(формат)Тарг
.pdfSTOM COfJiaCHO COOTHOllleHHHM (53):
vA=w-PA (vA_LPA);
vn = w·P B (Ve .L PB) H T. ,.u. |
(55) |
113 paBeHCTB (55) CJie,.uyeT ew;e, 'ITO
(56)
T. e. 'ITOCKOpocmu mofl.eK nAOCKOU rpU<!ljpbt nponopt{UOHa!lbHbl UX paccmOfl· HUfl!fl om McHOBertHoco l{eHmpa CKopocmeii.
f1oJiyqeHHbie pesyJibTaTbi npHBO,UHT K CJie,UyiOID;HM BbiBO,UaM.
I. Jl,Afl onpeae.~eHUfl MZHOOeHHO<?o l{eHmpa cFwpocmeii HaiJo aHamb mo-
.llbtW HanpasAeHUfl cKopocmeii vA H vB KaKux-Hu6yab oByx motteK A H B nJlOCKOU rpU<!ljpbt (HJIH TpaeKTOpHH 3Tl1X TOtreK); MfHOBemmii: ueHTp CKOpOcTeH HaXO,UHTCH B T04Ke nepecetreHHH nepneH,UHKymlpOB, BOCCTaBJieHHbiX H3 ToqeK A H B K cKopocTHM 3THX TO'IeK(HJIH K KacaTeJibllhiM K TpaeKTOpHHM).
2. Jl,Afl onpeaeAeHUfl CKOpOCtnU AF06ot1 tnOiiKU nAOCKOU rpucypbl HaOO 31-Wtnb .MOOljllb U Hanpa6AeHUe CKOpocmu KaKOU-HU6ljOb oOHOU tnOiiKU A rpucypbt u Hanpa6AeHUe CKopocmu opycou ee mottKU B. Tor,.ua, BOC-
CTaBHB H3 To'IeKA H B nepneH,.uHKyJIHphi K vA H V"e. noCTpom.1 MrHoBeHHh!H ueHTp CKopocTeii P H no HanpaBJiemnovA onpe,.ueJIHM HanpaBJiemre nosopoTa ¢11rypb1. T1ocJie 3Toro, sHaH vA, Haii:,.ueM no ¢opMyJie (56) cKopocTb v1\l mo6oii: TOtrKH M n.'IOCKoii:¢nryphi. HanpaB.TieH BeK-
Top vM nepneH,UHKYJIHpHo PM B cTopoHy nosopoTa ¢Hrypb!.
3. YcA06afl CKOpocmb (!) nAOCKOU rpucypbt pasHa 6 Ka:JICOblU oaHHbll'i
.MOA'le'ifli! 6peMeHU omHotueHUIO CKopocmu KaKOU-HU6ljOb tnOiiKU rpU<!ljpbt K
ee pdtiJnOflHUIO om Mcft06eHHOcO l{eHmpa CICO- |
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pocmeu |
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ffi= ;~, |
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y 1 uM |
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(57) |
D |
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'ITO BH,UHO |
H3 |
4JopMyJI |
(55). |
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Haii:,.ueM |
erue ,.upyroe |
Bhrpa)KeHHe |
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co. |
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113 paBeHCTB (52) H (53) CJie):(yeT, 'ITO |
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VBA=JVB-VAJ |
H |
VBA=cu ·AB, |
OTKy,.ua |
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W= |
1Ve-VA 1 |
lvn+<- VA) 1 |
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(58) |
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AB |
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Kor,.ua |
vA =0 |
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(TO'lKa |
A - |
MrHoBeHHbiH |
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ueHTp |
cKopocTeii:), ¢opMyJia |
(58) |
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nepexo- |
PHc. 151 |
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,UHT B |
(57). |
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PaBeHcTBa (57) H (58) onpe,.ueJIHIOT o,.uHy H Ty )Ke BeJIH'IHHy,TaK KaK |
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no ,.uoKasaHHOMy (eM. § 52) |
nosopoT nJIOCKOH ¢urypbi BOKpyr TOtrKII |
A |
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HJIH TO'IKH p |
npOHCXO,UHT |
C O,UHOH |
H TOH |
)Ke |
yrJIOBOH CKOpOCTblO |
CO. |
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§58*. OfiPE)J,EJIEHHE YCKOPEHHfl TOliEK UJlOCKOfl <I»HfYPbl
DoKa.x<eM, 4TO ycKopetme mo6oii TO'IKHM ITJiocKoii qmrypbi (TaK )!{e, KaK II CKOpOCTb) CKJla,I\biBaeTC5I 113 ycKopemJii, KOTOpb!e T04Ka ITOJiytraE'TrrpH ITOCTyiiaTeJibHOM H BpamaTeJ1bHOM ,1:\BH)!{eHHHX 3TOH tPII-
rypb!. I1oJio)Kemre TO'IKHM ITO OTHoll!eHmo K ocnM Oxy (eM. pnc. 146) |
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OITpe,n:eJIHeTC5I |
pa,n:nyco'vl-BeKTOpOM r=rA+r''r,n:e r' |
AM. Tor,n:a |
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d2r d27A |
d2r~ |
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aM=(it2 = Cft2+Cft2. |
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B ITpasoil tracTH 3Toro paBeHcTBa ITepsoe cJiaraeMoe ecTb ycKopeHue |
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aA ITO.'I!Oca A, a BTOpoe CJiarae)10€ |
onpe,n:eJIHeT ycKopeHHe aMA• KOTO- |
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poe T04Ka M no.'!yqaeT rrpH spalll.eHHH |
¢uryphr BoKpyr nomoca A |
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(eM. § 54). CJie,n:oBaTeJibHO, |
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(59) |
3Hatremre |
aMA• |
KaK |
ycKopemm TOtrKH spammomerocH TBep,n:oro |
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q-eJia, orrpe,n:eJIHeTCH |
ITO |
¢opMyJiaM |
(46) n |
(47) 113 §51: |
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(60) |
r,n:e ro n B - yrJioBaH |
CKOpocTb |
H |
yrJioBoe |
ycKopeHHe |
¢urypbr *, a |
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~- yroJI Melli,n:y BeKTOpOM aA1A |
ll |
0Tpe3KOM |
MA (puc. |
163). |
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TaKHM o6pa30M, yc1wpetwe ;uo6oii moi!KU |
M nAoCKoii |
rjJuzypbt |
i!eo- |
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Mempui!eCKU CKAaablBaemcH U3 ycKopetWH KaKOU-HU6yab apyi!OU mOi!KU |
A. |
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npurLHmoii 3a nOAIOC, u yCKopeHUfl, Komopoe mwKa M noAyi!aem npu epaU{eHuu ¢u;;ypbteoKpy2 :mw;;o noJJ/Oca. Mo,D.yJib n HaiTpasJienne ycKope-
* Ha uepTe)Ke cn.1omHaSI ,!(yroBaSI crpeJJKa noKa3LIBaer HanpaBJieHlie w (HanpaBJieHHe Bpam:cHHll), a nymnHpHaSI - nanpaBJJeHHe (sHaK) e. flpH ycKopeHIIOM BparnePI!H o6e crpemm 6yll:YT nanpaBJieHbi B o.n;ny cTopoHy, a npH 3aMe.QJieHHOM - B pa3Hhle.
140
HIHI aM uaxo}l.HTC51 nocrpoeuueM cooTBeTCTBYIOlll.ero napaJIJieJiorpaMMa (puc.
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0)l.HaKO BbPIHCJiemie aM C TIOMOlll,blO napaJIJieJIOrpaMMa, H306pallieH- |
HOfO Ha pHC. 163, ycJIOlliHHeT pacqeT, TaK KaK npe)l.BapiiTeJibHO Ha)l.O 6y- |
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uaxo,n;HTb 3Haqem1e yrJia f!, a sareMyrJia Melli)l.Y BeKTopaMH |
aMAH a:. fl03TOMY npH perueHHH 3a)l.aq Y.ll.06Hee BeKTOp aM A 3aMeH51Tb |
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ero |
KacaTeJibHOH (a1M) l1 HOpMaJibHOH (a11A) COCTaBJIH!Oill,HMH H npe,n;- |
CTaBHTh paBeHCTBO (59) B BH)l.e
a-,1=aA+aXtA+a~A· (61)
TlpH 3TOM BeKTOp aX1A HanpaBJieH nepneH)l.HKyJIHpHO AM B CTOpOHY Bpali1,eHH51, eCJIH OHO YCKOpeHHOe, H ppOTIIB Bpaw.eHH51, eCJIH OHO 3aMe}l.JleHHOe; BeKTOp a~A Bcer.n.a HanpaBJieH OT TOqKH M K TIOJI!Ocy A
(puc. 164). 4rrcJieHHO llie
(62)
EcJiu noJimc A )l.BHllieTCH He np5IMOJIHHefiuo, To ero ycKopeHrre MolliHO TOllie npe)l.CTaBHTb 1\:aK cyMMy KaCaTeJibHOH llJ H HOpMaJibHOH llA
COCTaBJIH!Olll,HX, TOf)l.a
(63)
HaKoHeu, Kor.n.a ToqKa M )l.BrrllieTcH KpHBOJIHHeii:Ho H ee TpaeKTO·
pH51 H3BeCTHa, TO aM B JieBbiX qaCTHX paBeHCTB (61) H (63) MOlliHO 3aMeHHTb cyMMOH a11+a'if. <PopMyJiaMH (61) - (63) H TIOJlb3YlOTC51
o6brquo npu peweHrrH sa.n.aq.
PHc. 163 |
Puc. 164 |
P e III e H He |
3 a .n; a q, YcKopeHrre JII06o:U: ToqKu TIJIOCKo:U: <Purypbi |
B )l.aHHhiH MOMeHT BpeM.eHH MOlliHO HaHTH, eCJIH H3BeCTHbi: l) BeKTOpbl CKOpOCTH VA H ycKopeHH51 aA KaKoii-Hrr6y)l.b ToqKH A 3TOH <Purypbl B
.n.aHHhiH MOMeHT, 2) TpaeKTOpHH KaKoil.-mr6y.n.h .n.pyro:U: ToqKH B <Purypbr. B pH)l.e CJiyqaeB BMecro TpaeKTOpHH BTOpOH TOqKH <flnrypbl )l.O· CTaTOqHQ 3HaTb TIOJIOJl{eHrre MfHOBeHJWfO ueHTpa CKOpOCTeH.
TeJio (HJIH MexaHusM) nprr peweuurr sa.n.aq Ha.n.o rrso6pa.llWTb B TOM
nonomeuurr, )l.JIH KOToporo Tpe6yercH onpe.n.eJIHTb ycKopeHrre COOTBeTCTByiOw.eii ToqKu. PacqeT HaqrrHaeTcfl c onpe.neJieHHH no ,I~.aHHhiM sa.n.aqu
CKOpOCTH H ycKOpeHH51 TOqKH, npHHHMaeMOH 3a f!OJI!OC. ,UaJibHeHIIIHe OC06eHHOCTH pacqeTa TIO,ll.p06HO paCCMaTprmaiOTCfl B perneHHbiX HHllie sa.n.aqax. TaM me .n.awTCH Heo6xo)l.HMbre .n.onoJIHHTeJibHble yKasaHHH.
141
fJJasa XIII
CJIO)I(HOE ~BM)I(EHME TOljKH
§ 64. OTHOCliTEJlbHOE, llEPEHOCHOE
H AECOJIIOTHOE ,nBH)l(EHH}I
)lo CHX ITOp Mbl nsyqaJIH .ll.BIDKeHlle TOqKH HJlH TeJia no OTHotlleHH!O K O.lJ.HOH sa)J.aHHofi cHcTeMe oTcqera. O.rr:HaKo B p5Ii1,e cJlyqaes npH peweHHH 33)J.aq MeXaHHKH OK33blB3CTC5! UeJlecOo6pa3Hbll\1 (a l1HOr,lla H He-
06XO)J.HMbiM) |
paccMaTpHB3Tb .lLBH.IKe- |
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HHe TOqKH (HJIH TeJla) OII:HOBpeMCHHO |
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no OTHOIIIeHHIO K .lJ.BYM |
CI-!CTeMaM OT- |
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cqeTa, H3 KOTOpbiX O;J:Ha C1.JHT3CTC51 |
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OCHOBHOH liJlH ycJlOBHO HenO)J.BH.IK- |
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HOfl, a ,ll.pyraH onpe)J.eJleHHh!M o6pa3oM |
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)J.BH.IKeTC51 no OTHOIIIeHHIO |
K nepBOH. |
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,llBHllieHHe, |
cosepiiiaeMoe |
npu 3TOM |
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TO'IKOH (HJlH |
TeJlOM), |
H33biB3IOT CO· |
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cma6flbtM |
HJlH c,wJICHbW. Hanp HMep , |
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map, KaTHlll.Hikn no naJiy6e Jl.BH.IKy- |
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m:erocfl |
napOXO)J.a, |
MOR<HO C'IHT3Tb |
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COBepWa!Olll,HM |
no |
OTHOIIICHHIO K 6e- |
PHc. 182 |
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pery CJlOlliHOe |
JJ.BH)KeHHe, COCTOHUJ,ee |
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li3 KaqeHH51 |
no OHIOWCHHIO K naJly6e (nO)J.BH.IKH351 CHCTCMa OTcqeTa), |
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u .lJ.BH.IKeHHe |
BMecTe c |
naJly6oii napoxo)J.a no OTHOIIIeHHIO K 6epery (ne- |
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IIOJI.BHlliHaH CHCTeMa OTCl.JeTa). TaKHM nyTeM CJlOJKHoe n:sulliemre IIIapa pasJlaraeTCH Ha .n.sa 6oJlee rrpocTbiX n 6oJlee JlerKo HCCJle)J.yeMbiX. BosMOJKHOCTh pasJlOJKHTh nyTeM BBe.ll.eHHH )J.OnOJIHHTeJlhHOH (no)J.BHii\- HOfl) CHCTeMbi OTcqeTa 60Jlee CJlOlliHOe JJ.BHJKeHHC TOl.JKH HJIH TeJla Wl
60Jlee npOCTh!e IIIHpOKO HCnOJlh3yeTC5I npH KHHeMaTH'ICCKHX paCl.JCTaX
li onpe.n.eJlHeT npaKTH'IeCKYIO UCHHOCTh TCOpHI! CJlOJKHOrO JI.Blf)KCH!f51, paccMaTpHBaeMoii B ~non H CJleJJ.yiOIII,eii rJlasax. KpoMe Toro, pesyJihTaThi 3TOH TeOpHH HCnOJlh3YIOTC51 B JI.H!Ia:\-lHKe )J.Jl51 H3yqeHH51 OTHOCHTCJlhHOfO paBHOBeCHH H OTHOCHTCJlbHOrO ,lLBI!JKei!H51 TeJl no.n..n.eikTBHeM CIW.
PaccMoTpHM ToqKy M, JJ.BHJKYIII,YIOCH no OTHOIIIeHHIO K no.n.BHJKHO(I CHCTelVle OTCl.JeTa Qxyz, KOTOpaH B CBOIO Ol.Jepe.n.h KaK-TO )l,BHJKCTC51 OTHOCHTCJlhHO il,pyroii CHCTeMbl OTCl.JeTa 01 X KOTopyiO H33blBaeM OCHOBHOli HJlH ycJlOBHO HenO)J.BHJKHOH (pHc. 182). KaJK)J.aH H3 3THX cHcTe?,I OTCqeTa CB5133Ha, KOHCl.JHO, C onpe.n.e.rreHHblM TeJlOM, Ha qepTeJKe He noKa3aHHhiM. Bse)J.eM CJle)l,yiOIII,He onpeil,eJleHHH.
1. .lJ.BHllieHHe, COBeprnaeMoe TOl.JKOH M no OTHOWeHHIO K llO.lJ.BHJK·
Hoii CHCTeMe OTCl.JeTa ( K ocHM Oxyz), Ha3biBaeTC51 omHocumeAbHbtAl d6U~eHUeM (TaKoe J!.BHllieHHe 6y,ll.eT BH)l,eTb Ha6JIIO)J.aTeJlb, CBR33HHblH
155
c 3THMH ocHMH 11 nepeMelll,aiOUJ,HllCH BMecTe c HHMH). TpaeKTopuH AB,
OnHChiBaeMa51 TO'IKOllB OTHOCHTeJibHOM JJ.BHllieHHH, Ha3biBaeTC51 OtnHOCUtneflbHOU mpaeKmopueu. CKopocTb TO'IKHM no oTHOIIIeHHIO K ocHM
Oxyz Ha3biBaeTcH omuocume!lbHOU cKopocmbiO (o6osHaqaeTcH V0T), a
ycKopeHHe- omH.ocume!lbHbtM ycKopeHueM _(o6o~HaqaeTCH GT). lis
0
OnpeJJ.eJieHH51 CJie.n.yeT, 'ITOnpH Bbl'IHCJieHHHV0 r H a0 T MOlliHO JI.BHllieHUe OCeH Oxyz BO BHHMaHHe He npHHHMaTb (paccMaTpHBaTb HX KaK HenOJJ.· BH)KHb!e).
2. .UBHllieHHe, COBepiiiaeMoe nOJI.BlilliHOH CHCTeMOH OTC'leTaOxyz (H BCE'MHHeH3MeHHO CB513aHHhiMH C HelO TO'IKaMHnpOCTpaHCTBa) no OTHOIUeHHIO K HenOJI.BHlliHOii CHCTeMe 0 1x 1y1z 1, flBJIHeTCH JJ.JIH TO'IKHM nepeHOCHbtM aeu;)!CeHUeM.
CKopocTh TOll HeHsMeHHo cBHsaHHofi c no.n.BHlliHhiMH ocHMH Oxyz
TO'IKHtn, C KOTOpOH B JJ.aiiHblll MOMeHT BpeMeHH COBna.n.aeT J!.BHlliyUJ,a51C5I TO'IKaM, Ha3hiBaeTCH nepeH.ocuoii cKopoctnbiO TO'IKH M B 3TOT MOMeHT
(o6osHaqaeTcH Vnep), a ycKopeHHe 3TOll TO'IKHm- nepe!iOCHblAt ycKo-
peHueM TO'IKH M (o6osHa'laeTcH cl;:e11). TaKHM |
o6pasoM, |
VneP = Vm, anell =am. |
(83) |
EcJIH npeJI.CTaBHTh ce6e, 'ITOOTHOCHTe,'IhHOeJI.BHllieHHe TO'IKH npoHCXOJI.HT no nosepxHOCTH (HJIH BHYTPH) TBep.n.oro TeJia, c KOTOpbiM llieCTKO CB513aHbl nO;:I:BHlliHhie OCH Oxyz, TO nepeHOCHOH CKOpOCThlO (H.'IHycKopeHHeM) TO'IKH M B .n.aHHhiH ~roMeHT spe~teHH 6y.n.eT cKopocTh (HJIH YCKOpeHHe) TOll TO'IKHm TeJia, C KOTOpOH B 3TOT MOMeHT COBna.n.aeT TO'IKa M.
3. .UBHllieHHe, COBepiiiaeMOe TO'IKOHno OTHOIIIeHHlO K HenOJ!.BHlliHOH CHCTeMe OTC'leTa 0tX1YtZh Ha3biBaeTC51 a6COJliOtnliblM HJIH C/lO;}ICHbt.M. TpaeKTOpHH CD 3Toro JJ.BHllieHHJI Ha3biBaeTCH a6cOJIIOtnHOU mpaeKmopueii, CKOpOCTh- a6coAIOtnHoii cKopocmbiO (o6osHaqaeTcH va6) H ycKopeHHe - a6coAIOtnHbtM ycKopeuueAt (o6o3Ha'!aeTcH aa6).
B npHBeJJ.eHHOM Bbrwe npHMepe JJ.BHllieHne IIIapa OTHOCHTeJihHO naJiy-
6br napOXOJJ.a 6y.n.eT OTHOCHTeJihHbll'II, a CKOpOCThOTHOCHTeJihHOH CKO· poCThlO wapa; JJ.BHllieHHe napoxo.n.a no OTHorneHHIO K 6epery 6y.n.eT JJ.JIH mapa nepeHOCHbiM JJ.BHllieHHeM, a CIWpOCTh TOll TO'IKHnaJiy6bi, KOTOpOH B JJ.aHHbiH MOMeHT BpeMeHH KacaeTC51 IIIap, 6y.n.eT B 3TOT I\10MeHT ero nepeHOCHOH CKOpOCThlO; HaKOHeU, JI.BHllieHHe ruapa no OTHOIIIeHHIO K 6epery 6y.n.eT ero a6COJilOTHbiM JJ.BHllieHHeM, Q CKOpOCTba6COJIIOTHOH CKQpOCThlO wapa .
.UJIH perueH\151 COOTBeTCTBYlOIUHX 3aJJ.a'-I KHHeMaTHKH He06XOJ!.In;iO ycTaHOBHTb 3aBHCHMOCTH Me)KJJ.Y OTHOCHTeJihHb!MH, nepeHOCHhiMH H a6COJilOTHhiMH CKOpOCTHMH H ycKOpeHHHMU TO'IKH, K '!eMyMbl H nepeHJJ.eM.
§ 65. TEOPEMA 0 CJIO)I(EHMM CKOPOCTEA
PaccMOTpHM CJIO:iKHOe JJ.BH)}{eHHe TO'IKHM. DycTh 3Ta To'!KacosepIIIaeT sa npoMe)}{yToK speMeHH t!t=t1-t BJJ.OJih TpaeKTOpHH AB oTHOCHTeJibHOe nepeMelll,eHHe, onpeJI.eJIHeMoe BeKTopoM MM' (pHc. 183, a).
156
CaMa KpHBaH AB, JI.BHraHCb BMecTe c TJOJI.BHlliHbiMH OCHMH Oxyz (Ha pHCyHKe He TlOKaSaHb!), nepe:liJI,eT sa TOT llie npoMelliyTOK BpeMeHH B KaKoe-To HOBoe noJiollieHHe A1 B1. 0JI,HOBpeMeHHO Ta ToqKa m KpHBoii AB, c KOTopoii B MOMeHT BpeMeHH t coBnaJI,aeT ToqKa M, coBeprnHT nepe-
HOcHoe nepeMeW,eHHe mm1 =Mm1 • B pesyJII>TaTe ToqKa M npHJI.eT B DOJIQ;.KeHHCJ\11 11 COBepWHT sa BpeMH /).f a6COJI!OHIOe nepeMeUJ,eHHel\1l\1 1 •
11s BeKTOpHoro TpeyrOJihHHKa Mm1l\11 HMeeM
MM1 = Mm1 +m1M 1 .
neJIH o6e qacTH ::noro paBeHCTBa Ha /).t H IIepeXOJI.51 K npeJI,eJiy,
IIOJiyqHM |
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lim (Mm1/M) + lim |
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lim |
(MM 1/t,.t) = |
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6.1 - |
0 |
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M - 0 |
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D. I - |
0 |
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Ho, no |
onpeJI,eJieHHIO, |
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lim (MM 1/M) =vao• |
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D. I~ 0 |
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11) |
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7-} |
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1107 |
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f1 |
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ml |
11 |
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A |
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y, |
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Pnc. |
183 |
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4To KacaeTCH nocJieJI,Hero cJiaraer-mro, TO, |
TaK'KaK npH t,.t ~ 0 |
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Kpnsmr |
A1 B1 CTpeMHTCH K cosnaJI,eHHIO c KpHBoii AB, B npeJI,eJie |
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lim (m1M 1 /M)= lim (MM';M)=~r |
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t.t-o |
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M~ o |
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B |
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pesyJihTaTe |
HaXOJI.HM, |
qTo |
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Va6 = VoT +Vncp• |
(84) |
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HanpaBJieHhl BeKTOpbi Va0, V0 n |
Vnep IIO KaCaTeJibHbiM K COOTBeTCTBYIQ- |
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Ill,HM |
TpaeKTOpHHM |
(puc. |
183, 6). |
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TaKHM o6pasoM, Mbi JI.OKa3aJIH cJieJI,yrow.yiO TeopeMy o CJIOllieHHH CKOpOCTeii: n,pu CJlOJICH.Ol>t d8UJICCH.UU a6COJlJOtnflafl CKOpOCtnb tnOfiKU pa8Ha
CY/~fJvte OtnrWCUtnCJlbflOU U n.eperiOCI-IOU CKOpocmeu.
183, 6
Ec.nii yroJI Me*)J.Y BeKropaMH V0r H vnep paBeH a, TO no MO)J.YJI!O
(84')
§ 66. TEOPEMA 0 CJIO)I(EHHH YCI(OPEHHA:
(TEOPEMA J<OPHOJIHCA)
Haii.n.eM 3aBHeHMOCTh Melliil.Y OTHoeHTeJibHbiM, nepeHOCHbiM H a6eoJIIOTHbiM yeKOpeHHf!MH TOqKH. J13 paBeHCTBa (84) IIOJiyq!fM
- _ |
d0a6 _ |
dvoT |
+ dvpep |
(85) |
aa6 - |
dt - |
dt |
dt • |
DpoH3BO)l,Hhie 3)l,eeb onpe.n.eJIRIOT mMeHeHHe Ka.lli:.n.oro H3 seKTopos TipH a6eOJIIOTHOM )l,BHllieHHH. 9TH H3MeHeHHf! eJiaraiOTe5l B o6w,eM eJiyqae
H3 H3MeHeHHH IIpH OTHOeHTeJihHOM H npH nepeHOeHOM )l,BH2I\eHH5IX, qTO HH.lli:e 6y.n.eT Henoepe.n.eTBeHHO noKa3aH~: C~.n.oBaTeJibHO, ecJIH yeJio-
BHTbe5I H3MeHeHH5I, KOTOpb!e BeKTOpb! V0 T H Vnep IIOJiyqaiOT npu OmHO·
cumeAbflOM a6uJICeHUU, OTMeqaTh HH)J.eKeOM «1», a npu nepeHOCflOM a6U·
JtCeHuU - HH.D.eKeOM |
«2», TO paBeHeTBO (85) |
npHMeT |
BH)l, |
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- = |
(dvoTh |
+(dvoT)2 -1- |
(dvncph +(dvneph |
(86) |
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Ga6 |
dt |
dt |
dt |
dt |
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Ho no onpe)J.eJieHHIO (eM. § 64, n. 1) omHocume!lbHoe ycKopeHue
xapaKmepu3yem U3MeHeHue omHocumeflbHOU cKopocmu mo.llbKO npu
omHocume!lbflO.M aeu;)!CeHuu; )l,BH.lli:eHne oee:i'i Oxyz, T. e. nepeHOeHoe ,D,BHllieHHe npH 3TOM so BHHMaHHe He npHHHMaeTe5l. Do3TOMy
(87)
B esow oqepeJJ.h, nepeHocHoe ycKopeHue xapaKmepusyem usMeHeHue nepeHOCHOU CKopocmu mOAbKO npu nepeHOCfiO,ff GBUO!CeHUU, TaK KaK llnep=
=~ (eM.§ 64, II. 2), r.n.e m- TOqKa, HeH3MeHHO eB5l33HHa5I C Oe5IMH
Oxyz H, CJie)J.OBaTeJibHO, noJiyqaww.aH yeKopeHHe TOJihKO npu )l,BHllienu:a BMeeTe e 3THMH oeHMH, T. e. npH nepeHoeHoM )l,BHllieHHH. DOOToMy
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(dune ph |
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(88) |
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Gnep = __d_t_ • |
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B pe3YJibTaTe H3 |
paBeHeTBa |
(86) noJiyqiiM |
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- |
- |
- |
(dVoTh |
+ |
(dvnep)i |
(89) |
Ga6 = aOT +Gnep +-- dt - |
dt |
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160
(90)
Be.llwwna aKop• xapaKmepu3ytoutp,Jl U3MeHenue onmocume.llbHOii cKopocmu mOLtKU npu nepCHOCHOM iJBUJICCHUU U nepeHOCHOt1 CKOpocmu mO'iKU npu ee omnocume.llbHOM iJeuJtCenuu, Ha3bteaemcfl noeopomHbtM, u.11u KOpuo-
.llUCOBbtM, ycKopenue.M moLtKU. B pe3yJihTaTe paBeHCTBo (89) npHMeT BH~
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Ga6 = aOT +anep +GKOP' |
(91) |
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¢opMyJia (91) |
Bbipa)!{aeT |
cJieAy- |
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JOI.I.J,yJO |
T |
e o p e M y |
K o p II o JI H- |
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e a |
0 |
CJIO)KeHHH ycKope- |
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H H ii*: |
npu |
C.llOJICHOM |
iJ6UJICCHUU |
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ycKopenue moLtKU |
paeno |
zeo.Mempu- |
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LtecKot1 cyMAte mpex ycKopenuii: om- |
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Hocume.llbHozo, nepenocnozo u noeo- |
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A |
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pomnozo, |
U.llU |
KOpUO.IlUC06a. |
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HaiiAeM AJI5I |
Bbi'IllCJieH!l5I a~op |
~~--------------At~~,~ |
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¢op 'v!YJiy, BbiTeKaiOW.YIO H3 paBeHCTBa |
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(90). 0pH3TOM, paCCMaTpHBafl 06U1,Hllr1 |
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CJiyqafi, |
6yAeM |
CliHTaTb |
rrepeHOCIIOe |
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Pnc. 188 |
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ABll)!{f'HHe, T. e. |
ABH)!{eHHe ITOABH)!{- |
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Hh!X |
oceli Oxyz, |
a c |
HH\1H |
n KpH- |
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Boli AB (eM. pnc. 182), cJiaraiOu~H\1CH H3 nocTynaTeJibHoro ABH)!{eHHH BMeCTe C HeKOTOpblM _!JOJIIOCOM H BpaU1,eHH5I BOKpyr clTOfO llOJIIOCa C
yrJIOBOH CKOpOCTbiO ffi, H33biBaeMOll nepCtiOCHOt1 Yc.IIOBOU CKOpOC1°!b!O.
BeJIH'U!HaW, KaK ITOKa3aHO B § 63, OT Bbi6opa ITOJIIOCa He 33BHCHT H |
Ha |
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ll306pa)!{eHHbiX pHc. |
188, |
fAe |
IlOJIIOC TOqKa m, H pnc. 189, |
fAe |
llOJIIOC 0, HMeeT OAHO H TO |
)!{e |
3HaqeHHe. |
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HaqHeM c onpeAeJieH~H |
(dv0 T) 2 1dt. OpH paccMaTpnBaeMoM nepeHoc- |
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HOM ABH)!{eHHH BeKTOp |
V0 n |
HanpaBJieHHb!H 110 KaCaTeJibHOH K KpHBOH |
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AB, rrepeMeCTHTC5I BMeCTe c :noli KPHBOH noCTyrraTeJibHO (rrpHAeT B llOJIO)KeHHe m1 b, pHC. 188) H OAHOBpeMeHHO IJOBepHeTC5I BOKpyr TOL!Kll
m1 AO noJio)KeHH5I m1b1. B |
pe3yJihTaTe BeKTop |
V.,T noJiyqHT B nepeHoc- |
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HOM ABH2KeHHH |
npHpalll,eHHe (dV0 T) 2 =bb1 =Vb ·dt, fAe Vb- CKOpOCTh, |
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C KOTOpOH |
rrepeMelll,aeTCH |
TO'lKa b llpll llOBOpOTe BeKTOpa m1 b=VnT |
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BOKpyr |
TOl.JKH |
m 1 • TaK KaK 3TOT noBopoT rrpoHCXOAHT c yrJioBoli CKO- |
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pocThiO |
ffi, |
To |
no ¢opMyJie (76) |
v;,=mXm1b |
ffix~r B pe3yJihTaTe |
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nOJiyqaeM |
(dvor)2=vb·dt=ffixv;,,dt II |
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(ctv ) |
- - |
(92) |
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~=ffiXV |
or |
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dt |
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* fJOCTaB 1\opHOJIHC (1792-1843) - <jlpaHUY3CKHH yqeHb!H, li3B€CTHb!H CBOHMH Tpy.n.aMH no reopeTnqecKoii 11 npliKJia)I,HOH MexaHHKe. KopHOJIHCOBO ycKopenne Ha3b!Ba!OT €JU€ HOBOpOTHhiM, TaK KaK OHO HOliBJili€TCll HpH HaJinqHH y HO)I,BHJKHbiX ocell BpameHHll (noBopoTa).
6 J\1'• 2173 |
161 |
Tenepb |
orrpe,!I,eJIII~ |
(dvneph/d/. CKopocTh Vnep paBHa CKOpocTII TOH |
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Heii3MeHHO |
CB5I3aHHOII |
c no,!I,Bll)!{HhiMII OCHMII TO'IKII m KPIIBOH |
AB, |
C KOTOpOH |
B ,!I,aHHhiH MOMeHT BpeMeHII COBITa,!I,aeT TO'lKaM (piiC. |
189). |
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EcJIII TO'IKY 0 npiiH5ITh 3a nomoc H o6o3Ha'liiThqepe3 rBeKTOp |
Om= |
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:r, h
PHc. 189
TeJihHOe nepeMe~eHIIe
~eHHe
OTKy,!I,a
=OM, TO no ¢opMyJie (81)
Vnep = Vo + ffi X r.
(d~ep),
CosepnmB 3a npoMe)!{yToK speMeHII dt OTHOCIITeJibHOe nepeMe~e-
Hlle MM' |
V0 T ·dt, |
TO'lKa npii,!I,eT |
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B noJio)KeHIIe M', ,!I,JI5I KoToporo |
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f'=r+MM' |
II |
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-, |
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-; |
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-+- |
= |
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Vnep = |
Vo |
ffi |
X r |
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=vo +ffix Cr+MM'). |
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CJie,!I,oBaTeJihHO, scJie,!I,CTBIIe TO- |
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fO, |
'ITO TO'lKaCOBeplllaeT OTHOCll· |
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MM '=ii;,Tdt, |
BeKTOp |
~ep |
noJiy'laeT npupa- |
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(93)
flo,!I,CTaBJIJUl BeJIH'lllHhl(92) H (93) B paBeHCTBO (90), llOJIY'IIli\f
(94)
TaKIIM o6pa30M, 1wpuo.wcoeo ycKopenue paeno yiJeoeHHOMyeeKmopHOMY npOU3BeiJeHUIO nepeHOCHOU YCilOBOU CKOpocmu (yrJIOBOH CKOpOCTli
llO,!I,Bll)!{HOH CllCTeMbi |
OTC'leTa) HG |
OmHocumeAbHYIO CKOpOCmb |
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moLtKU. |
a i't n o c T y |
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C JI y q |
n a T e JI b H o r |
o n e p e H o |
c H o r o ,!1, B II- |
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)!{ e H II 51. |
B 3TOM cJiy'laeffi=O II, |
cJie,!I,oBaTeJihHO, ll;.011 =0. B pe3yJih- |
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TaTe paBeHCTBO (91) ,!J,aeT * |
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(95) |
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* 3ToT |
pe3yJihT3T BHJJ.eH |
H H3 pHc. |
188, 189 |
Kor.n.a KpHBaH |
AB rrepeMelll,aeTCH |
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rro<.:TyrraTeJibHO, TO BeKTopVoT rrpH.n.eT B rroJiolKeHne m1 b, rroKa3aHHoe na pHc. 188 nyHKrnpoM, T. e. He ll3M('HHTC5!,H 6y)J.eT (dv0 r)2=Q, 0)J.HOBpe'l!eHHOTipH 9TOM BCe TOqKH KpHBOH AB HMeiOT OJJ.HHaKOBbJe cKopocTH H B ToqKe M' (pHc. 189) Vnep 6y.n.eT TaKHM Me,
KaK B TOqKe M, T. e. IIOK333HHbiM nyHKTHpOM1 BCJie,li.CTBHe qero (dUneph=O.
162