(формат)Тарг

C. M. Tapr

KPATKYIYI KYPC TEOPETYIYECKOYI MEXAHI1KI1

113.UAHI1E 10-e, TIEPEPABOTAHHOE 11 .U0TIOJ1HEHHOE

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MOCKBA «BblClliMI lliKOJlA» 1986

BBK 22.21

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Tapr C. M.

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B XVIII B. Ha'IHHaeTcflHHTeHcHBHoe pa3BHTne a MexaHHKe aua.nHTIItieCKHX MeTO.IJ:OB, T. e. MeTO,'J.OB, OCHOBaHHhiX Ha IIpHMeHeHHH ,'I.H¢qlepeHU.H8JlhHOrO n HHTerpa.nhHOro HCIIrrc.neHHH. MeTO.IJ:hi peiiieHHfl 3a,n,aq

,l(IIHaMIIKH TO'IKllll TBep,n:orO TeJia IIYT€M COCTaBJieHH51 H llHTerpHpOBaHllfl COOTBeTCTByiOIIJ;HX ,'I.H¢qlepeHU.HaJihHhiXypaBHeHHH 6hiJ!ll pa3pa6o-

TaHbi BeJillKllM MaTeMaTHKOM H MeXaHHKOM Jl. 9iiJiepOM (1707-1783). Hs ,'l.pyrnxnccJie,n:osaunii B 3TOI1 o6JiacTH Han60Jihiiiee 3HatieHH~ .l(Jlfl

pasBHTHfl MexaHHKH nMe.nn TPY.IJ:hi Bhi,n:aror.quxc51 cppauu.yscKHX yll'eHhiX

)1(. Jl.a.naM6epa ( 1717-1783), rrpe,'I.J!OJKHBIIIero CBOH H3BeCTHhiH rrpHHUIIII perneHHfl 3a,n:aq .IJ:HHaMHKll, H /K.. JlarpaHlKa (1736-1813), pa3-

paOOTaBI.llero 06UJ.HH aHaJIHTH'leCKHllMeTO.IJ: peiiieHHfl 3a,'l.ati.IJ:HHaMHKll Ha OCHOBe npHHU.HIIa Jla.naM6epa I1 IIpHHU.HIIa B03MO.IKHhiX rrepeMei.qeHHH.

B HaCTOHmee npeMfl aHaJIHTHtiecKne MeTO,'I.hipeiiieHnfl sa,'I.ati5IBJ15IIOTCH B .IJ:HHaMilKe OCHOBHhlMH.

I\IIHeMaTHKa, KaK OT,'I.eJ!hHhiHpa3,n:eJI MeXaHHKH, Bhi,'I.eJIHJiaChJlHIIIh B XIX B. rro.n: BJIHHnrreM 3arrpocos pasnrrnarow.erocH MaiiiHHoctpoeHnH.

B Hacroflmee npeMfl KHHeMaTHKa HMeeT n 60JihiiiOe caMOCTOHTeJihHoe BHatieHHe ,'1..1151 H3ylJ'eHH51,'I.BHJKeHllfl MeXaHH3MOB H M8IIIHH.

B Poccrrn Ha pasBHTne rrepBhiX rrccJie,n:onaHHH no MexaHnKe 60Jihmoe BJIHHHHe oKasaJIH rpy,n:hr reHHaJibHoro yqeftoro n Mhlc.nrrre.nH

* TepMHH «MexaHHKal> BnepBbie nOHBJmeTcsr B CO'II!HeHI!HXO,!lHoro 113 Bbl,!laiOIUI!x-

cH !j>IIJiocO<j>oB ,!lpeBHOCTII Ap!!CTOTeJisr (384-322 r • .llO H. 3.) 11 rrpo!!CXO.lli!T oT rpe'leCKO· ro mechane, osua'laiOw.erono coBpeMeHHblM rrOHHTIIHM ~coopyJKeHI!e», ~MaUIIIHa».

M. B. JloMOHOCoBa (1711-1765), a TaKJKe TBOpiieCTBO JI. 3fiJiepa,.,!\OJIroe npeMfl JKHBillero B Poccnn II pa6oran111ero B I1eTep6yprcKoii aKa,!\e-

MIIH HayK. l13 MHOfOIJIICJ!eHHbiX OTeiJeCTBeHHbiX ytieHbiX, BHeCillllX 3Ha-

tUfTeJiblfblH BKJia,!\ B pa3BHTHe pa3JIIItiHbiX 06JiaCTeH MeXaHHKH, rrpeJKJJ;e ncero ,1\0JIJKHbi 6b!Tb HasBaHbl: M. B. OcTporpaJJ;cKuii (1801-1861), KO-

TopoMy npnHaJJ;JieJKHT P5UI. BaJKHbrx 11ccJieJJ;OBaHnfi no aHaJIHTniiecKIIM MeToJJ;aM pe111eH11fl saJJ;aii MexaHHKn; TI. JI. 4e6bll11eB (1821-1894), cosJJ;aB111HH HOBoe HarrpaBJieHIIe B llCCJieJJ;OBaHIIII JJ;BIIJKeHHH MeXaHII3MOB;

C. B. KosaJieBcKafl (1850-1891), pe111nB111a51 OJJ;HY us TpyJJ;HeH11111X saJJ;ati ,n,nHaMIIKII TBepJJ;oro TeJia; A.M. JlflrryHoB (1857-1918), KOTOpblii

,n,aJI CTporyiO IIOCTaHOBKY OJJ;HOH 113 cpyn,n,aMeHTaJibHbiX sa,n,aq MexaHIIKH

n ncero ecTeCTB03HaHII51 - sa,n,aqn o6 ycTofitii1BOCTH pamwsec1151 n JJ;BI1JKeHH51 n paspa6oTaJI Han6oJiee o6mne MeTO,ll,bl ee pe111eHnH; 11. B. MemepcKIIH (1859-1935), BHeCilliiH OOJibillOH BKJia,n; B pe111eHHe 3aJJ;ati MexaHHKll TeJI rrepeMeHHOH MaCChi; K. 3. UnoJIKOBCKIIH (1857-1935), asTOp p5I)l;a cpyH,n,aMeHTaJibHblX llCCJ!e,ll,OBaHI1H IIO TeOpHll peaKTIIBHOrO

.n.snJKeH115I; A. H. Kpb!JIOB (1863-1945), paspa6oTaBI11HH TeOpHIO Ka- pa6.rm II MHOrO BHeCillllH B pa3BllTIIe Teopnn rnpOCKOIIa ll rHpOCKOIIII-

treCKHX IIpii6opOB.

Bbi,lJ,aiOIII.eecfl sHatieHne ,n:Jifl ,n,aJibHei1:111ero pasBHTHfl MexaHMKH nMe-

JIH Tpy.n;hi «oTua pyccKOH annauiiH»		H. E. /I\yKoBcKoro (1847-1921) 11
ero 6JIHJKaHI11ero	yiieHHKa OCHOBOIIOJIO.>KHHKa		ra30BOH	.IJ:HHaMHKU
C. A. llanJihirHHa	(1869-1942).	XapaKTeprmfi	"IepTorr	TBopqecTBa

H. E. )I\yKoBcKoro 6biJIO rrpnJIOJKeHIIe MeTo,n,os MexaHHKI1 K pe111eHn10 aKTya.T!bHblX TexHntieCKHX sa.n.a~. npnMepoM tieMy cJiyJKaT MHorne ero TPY,'I.bino ,n,nHaMnKe caMoJieTa, _paspa60TaHHa51 HM TeopnH rn,'l.paBJIHqeCKOro y,'l.apa B Tpy6ax n ,n:p. BoJibi110e BJIHflHHe n,n,en H. E. /I\yKoB-

cKoro OKa3aJIH H Ha npeiiO,'I.aBaHHeMeXaHHKH B BbiCWllX TeXHIItieCKHX

ytre6Hb!X 3aBe,'J.eHH5IX Harnefi CTpaHbl.

B HaUIH .IJ:Hll rrepe,'l.OTeqeCTBeHHOH HayKOH H TeXHHKOH CT05IT Ba.>K-

Hbie 3a,'l.atillIIO yCKOpeHHIO HaytiHG-TeXHHtieCKOfO rrporpecca ll ,'l.aJ!bHeii:- illeMy pa3BllTHIO H COBepilleHCTBOBaHIUO COIJ.HaJIHCTllliCCI\OfO IIpOH3BO.IJ:-

CTBa. B	tii1CJie 3THX sa,'l.atiTaKne aKTyaJibHbre rrpo6JieMhi, KaK anToMaTn-
sauHfl	IIpOH3BO,'I.CTBeHHbiX rrpoueccOB ll HX OIITHMH3aUHH, C03,'1.aHHe H
BHe,'l.peHneIIpOMblWJieHHbiX po60TOB, 3qxpeKTHBHOe HCIIOJ!b30BaHHe		Bcex
KOHCTPYKIJ.HOHHbiX MaTepnaJIOB H MHorue .n:pyrue. .UJifl peweHHH		3THX
sa.n.aq BaJKHOe sHatieHue HMeeT .n.aJibHefiillee IIOBbiWeHne KatieCTBa		no.n:-

roTOBKII HH:meHepHbiX Ka,'I.pOB, paCI11HpeHHe TeOpeTH'leCI<Oll 6a3bi 11X 3HaHHH, B TOM <mcJie H 3HaHHH B o6JiaCTH O,n:HOH 113 cpyH,'I.aMeHTaJ!bHblX 06IIJ.eHaytrHbiX ,'I.llCIJ.HIIJ!IIHTeOpeTIItieCKOH MeXaHHKll.

Pa3)J.eJI nepsbiH

CTATHKA TBEPAOfO TEJIA

rnasa I

OCHOBHbiE nOHSITIUI H HCXO)J,HbiE nOJlO)I(EHIHI

CTATHKH

§ I. A6COJUOTHO TBEP,ll,OE TEJIO; CHJIA. 3A,lJ,Al.fH CTATHl(H

Cmamwwt1 Ha3hiBaeTcH pa3,n:eJI MexaHnKII, B KOTopo.\1 II3J1araeTCH o6mee yiieHHe 0 CllJ!aX II H3yqa!OTCH ycJIOBllH paBIIOBeCHH MaTepiiaJibHbiX TeJI, HaXO,ll,HUJ.llXeH IIO,ll, ,n:encTBHeM CHJI.

f10,ll, paBHOBeCHeM 6y,n:eM IIOHHMaTb eOCTOHHlle IIOKOH Te.'laIIO OTHOllieHH!O K ,n:pyrrrM TeJiaM, HarrpiiMep ITO OTHOllieHHIO K 3eMJie. YcJIOBHH paBHOBeeHH TeJia cyrn.eCTBeHHO 3aBHeHT OT TOrO, HBJIHeTCH Jill 3TO TeJIO TBep,ll,biM, JKH,ll,KHM HJIII ra3oo6pa3HbiM. PaBHOBeciie JKH,li,KHX H ra3oo6pa3HbiX TeJI n3yqaeTcH B Kypea,x rn,n:pocTaTHKH HJIH a3pOCTaTHKH. B o6-

meM Kypee MeXaHHKH paceMaTpHBaiOTCH 06b!IJHO TOJ!bKO 3a,n:aqrr 0 paBHOBeCHH TBep,ll,biX Te.'l.Твердые-условно. Поскольку имеют некоторую конечную тв-ть.

Bee BeTpeiiaiOUJ.HeCH B rrprrpo.:I,e TBep,ll,bie TeJia IIO,ll, BJ!H51HlleM BHeillHllX B03,n:eikTBHH B TOll HJ!H HHOH Mepe ll3MeHHIOT CBOIO cpopMy (,n:ecpopMrrpyiOTeH). BeJIHIIHHhi 3THX .n:ecpopMau.rrii 3aBHC5IT OT MaTepHaJia TeJI, HX reoMeTpHIIeCKOH cpopMbl II pa3MepOB ll OT ,ll,eHeTBYIOUJ.llX Harpy3oK. )lJIH o6eerreiieHHH npOIIHOeTH pa3JIHqHbiX IIHJKeHepHbiX eoopyJKeHHH II KOHCTPYKU.HH MaTepnaJI H pa3Mepbi IIX IIacTeii rro,n:onpaiOT TaK, IITo6hi ,ll,ecpOpMaU.HH IIpll ,ll,eiicTBYIOUJ.HX Harpy3KaX 6b!Jlll ,li,OCTaTOIIHO MaJ!bl *.

BeJie,li,CTBne 3Toro rrpn n3yiieHrrrr ycJionuH: paBHOBeCHfl BIIOJIHe .n:orryeTHMO rrpeHe6peraTb MaJib!MH ,AecpopMaU.HHMll COOTBeTCTBYIOUJ.HX TBep,ll,biX TeJI ll paeeMaTpHBaTh llX KaK He,ll,ecpOpMHpyeMbie llJ!ll a6eOJIIOTHO TBep- ,l(bie. A6co;uomrw tn8epabtM me.lloM Ha3biBaiOT TaKoe TeJio, paccTOflHHe MeJK,n:y KaJK,ll,h!Mll ,li,BYM51 TOqKaMH KOTOporo Bcer,l(a OeTaeTCH noeT05IHHbiM. B .n:aJibHeiiweM IIf>H peweHHH 3a.n:aq CTanmn nee Te.'lapaeeMaTpHBaiOTCfl KaK a6COJI!OTHO TBep,ll,bie, XOTH qaeTO ,li,J!H KpaTKOCTH llX Ha3bl· BaiOT IIpOCTO TBep,ll,biMH Te.'laMll.

* HanpRMep, MaTepRaJI II pa3Mepb1 CTepJKHeii, BXO,li.Silll.RX B Te 11.rm I!Hhle KOHCT• PYKU.RR, BhlonpaJOT TaKRMR, 'ITOnp11 .n.eiiCTBYIO!ll,HX Harpy3Kax creplKHR Yil.,1HHHIOTCH

(HJIII yKopa'IHBaJOTC5!)MeHee '!eMHa Oi!.HY Th!CWIHYIO )l.OJIIO RX nepBOHa'!a.1bHOil,1(,1HHbl. TaKoB JKe rropsr.n.oK .n.orrycKaeMhlX Ae¢opMaU.H~ op11 namoe, Kpy'leHI!!!11 T. rr.

9

CocTOHHIIe paBHoBeCHH HJIH .n;srnKeHHH .n;aHHoro TeJia sasiiCHT OT xa- pmnepa erO MeXaHII'leCKHX B3aHMO,neikTBllll C ,npyrHMII TeJiaMII, T. e. OT TeX ,!l.aBJieHHll, IIpllT5VKeHIIlliiJ!II OTTaJIKHBaHHH, KOTOpble TeJIO IICIIbi-

TblBaeT B pesyJihTaTe .9THX ssaHMOAeiicTBHH. BeJIH'lHHa, HBJIHIOII.J.ancH: OCHOBHOH Mepoii MeXaHII'leCKOfO B3aiiMO)J;elicTBHH MayepnaJibWhlX ten, Ha3biBaeTCH B MeXaHHKe CU./lOU.

PaccMaTpiisaeMble B MexaHHKe BeJIH'lHHbiMOJKHO pa3,'1.MHTbua CKtl-

.tlJlpHble, T. e. TaKHe, KOTOpbre IIOJIHOCTblO xapaKTepnsyiOTCH HX 'liiCJIO-

BbL'>i3Ha'leHIIeM,ll BeKmoprtbte, T. e. TaKHe, KOTOpble f!OMHMO tiiiCJ!OBOro SHaiieHH5I XapaKTepn3yiOTCH ~e II HarrpaBJieHHeM B rrpoCTpaHCTBe.

1)	CnJia - BeJJIItiiiHa BeKTOpHaH. Ee ,'l.eiictsneHa TeJio orrpe,'l.eJIHetcH::
	ttUC.il08btM 3HattertueM	IIJIII MOay.lleM CHJibl,	2)	Hanpae.!leH.ueM CfiJIIi,
3)	mottKOU npu.!lOCI/CeHUJl	CHJlbl.
	Mo,'I.yJihcnJibi Haxo,n,HT rryTeM ee cpasneHHH		c	cHJioii, rrpnHHTOH sa

e,n,HHHUY. Ocuonuoii e,n,nnnueii IISMepeHHH cHJibi B MeJK,'I.yHapO,'I.HOHciic-

TeMe	e,'I.HHHII (CH), KOTOpOH	Mbl	6y,neM IIOJ!b30BaTbC5I	(rro,npo6nee CM.
§ 75),	HBJIHeTCH 1 Hb!OTOH (1	H);	rrpHMeHHeTCH ll 6oJiee	KpyrrHaH e,n;R-
HllUa	1 KHJIOHhiOTOH (1 KH = 1000 H) . .UJIH cTaTH'lecKoro nsMepeHIIH

CHJibi CJiy.>KaT nssecTHbre II3 cpH3HKH rrpn6opbr, HaSbiBaeMble aurtruw-ttem- paMu.

CHJiy, KaK II see ,'l.pyrrreBeKTOpHbie BeJIH'liiHbl, 6y,n,evr o6osHatraTb

6yKBOii C treptoft Ha,'l.HeiO (HaiipHMep, f), a MO,ll,YJ!b CHJlblCHMBOJIOM

jfl llJIH TOll JKe 6yKBOH, HO 6es 'lepTblHa,'l.HeiO (f). fpacpnqeCKll CHJia,

KaK n .l(pyrne seKTOpbi, nso6pa.lKaeTcH uarrpaBJieHHbiM otpe3KOM (pHC. 1). L{JIJI:Ha Enoro 0Tpe3Ka Bb!paJKaeT B Bbi6paHHOM MaCWTa6e MO·

.ll.YJ!b CllJ!bl, narrpaBJieHHe oTpe3Ka COOTBeTCTByeT HanpaBJieHHIO CHJibl, TO'!KaA Ha puc. 1 HBJIHeTCH TO'!Koft rrpn.'loJKeHHHCH.1bi (CHJIY MO)I{HO

H3o6pa3HTb II TaK,		'ITOTO'lKOll 1IpHJIO.>KeHH5I 6y,'l.eT KOHeii					CHJibl, KaK
		£	na pnc. 4, e).		IlpnMaH	DE,	B,'I.OJib KO·
			topoft	HarrpasJieHa cnJia,		HaSbiBaeTCH AU·
			HUeU	aeiiCmBUfl	CU.ilbt. YCJ!OBHMCH			eiUe 0
			CJie,!l,yiOIUllX orrpe,'l.e.JieHHHX.
			1. CucmeMoCi cu.!l 6yJJ.eM nasb!BaTb coso-
			KyrrnocTI> CHJI,		,'l.eiicTBYIOII.J.HX Ha paCCMaT-
Линия			piiBaei\!Oe TeJio (nJIH TeJia). EcJIH JIHHHH ,'l.eH-
	Pnc. 1		CTBHH BCeX CllJ!		JieJKaT B O)J;HOll		IIJ!OCKOCTII,
действия
			CHCTeMa CHJ! Ha3biBaeTC5I			n.ilOCKOU, a		ecJII!

3TH JillHIIII ,neftCTBllH He JieJKaT B O,nHOll fiJ!OCKOCTH,- npocmpartCmBeltHOU. KpoMe Toro, CHJibi, JIHHHH ,'l.eiicTBHHKOTOpbiX rrepeceKaiOTCH B Ok non TOtrKe, Ha3biBaiOTCH cxoaHU{UMUCfl, a CHJibi, JIHHHII .n;eiicTBHH KoTopbiX rrapaJIJieJihHbi .n;pyr .l(pyry,- napa.!l.!le.ilbHbtMU.

2. Te.11o, KOTopoMy H3 ,'l.aHHoronoJioJKeHHH MOJKHo coo6IUHTb JII06oe nepeMeiUeHne B npocTpaHcTBe, nasbmaeTcH ceo6oaHbt.M.

3.ECJIH O,'I.HY CHCTeMy CHJI, ,'l.eHCTByiOUJ,HX Ha CB060,'I.HOe TBep,'l.oe TeJio, MO.>KHO 3aMeHHTb ,'l.pyrOHCHCT€MOH, He H3MeH5I5I IIpH 3TOM COCTOHHll5! IIOKOH IIJIII ,'J.BHJKeHHH, B KOTOpOM HaXO,'I.llTCH TeJio, TO TaKHe )J;Be CHCTeMbl CIIJ! Ha3biBaiOTCH 8K6U6a.!lertmHbtMU.

4.CncTeMa cnJI, rro,'l. .n;eucTBIIeM Kotopo.H cso6o.u,noe TBep.n.oe teJio

10