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. 3aJJ.a•m 86. Bo3.UYlllllblii map BecoM P onyCKaercH c ycKopeHHeM a. KaKoi'rrpy3 Q (6aJJJJaCT) Ha,U:O C6pOCHTb, '!T06bllllap CTaJJ ITO)J:HHMaTbCH C TaKIIM JKe ycKopeHI!eM.
p e ill e H II e. Ha rra.uruomm'illlap,UCHCTBYJOT C!l.~a THMeCTll p II ITO)J:beM!laH CHJI3
F (pHc. 211, a). CocTaBJJHH ypaBHerme (2) B rrpoeKU,HH Ha BepTHKaJJb, Haii.ueM, 'ITO
(Pig) a=P-F.
Kon1.a 6y,u:eT c6pollleH 6aJJJJacT (pHc. 211, 6), Bee mapa cTaHeT paBeH P-Q, a TIO)J:bCMH3H CHJ13 OCTaHeTcH TOll Me. Tor,u:a, )''lllTb!BaH'ITO lllap Ilpll STOM ,UBIIMeTCll l!Bepx, ITOJJY'IIIM
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(P-Q)alg=F-(P-Q\. |
HcK.1JO'laH H3 STHX |
ypaBHCHHH HeHaBeCTHYJO CIIJIY F, naii,u:eM |
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Q=2PI(!+gla). |
3a,ll.a'!a 87. |
JlH<fJT BeCOM p (pHC. 212) Ha'll!HaeTITO)J:HHMaTbCH C ycKOpCHIICM a. |
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Onpe,u:eJJI!Tb HaTHMeHI!e |
Tpoca. |
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PHC. 211 |
PHc. 212 |
P e m e H 11 |
e. Ha .~H<fJT .ueiicTBYIOT CIIJia THMeCTH P 11 peaKu,HH Tpoca T. Coc- |
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TaBJJHll ypaBHCHI!e (2) B rrpoeKU,llll Ha BepTHK8Jlb, |
ITOJiy'lHM (P/g)a=T-P, OTKyAa |
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T=P(!+alg). |
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EcJIH JIH¢r onycKacTcll c TaKHM JKe ycKopeHHeM, ro H3THMeHHe Tpoca 6y,neT paB- |
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HO T1 =P(1-alg). |
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3a,n:aqa 88. |
Pa,u:11yc aaKpyrJicHHH B T01JKe A Mocra paBeii R (pHc. 213). Hai'rTH, |
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Kahoe ,ll3B.1eHHC |
Ha MOCT B TO'!KeA OKaMeT aBTOM06HJJb M3CCbl m, )l.BHMY!ll_IIHCH CO. |
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CKopOCTbiO V, |
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PHc. 213 |
PHc. |
214 |
P e ill e H 11 e. B TO'IKe A aBTOMOOI!Jib HMeeT HOpMaJJbHoe ycKopeHI!e an~v2!R. |
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Tip11 9TOM na 11ero )l.eiicTBYJOT CI!JJa THMeCTII |
P= mg 11 peaKu,HH |
N. Tor)l.a no ypaBne- |
HIIJO (2), COCTaBJieHHOMY B rrpoeKli,Hll Ha HOpMaJJb, IIJIH IICITOcpe)l.CTBeHHO flO BTOpOMY
188
H3 ypaBHCHfdi (!!) 6y;leT
mv21R=mg-N, oTKy.ua N=m(g-u21R).
C11JJa ,D;aBJJel!HH Ha MOCT paBHa no '-IO.UYJJJO N, no HanpaBJiena BIIH3.
3a,n:aqa 89. KpllBOlliiin OA Jl!lHHhl l, spamaHcb par~noMepno c yrJiosoii: crmpoCTbJO w, nepeMemaer KYJJHcy 1(, JlDH/KymyrocH rrocrynareJibHO B.UOJib narrpasJIHJOmnx 1, 1 (p11c. 214). Haflm, rrpeHe6pcraH rpeHHeM, 'leMyrrp119TOM pasHa crwa .uasJICHIIH Q
noJJsyua A Ha Kym1cy, ec.111 Bee KpiHCbi P.
P e III e H 11 e. Tipose.ueM Koop,~llHaTHYJO ocb Ox. Tor.ua rroJJO)!{eHile KYJJIICLI orrpe-
}l,rJIHTCH KoOp,!l,UH3TIIOfl X= l COS (j) |
li, TIOCKOJJbKY (j!=Wf, saKOil |
,li.BII)!{CHIIH KYJIIICbl 6y- |
,li.CT x=l cos wt. 3HaH 9TOT saKon, |
socrrO.l][,3yeMCH rrepBbiM 113 |
ypasneanil (10'). Bbl- |
l!IICJJHH ilpOH3BO.I\HYJO OT X, no,1ylJH\l
x= -w2 l cos wt = -w2 x.
KpoMe roro, Qx=-Q. B pesyJILTare Haxo.umt
-(Pig)w~x=-Q 11 Q=(Pig)w2 x.
CJJe.uosareJJLIIO, c11.1a .uasJieHIIH no.~syna na KYJJIICY IIJMeHHercH nporropurwHaJJbiiO paCCTOHHIIfO X KyJIHCbl OT OCll 0.
§ 82. PEIIIEHHE OCHOBHOA 3A,ll.AqH ,IJ.HHAMHKH
UPH KPHBOJIHHEAHOM ,IJ.BH)KEHHH TO'-IKH
B cJiyqae KpnsoJIHHeilHoro ~BHJKeHnH TO'lKH ocHOBHaH 3a~aqa
~HHa:vl:HKH pewaeTC51 C IIOMOill.biO ~HqxpepeHUH3JibHbiX ypaBHeHHH ~BH
)KeHIUI, noJiyqeHHbiX B § 77. EcJIH 3a~aqa pewaeTCH B II!'JHMoyroJibHbiX ~eKapTOBbiX KOOp~HHaTaX, T. e. C IIOMO!UbiO ypaBH€HHH (10), TO H3'l3Jlb-
Hbi€ ycJIOBH51, onpe~eJI51IOIUHe llOJIOJKeHHe H CKOpOCTb TO'lKHB H3'l3JlbHblll MOMeHT BpeMeHH 3a~aiOTC51 B Bll~e:
llpH t =0 x=Xo, y=ljo, Z=Zo; |
(23) |
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Vx=Vxo, Vy=Vyo• Vz=Vzo• |
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197
TipOIIHTerpHpOBaB ypaBHeHIISI (10), HaXO,li.SIT KOOp,li.IIH3Tbl X, y, Z ,ll.BR• >KyiU.eikH TOIJKII, KaK cpyHKUIIII BpeMeHII t, T. e. onpe,ll.eJIHIOT 3aKOH ,li.BII· )KeHIIH TOIJKII. Dpn 3TOM no.rryqeHHble pernemm OY.li.YT CO,ll.epJKaT& rnecTb TIOCTOHHHbiX HHTerpHpOB3HH51 Cr, c2,• .., Cs, 3HatJ:eHH51 KOTOpb!X ,li.OJDKHbi Onpe,ll.eJIHTbCfl TIO HaqaJibHbiM YCJIOBIIf!M (23).
KoHKpeTHhiH XO.ll. perneHIIH |
noKa3aH |
B paccMaTpiisaeMOH HHJKe 3a- |
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,ll.a1Je. |
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Jl B II JK e H II e |
TO q K H, |
6 p |
0 ill |
e H H 0 H |
TI 0 ,ll. |
y r Jl |
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rOp1I30HT3JibHOH |
TIJIOCKOCTII |
B |
O,li.HOpO,li.HOM |
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TI 0 JI e T 5I |
1K e |
C T II. l13YIJIIM |
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HHe |
TeJia, |
~porneHHoro c HaiJaJibHOH |
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CKOpOCTbiO |
Vo, |
HanpaBJieHHOH |
TIO,ll. yr- |
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JIOM |
a K |
rOp1I30HTaJibHOH |
TIJIOCKOCTII, |
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paccMaTpHBaf! ero |
KaK MaTepiiaJibHYIO |
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TOIJKY c Maccoii m. |
Dpii |
3TOM |
conpo- |
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J.JF-;,._;:;;.~.~..-t-t----~-x |
TIIBJI.el:meM aoa,ll.yxa upeHe6peraeM, a |
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PHc. 220 |
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TIOJre |
T.lflKeeTI'I 6y).l.eM Ctm'E'aTbO,ll.liOpO).I.- |
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Hbi.M (P=const), |
noJiaraJI. |
qTQ ).l.aJib- |
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IriOCTb TIOJieTa li |
BhlCOTa TpaeKTOpiUi |
Ma- |
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Jlbl TIO cpaBHeHIIIO |
C p.a,niJ:yCOM 3eMJUL |
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DoMeCTIIM HattaJio Koop,n;RHM 0 s Ratra.mbH<lM JT~emru TO>'IK1i. |
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HanpaBHM |
OCh Oy BeP'fHK<rJI'l'>HOBBepx; |
ropH30HTa.Jl'bi'Ij!'IOocr, Ox pac- |
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IIOJIOJKIIM s |
n.rroCKOCTH, upoxo~w ttepe-3 0'!} |
a. |
BeKTOJ) -t!'o., a |
O.Cb |
Oz |
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npoBe,ll.eM nepneH,nnyn~Ho rr.ep.Bt.FM ~YM ocmr (pm::. 220). Tm-.n:a yroJI Me)K.li.Y BeKTOpOM vi) l:l OCblO Ox 6y.ll.eT a..
l13o6pa31IM )l.B.yacymytocg TOtm.y M B rrpon.3BOJibOOM noo~rum. Ha Hee ,ll.elicTsyeT TOJlbP::O O)J.Ha cRJTa T1fJK~Tif P ~eM. npaMe•mmre K
3a,ll.aqe 93 B § 80), npoeKIVIlf KOTOPOH lla KOOp,l.li.HHaTHhle OCR paBHbl:
Px=O, Py=-P=-mg, Pz=O.
Do,li.CT3BJI5I5l |
'1111 Be.JIH'llllihl B ypa8H€HHR (10) 1l 3a.M.ettaa, liTO |
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d2x/dt 2 =dv)dt |
H T • .n., |
f!OCJJ:e |
COKfl'~eEllil11 H<l m BMy'lldM: |
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dvx=o |
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dvy |
dvz =0 |
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dt=-g, |
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dt |
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dt |
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YMHOJKaH o6e qacTII 3T:ax ypamtewua Ha dt |
R HHTerpapyn. HaXO)l.IIM |
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Vx=Cb Vy=-gt+C2, Vz=Ca. |
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HaqaJibHI>Ie ycoown |
(23) B Haweii sa)l!atre HMem ~ |
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np.u t=O x=O, y=O, z=O; |
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Vx=t111COSC», |
Vy=V'oSina, t'r=O. |
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Y,li.OBJieTBOpHH Haqam~HbiM YCJIOBJJ.S!M, IIOJIY'lliM
cl=V& cosa, C2=Vo sin a:, Ca=O.
198
TIO)l.CTaBJif15I 3TH 3HaqeHH51 Cl; c2 H Cs B HaH)l,eHHble Bbiiiie peiiieHHfl H 3aMeHf!fl Vx Ha dx/dt H T. )],., npH)l.eM K ypaBHeHl!f!M:
dx |
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dy |
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t |
dz |
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dt=V8 COSa, |
dt=V0 Sllla-g, |
dt= . |
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HaTerpHpyH 3TH |
ypasHeHH5I, |
noJiyqHM: |
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x=v0 t cosa+C 4 , |
y=v0 tsina-gN2+C5 , |
z=C6 • |
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Tio)l.cTaHOBKa HaqaJibHblX ,!l.al!HhlX ,ll,aer C~=Cfi =C6 = |
0, H OKoHqaTeJibHO |
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HaXO)l.HM ypa:sHeHHa )l.B.l:l:IKe.HHa |
TOlJ.K!I M B |
BK)l.e: |
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x=votoosa, y=v.o-isina-gf2!2, z=O. |
(24) |
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J13 TIOCJI€)1,Hero |
ypaBHeHHfl |
CJie)l,yeT, qTQ |
)l,BHJK€HHe |
npOHCXO)l,HT B |
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TIJIOCKOCTH Oxy.
HMe5I ypaBHeHHH )I,BIDKeHHSI TOtUrn, MO:iKHO MeT0)1,3MH KHHeMaTHKH
onpe)l.eJIHTb |
BCe x.apaK;rep HCTHKR ,ll.aHHOfO |
,ll;BHJKeHH.H. |
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T p a e K T o p |
rr 5I To q K 11. HcKJIIO'Ja.HH3 nepBbiX )l.Byx ypaB- |
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HeHHH |
(24) |
BpeMH f, |
TIOJiyqHM ypaBH€HHe |
TpaeKTOpHI! TOqKu: |
y=xtga- |
2 |
g x2 |
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(25) |
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2vo eos2 a: |
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3To ypaBHeHHe napa60Jibl c OCbiO, napaJIJieJihHOH OCH Oy. TaKHM
o6pa30M, 6pou.tefiH.aJl no{j !J2!tOM K ZOpUSOH.mG!tbH.OU n!tOCKOCmU trlJlJ!CeAaJl mottKa oeuJ~CemcR e 6e38030yl1l'floM npacmpaH.cmee no napa6oAe (faJIHJiefi).
2. r 0 p H 3 0 H T a Jl b H a fl .n: a JI b H 0 c T b. Onpe)J,eJIHM ropH30HTaJibHYIO ,naJibHOCTh, T. e. II3MepeHHoe B)l.OJib ocH Ox paccTOf!HHe
OC=X. TioJiaraH B paBeHcTse (25) y=D, Hafi)l.eM ToqKH nepeceqeHHH rpaeKTOpHH c OCbiO Ox. M3 ypaBHeHPIH x [tga-gx/ (2v~cos2a)l=O no-
JiyqaeM
Depsoe peiiieHHe )l.aeT roqKy 0, BTopoeToqKy C. CJie.I{OBaTeJibHO,
X =x2 II OKOHqaTeJILHO |
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X= Mig) sin 2-a. |
(26) |
J13 <!JopMyJibi (26) BH)l,HO, qTQ TaKaf! :iKe rOpH30HTaJibHa51 .I{aJibHOCTb X 6y.I{eT noJiyqeHa npH yrJie ~. AJIH KOToporo 2~=180°-2a, T. e. ecJIH
yroJI ~ =90°-a. CJie)l,OBaTeJibHO, npH ,naHHOH HaqaJibHOH CKOpoCTH Vo B OAHY H TY :iKe TOqKy C MO:iKHO nonacTb ,nsyMH TpaeKTopHHMH: HaCTHJibHOH (a<45°) H HaBeCHOH (a>45°).
TipH 3a)l,aHHOH HaqaJibHOH CKOpOCTH Vo HaH60Jibllla51 ropH30HTaJibHaf! )l,aJibHOCTb B 6e3B03)1.YIIIHOM npOCTpaHCTBe TIOJiyqaeTCH, KOr.I{a sin2a=J,
T.e. npH yrJie a=45°,
3.B hi co T a T p a e K T o p H H. EcJIH noJioJKHTh B ypasHeHHH
(25)x=X/2={vg/R") sinacosa, TO onpe)l.eJIHTC5I BbiCOTa TpaeKTOpHH H:
H = |
M12g) sin2 a. |
(26') |
4. B p e M 51 n o JI e T a. |
H3 nepsoro ypasHeHHfl CHCTeMbl |
(24) |
c.ne.n.yeT, qTo noJIHoe speMH noJieTa T onpe,zi.eJif!eTCfl paBeHCTBOM |
X= |
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199
=voTcos a;, 3aMeH5ui 3.I{ecb X ero 3Ha'IeHHeM, noJiy'IHM |
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T= (2v0/g) sin a. |
(26") |
TipH yrJie HaH60JibllleH AaJibHOCTH a* =45° Bee HafiAeHHhle BeJIH'IHHbl IIMeiOT 3Ha'IeHH.H:
X*= vUg. H* = vz/4g = X*/4, T* = (vo/g) V2. |
(27) |
TioJiy'IeHHbiepe3yJibT3Thl MOryT HaXOAHTb HeKOTOpbie npiiJIOJKeHHfl, HaTipHMep, BO BHeiiiHeH 6aJIJIHCTime AJI.H OIJ,eHKH TOrO, K3K H3MeH5IeTC.H A3JlbHOCTb TIOJieTa npH H3MeHeHHH yrJia a HJIH CKOpOCTH V0 Ha O'IeHb MaJiyiO BeJIH'II1HY, HJIJI me AJI.H OplleHTHpOBO'IHbiX Oll,eHOK B CJiy'Iaf!X, aHaJIOrH'IHb!X paCCMOTpeHHOMY B npHBOAHMOM npHMepe.
UpuMep. HssecTHo *, LITo HeMeuKnfi cHapH,n: <I>AY-2 rroc.rre sepTnKa.%Horo sarrycKa HMeJI Ha BblCOTe 20 KM CKOpOCTb Vo"" !700 M/C II yrOJI a""45° (rrosopOT CHapH,n:a rrpoH3BO,n:HJICH c rroMO!l\biO crreuua.rrbHbiX npn6opos 11 py.rrefi). )la.rrbHe!mmrc no.rreT cHapH,n:a npaKTHlJ€CKH IlpOHCXO.Il:HJI KaK ITOJieT 6pOlll€HHOf0 TeJia B 6e3B03JlYIIIHOVI IIpOCTpaHCTB€
H Ha |
BbiCOTax, ,n:.rrH KOTOpb!x MOMHO ell\e rpy6o C'lHTaTbP= canst Tor.n:a no ¢opMy.rraM |
(27) |
,!(OJI)!{HO 6b!Tb; |
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X *""300 KM, H *=75 KM, T *""'245 c. |
3TH pe3yJibT8Tbl OlJ€Hb 6JIH3KII K T€M, KOTOpb!e IIM€Jlll M€CTO ,!(J!H ,!(al!Hb!X CHapH,!(OB |
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<fJaKTHl!eCKH. |
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n e p B a fl K 0 c M H 'Ie c K a 5I c K 0 p 0 c T b • PacCMOTpHM |
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eme OAHY 3aAa'Iyo ABHmemm 6poiiieHHoro TeJia. Haii:AeM, KaKyiO HaqaJihHYIO CKOpOCTb H3AO C006JUHTb TeJiy, H3XOA.HIIJ,eMyCfl Ha paCCTOf!HHH
110 |
R OT IJ,eHTpa |
3eMJIH, |
'IT06hr OHO ABHraJIOCb |
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BOKpyr 3eMJIH |
no Kpyrosoil |
op6rne paAHyca |
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R (pHc. 221); conpOTHBJieHHe B03Ayxa C'IHTa- |
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eM OTCyTCTBYIOill.HM, |
a Te.lJO |
paCCMaTpHBaeM |
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KaK MaTepHaJihHYIO TO'IKy. |
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TipeJK.u,e scero |
3aMe'!aeM, 'ITO TaK KaK |
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CKOpOCTb |
TO'IKH B |
JII060H MOMeHT BpeMeHJ1 |
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AOJIJKHa 6hiTb HanpaBJieHa !!? KaCaTeJibHOH K |
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TpaeKTOpHH, TO CKOpOCTb Vo CJieAyeT Hanpa- |
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P!!C. 221 |
BIITb nepneHAHKyJIHpHO paAHycy CM 0 , rAe |
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M 0 - HaqaJibHoe |
noJioJKeHne TO'IKH. |
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)lJI.H ,1{3JlbHeHIIIero peiiieHH.H |
BOCTIOJib3yeMC.H ypaBHeHHf!MH (11 ). |
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PaccMaTpHBa.H TO'IKY B npoH3BOJibHOM noJiomeHHH M, npoBOAHM ocH
M• u Mn u ll306pamaeM |
Aei1cTBYIOill.YIO Ha TO'IKY crwy nl:rOTeHH.H |
F; 'IHCJieHHO F=mgo, rAe |
m - Macca TO'IKH, g 0 - ycKopemre CHJibl |
TflroreHH.H B nyHKTe M. TaK KaK F-r=O, a F11 =F, ypaBHemm (11) npnMYT BHA:
dv dT=O,
l13 nepBOrO ypaBHeHH.H H3XOAIJ:M, 'ITOV= canst H, CJieAOBaTeJibHO,
V=Vo. TiocJie aTOro BTopoe ypaBHeHue AaeT (ecJiu C'IHTaTb,'ITOR=Ro=
* CM.: K o o ii H., lOT e u 6 or apT H. .[LHHaMHKa paKeT. 06oponms, 1950.
200
=6378 KMpa,n;uyc 3eMHoro 3KBaTopa, a g 0 =9,82 Mlc2) |
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V0 = V g0 R0 = 7914 M/C ~ 7,9 KM/C. |
(28) |
3ra H8MMeHhlll851 CKOpOCTh, KOTOpyiO HYLKHO COOOill.HTh opoiiieHHOMY TeJiy, trr06bi OHO He yna.'lO 00p8THO Ha 3eMJIIO, H83h!B8eTC51 Kpye080U
HJin: nepeou KOCMUtieCKou ctwpocmb/0 (eM.
fJJaoa XVII
Olill.(ME TEOPEMbl ,li,MHAMMI(M T041(M
JI.JI51 peiiieHH51 MHOriTX 3a,n;aq ,IJ;HH8MHKH, OCOOeHHO B ,IJ;IIH8MHKe CHC-
TeMhi, BMeCTO Henocpe,n;CTBeHHOrO HHTerpHpOBaHHH ,Il;HqxpepeHI].H8Jlh· HhiX ypaBHeHHH ,n;BHLKeHHH OKa3biBaercH ooJiee 3qxpeKTHBHhiM noJih30-
B8ThC51 TaK H83hiBaeMhiMH oomHMH TeopeMaMH, HBJIHIOW.HMHCH cJie,n;crBHHMH OCHOBHOrO 38KOH8 )I.HH8MHKH.
3HaqeHHe OOill.HX TeopeM COCTOHT B TOM, qro OHH YCT8H8BJIHB810T H8fJI51)I.Hble 38BHCHMOCTH MeLK)I.y COOTBeTCTBY!Olll.HMH )I.HH8MHqecKHMH xapaKTepHCTHK8MH )I.BHLKeHHH M8TepH8JihHh!X TeJI H OTKpbiB810T TeM C8MhiM HOBble B03MOLKHOCTH HCCJie)I.OB8HHH )I.BHLKeHH51 MeXaHHqecKHX CHCTeM, nmpoKo npHMeHHeMhie B HHLKeHepHoll: npaKTHKe. K.poMe roro, npHMeHeHHe oomux TeopeM H36aBJIHeT or Heooxo)I.HMOCTH npo)I.eJihiBaTh )I.JIH K8LK,IJ;OH 38)!.8qif Te onepaiJ.Hli HHTerpHpOB8HHH, KOTOphie pa3 II HaBcer)I.a npOH3BO)I.HTCH npH Bb!BO)I,e 3THX TeopeM; TeM C8Mh!M ynpomaeTCH
npouecc perneHHH.
DepeH:,n;eM K paccMOTpeHHIO oomHx reopeM )I.HHaMHKH roqKH.
§ 83. I(OJIHIIECTBO )I.BH)I(EHH51 TOIJI(H. HMOYJibC CHJibl
O,n;Holl: H3 ocHOBHhiX )I.HHaMHqecKHX xapaKTepHCTHK )I.BHLKeHHH roqKH HBJIHeTC51 KOJIHqeCTBO ,IJ;BIILKeHH51 ~ .
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p e Ill e H li e. ITo J].aHHbiM 3aJ].3'!HBUJ].HO, 'ITO)l,Jill orrpeJ].eJieHUll BpeMellH ABUtKeHUll MO)KHO BOCIJ0.%30BaTbel! JJ.OK3331JHOH TeOpCMOH. J.-IJo6patKaeM rpys B I!pOH3BOJ!bHOM
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TaKHM o6paso\I, BpeMH TopMotKeaul! paeTeT rrporropuuouaJihHO Ha'!aJibHOii.cKopoCTU.
Pe!IlHM STY IKe 3aA3'!Y,C'IUTall,'ITOTOpM03lll.q3ll CUJia paBH3 Q U He IJOeTOl!HHa, a e MoMenTa na'!aJia TOpMOLKeHul! paeTeT rrporropuuouaJihUO BpeMeHii, T. e. Q=kt, rAe k - HeKOTOpb!H rroeTOliHHb!H K03cjlcpuuueHT, H eT3HOBUTel! p3BHOH F B MOMeHT OCTaHOBKil rpysa. TaK KaK CHJia 33BHCUT OT BpeMeHU, TO OI!l!Tb MOIKHO BOCIIOJ!b30BaTbCH
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CJie;I.OBaTeJJbPO, B ::JT01I cJiyqae spewl TopMotKeH!Ill |
YABauBaeTCH, |
§ 85. TEOPEMA 06 H3MEHEHMH MOMEHTA
KOJJH'.JECTBA)J,BH)I{EHH}l T04KH (TEOPEMA MOMEHTOB)
B HeKoropbix 3a,n,aqax B KaqecrBe ,ll.HHaMHqecKofi xapaKTepucTHKH
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204