TOtiKH

r .'1 a B a

XV. Bsei!,€HH€

B

)I,HHaMt!Ky. 3aKOHbl

.D.HHaMHKH

•

• • • • •

180

§ 73.

OcnOBHbie noHHTHH 11 onpc)lem"Hl!H • . . • . . • . . • •

180

§ 74.

3aKOilbl IJ:Hfi3M!lKl!. 3aJ(:l'lll il:HH3\111KII MilTC'p11a.1bHO~"I TO<JKH

J8J

s·

7 5

C!lcreJHhl e;unl)ju . . . . .

183

§

76:

OcHOBHbie BIIIJ:bi

c1w .

.

•

• • . • •

• • . . • • . . • •

184

r JI a B a

XVI. ,!J.n¢(/Jepcll!J,HJ.1bllbl€

ypaBifCHIHl

l(BH<hCIII!R

TO'lKH. PerneHI!e

186

33)1,3'1IJ:HH3MHKH

TO'IKH •

•

• . . • • , • • • • • . •

§ 77.

,il,H<jJ¢<:pCHUilaJibHG1€ ypaBHCHI!H .l\llHlKCHI!H \!3TCpHaJibHOH T04l\H

186

§ 78.

Perneuue nepnoH. 3a;J,3'lllIJ:I!HaMHKH (onpe,liMeHHe crw rro 33fi3HHO-

§ 79.

MY ,'(BHJKCH!!KL) • . . .

• .

. • • • •

• • • . .

• . . . • • . •

187

PeweHne OCHOBI!Ol! 33J\3'11!)l.liH3MI!KII llpH llpHMOJIHHCH!!OM JIBI!lK€-

189

§ 80.

IIHH T0'11{!1 .

.

• •

•

,

•

, • • • •

,

.

,

•

•

,

,

•

fipH~repbi peweHnH

33J13'I .

• .

•

•

•

.

•

•

•

•

•

•

•

•

•

•

•

191

§ 81 *.

na)leH!Ie re.'laB conporHl.l.:IH!Olll,ei'lcHcpe;le (n B03;J:yxe)

•

•

•

•

•

196

§ 82.

PeUICHH€ OCHOBIIOii 33,:\a<Jl! ,lii!HaMI!Kil

ll]lll KJlUB0.11lHel!HOM .l\Bl!lli€-

197

HilHT0'1KH.,.. •

•

•

•

• • • • •

•

•

r J] a B a

XVII. 06lii,H€

TeopeMbl

)I,HHaMHK!I

TO'IKH •

•

•

•

•

•

•

201

§ 81.

Ko.'ln<JeCTBO/l,BI!lK€HliH T0'1KIL 1-hmy.'TbCcH.%1 .

•

•

•

201

§ 84.

TeopeMa o6 li3MeHeHHll

KO.'IH'IecrnaiJ:BIOKermH

TO•I;m

~02

~ 85.

Teope~13 06 li3MeHCHlll! MO~l€HT3 KOm!'leCTBa,liBHlKCIJllil TO'JKH(TeO-

204

peMa MOMCIITOB) • . .

•

•

.

•

•

•

•

.

.

•

• .

. .

• • • • •

§ 86• . .llBHllieHH€ llO;( ,li€HCTBI!€M

U€HTp3.1lbiiOii

CHJ!bl. 3aKO!!

!l.'IO!Ua,ll.ei\

206

§ 87.

Pa6ora CHJibi. MolllHOCTb

. •

•

•

.

•

•

•

.

•

•

•

•

•

208

§ 88.

DpnMephl nhl~llCJlCHH5l. pa60'Ibl •

•

•

. • • • •

•

•

•

210

§ 89.

TeopeMa o6 H3MeHeHnH KHnerwrecKoii sneprnn T0'1KH

213

T JI a B a

XV111.

Hecwoo,!lnoeu OTHOCHTCJJbHoe )l.RI!JKeHHll TO'IKH

219

§ 90.

Hecno60iJ.HOe

.l\BlllKenHe

T0'1KH •

•

•

•

•

•

•

•

•

•

•

219

§ 9\.

0THOCHTCJ!bHO€

)l.Bl!)!{CHH€

TO'IKI! • .

. • • • •

•

•

.

•

223

§ 92.

BJJliHHll€ npau!eHHH 3eMJJH Ha paBHOBec!le If ,ZI.BHlKeHne Te.lJ

227

§ 93*,

0TKJIOH€l!HC ll3,!1,aKL!l\Cf! TO'IK!lOT B€JlTHK3.~1! BCJ!Cl(CTBHC B]l3!U€H!l51

230

3€11.:11!

•• , • ,

•

•

•

•

•

•

•

•

•

r Jl a B a

XIX. flpRMOJ!HHCHHble KOJie6aHI!R TO'IKH • • • • • • • • • • •

232

§ 94.

CBOOOl/,llbie KOJie6aHI!H 6e3 y'leTaCH.1

COII]JOTHM€111151 • • • • , •

232

§ 95.

Cno6o;n,Hhle Ko.1e6anmi npn BH3KOM conpoTHBJieHHH (saryxaKL!UIIE'

238

§ 96.

KOJJe6annH) • •

•

• • .

•

•

• . • • •

• • • • •

Bb!HYJK.lJ:eHHbre

KOJie6aHH!l.

Pe3onanc ,

•

,

•

•

241

r Jl a B a

XX~. )J.BHlKeHHe TeJla B noJle 3eMnoro TllfOTeHHH

250

§ 97,

]lBHlK€HHe 6pO!ll€HHOrO TeJia

B

llOJl€

T51f0T€HH51

3e~Wll

250

§ 98. HcKyccrneHHbie cnyrHHKll

3eMJIH. 3.'I.'IMITTll'!ecKHerpaeKTOpHH

254

§ 99,

nonHrue o nenecoMOCTH. MecrHble cncreMhi orciJeTa

•

•

•

•

•

•

257

414

PA3,QEJI llETBEPTbiVI

)]JIHAMHKA CHCTEl1-lbi H TBEPJ]OfO TEJL4.

r Jl a B a

XXI. Bsei!,CHHC B JI.HHaMHKY CHCTCMbl. MoMeHTbl

HHept(Hlt

263

~ 100.

McxaHH4CcKaH cncTc~w. CUJibl BHeillHlle H BUJ'IpemrH2

263

§ 101.

Marca cHcTeMbl. Uemp

Mace

• . .

• • • . . .

. .

• . .

264

§ J02.

MOMCIIT HHCpl.l,l-1>1 TC.1a OTHOCI!TC.%1!0 OCH. Pannyc

:~.'IC'pl.I,;1JI . .

263

§ 103.

MOMCI!Tb! l!HepUHII TE',~a

OTHOCHTCJlbUO rrapa.1.~C.7b!ibl\ OCCif, Teo-

263

peMa froiirenca

. • .

.

• .

•

• . .

. . • • . .

. . . . . • •

§ 104*. UeHTpo6e)!\HLie

MmH::HTbi

HHepll,IIH.

DoHHTllll

o

r.ij"BHbn

ocr\

§ 105*,

HHCplUH! TeJia •

• •

.

·

·

.

•

•

·

·

·

•

·

· . . . .

269

MOMCHT ll!ICpUIIH TeJia OTHOCHTCJlbHO rrpOH;)BO.I!bHO!l OC!!

271

r JI a B a

XXII. TeopeMa 0 JJ;BHlKCI!IfH

I:ICHTpa

Mace CHCTCMbl

• .

273

§ 106.

,Ut!<jltpepCHUHaJibHbiC

ypaBHCHilll

,l(B!l)KCH1151

C!ICTeMbl

273

§ 107.

TeopcMa o .l(BH:JKCHHH uenrpa Mace •

• . .

274

§ 108.

3aKOH COXpaHCI!1!5l !l.Bli:JKCHH51 UCI!Tpa M3CC

•

•

•

.

•

276

§ 109.

Pe!liCHHe sa,n;aq •

. .

•

•

•

.

•

•

•

. .

.

•

• .

• .

277

r JI all a

XXIII. TeopeMa oti H3MCHCHHH KOJ!H4CCT!la ll,BIIlKCHHR CHCH'Mb!

280

§ l 10.

KoJIH4ecrno .n;nu:JKeHHH

cncTeMbi

.

•

•

•

•

•

•

•

•

•

~80

§ Ill.

TeopeMa o6 nsMcHeHHH KOJJH4CCTBa ,annJKCHHH •

•

•

281

§ 112.

3aKOH C0Xp3HCHH51

K0•1114CCTBa

.l(BillKCHl\51 .

.

•

• .

282

§ 113*. DpHJJO:JKeHHe reopeMbi K !l-BH:lKeHHIO }Kil;J.KocTH (rasa)

284

§ 114*. TcJJo rrepeMeHnoii MaccLr. Jl.nHJKCHHe paKeTbi

• .

•

•

287

r JI a B a

XXIV. TeopeMa o6 H3MeHeHHI! MO'IICHTaKOJlll'lCCTB JI.BlllKCHI'II!CltC-

29;)

TCMbl • , •

• • • • •

•

•

•

•

•

•

•

•

• .

•

•

•

,

.

•

•

§ 115.

fJJaBHb!H MOMeHT KO.~lllJCCTB .l(BH}KCHIIH CHCTeMbl

.

•

. .

• . .

29J

§ 116.

TeopeMa 06 113MCHeiiHH fJiaBHOfO MOMCHTa KOJ!Il'leCTB)l:BHLI(C!IH!=l

292

§ 117.

CIICTCMhl (TeOpCMU MOMCHTOB) • • • . . . . . •

.

•

.

•

•

•

•

3aKOI! COXpaHeHHH r JI8BHOfO MOMCHTa KOJIH4CCTB .l(BH}KeHHH

•

•

294

§ 118.

Pe!lieHne 3a]!.a<t

• • •

•

•

•

•

• . .

.

•

•

•

.

•

•

• . .

295

§ 119*. DpH.~O}KeHHe TeopeMbl MOMeHTOB K

.l(Bl!}KeHHKJ

}KH;J:KOCTH

(ra3a)

298

§ 120.

YcJJOBHH paBHOBecnH MexaHH4ecKoii clfcTeMbl . •

•

.

• . .

300

r J] a B a

XXV. TeopeMa 00 H3MCHCHHII KHHCTH'IeCKOH snepnm CHCTeMbl

3:J I

§ 121.

KnHeTH4ecKaH 3HeprHH CIICTeMbi . . •

•

• .

• .

•

•

•

301

§ 122.

HeKoropbie cJiyqaH Bbi4HCJJeHHH pa60Tbi • •

•

•

•

• . .

305

§ 123.

TeopeMa o6 H3MeHeHHH KHHeTWICCKOH 3HeprHH CHCTCMbi

307

§ 124.

Pe!liCHHe 3a)J:a<r

• • •

•

•

•

• . . .

• .

.

•

• .

•

.

•

310

§ 125 *. CMelllaHHhie 3a,n;aqrr

. •

• .

•

•

.

•

•

•

• .

• .

•

•

•

314

§ 126.

00TCHUHaJ!bHOe CHJIOBOe 110,1e II CIIJIOB351 <jlyHKUHH

. • . . . .

317

§ 127,

J10TCH!l,H8JlbHa51

3HeprH51.

3aKOH

COXpaueHH51

MCXUHH4CCKOI!

320

r Jl a B a

3HeprHH • , • •

• .

.

.

•

• .

.

•

.

•

•

•

•

•

•

.

. . • • •

XXVI. UpHJJO}KCHHe OOJliHX TeopeM K )I,HHaMHKC TBepJJ.OfO

TeJla

•

•

323

§ 128,

Bpa~~:~areJibHOC

)l:BH:lKCHHe

TBep)l:OfO

TCJia

BOKp)'r HCllO)l:BillKHOH

323

§ 129.

OCH ••••••• .. •••

,

• . ••••••

,

•

,

,

•

. •

<llH3H'!eCKHHMaKTHHK. 3KcrrepHMCHTaJibHOC orrpeJl,eJleHHC MO~CH-

326

§ 130.

TOB HHepUHH •• , • , • , • , . • • • • • . ,

•

•

• .

.

.

•

0JIOCKOrrapaJIJICJ!bHOe .l(Bll}KCHIIC TBCp,!!,OfO TeJia

• •

•

.

•

,

.

•

•

32,3

§ 131 *. 3JJeMl.'HTapHaHreopHH rnpocKorra . . .

•

• .

.

•

•

•

•

•

.

•

•

334

§ 132*, .QB!I}KCHIIC TBCp.l(OfO TeJ!a

BOKpyr HCITO.l(Bli}KHOH TO'!KHH .l(B!l}Ke--

340

r Jl a B a

HHC CB060.l(HOfO

TBCp.l(OfO

TCJI3

,

• .

,

•

•

,

,

•

•

,

,

XXVII. UpHHl(HU

)J,aJiaM6epa •

•

•

•

•

•

•

•

•

•

•

•

•

•

•

344

§ 133,

DpHIIUHil )],aJiaM6epa .l(JIH TOlJKH H MCXaHH4eCKOH

CHCTCMbl

344

§ 134.

fJiaBHblH BCKTOp ll fJ18Btlblfi MOMeHT CH.~ HHepl\IIH

,

•

• .

31c6

§ 135.

Pe!lieHne 3a)'(a4 • • •

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

.

•

•

•

•

318

§ 136*. ,UHH3Mlll!CCKHC

peaKUHH,

)leHCTBYKJJliHC

Ha

OCb BpamaJOU(CfOCH

352

TeJia. YpaBuoBelllnBaHHe Bpa~~:~aiOmnxcH

TeJI

,

,

•

•

•

•

•

•

•

415

r .n

a B a

XXVIII. npullll,Hll B03MOlKllbiX

nepeMeiiJ,etmii

H

o6w,ee

ypasneune

357

,II;HHaMiiK!I . . . . . . . . . . .

. . . . . •

§ 137.

KJiaccmjmKaUHH CB<J3ei'r . . . . • . . . . . . . . .

357

§ 138.

803MO:lKHbie nepeMelll,CfllHI CHCTCMbl. 4HCJIO CTC!lCHCH CB060,l,;

358

§ 139.

IlpHHUliiT B03MO:JKHblX rrcpCMCUl,CHHH . .

360

§ 140.

Pcl!lcHne

3ail:aq . . . . . . . .

.

362

§ 141.

06ruee ypanneHne ~nua~nmn . . . . .

367

r .1 a B a

XXIX. YCJJOBHH paBHOEeC!HI

H

ypaBHCHI!!l

.IJ.!llllKCHI!H

CHCTCMtl

[l

369

OOOOUl,eHHbiX KOOp)l,HHaTaX . . . , . . , . .

§ 142.

06o6rueHHLJe

KOOp!J.HH3TLI

n

o6o6ruemiLJe

cKopocm . . . .

369

§ !43.

0606IUCHHbiC

CI!Jlbl . . . . . . . . . . . . . . . . . . . .

371

§ 144.

YCJIOBHH paBHOBCCHll CIICTCMbi B o6o6rueiiHblX KCOp;UIH3I3\

375

§

145.

YpanHE'HHHJJarpaH:JKa . . . . . . . . . . . . . . . . . .

376

§

146.

Pel!leHne

33)1:3'1 . . . . . . . . . . . . . . . . . . . . .

379

r .n

aD a

XXX* . .MaJible KOJieOaHHH CllCTeMbl OKOJIO !lO.'!OMeHIIHyCToii•msoro

387

paBHOBCCHH . . . . . . , , . . , . . . . . • . . . . .

§ 147.

IlOHHTHC

00

ycTOHCJliBOCTll

p3BHOBCCHH . . . . . . . . . . . .

387

§ 148. MaJibie CBOOO)I:Hb!C KOJie6allllll CIICTCMbi C O)JHOH CTCITCHbJO CB060)I:hl

389

§

149. MaJILre saryxmoruue n BbiiiY)K)I:eiiHLie Ko.neCaunH CHCT~ILI c o,anoft

392

CTCUCHb!O

CBOOO)I:bl . . . . . . . . . . .

. . . . . .

. . . .

•

§ 150. MaJILie cno6o,n;nble KOJie6aHHH CI'CTeMblc ii:BYMil creneHHMH cno6o,n;LI

394

r JI a B a

XXXI. 3.neMenTapHall

TeopHH

y.D.apa .

396

§

151.

OcHOBHOe ypaBHeHne '!'eopHHy,11apa

396

§ 152.

06rune reopeMLI TeopHn

Yil:apa . . . .

.

397

§ 153.

Ko9¢<llliHHE'HTnoccTanon.nennH npH yil:ape .

399

§

154.

Y.rr;ap TeJia

o ner!Oii:Illi:JKIIYJO

nperpa.rr;y . . . . .

400

§

155.

IlpHMoii uenTpa.'!bHLii'Iy.rr;ap .rr;nyx Te.'!(y,1ap lllapon)

401

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