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ISBN: 975-5-8054-0860-9
Текст
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ISBN 975-5-8054-0860-9
QUO 22.2 у 73
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hjGqppGbp......-...-........................................90
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'I)Luhu|iuOdiiiO opbGpGbp.......................................91
§20 . <шйшМрЬ Ь^щпцио' Ьрш QinQin|ui5wG opbGpg................96
§21 . hGbpgpiujh GbGuipnG, Gpw jwpddwG pbnpbdp <шгЦшрф C
hwdwQwpq...................................................100
l §& ЬОсцпщф u|whiqwGdwG opbGpo................................103
§53 . JbtuwG|il|wl|wG w^fuiumwGp..............................107
§24 . ^nuibGghw(WjfiG гндияциг^Ьр.............................111
§25 . '’IntnbGgpwi tbbpqpw, Gpw Циищр mdp hbin................114
§26 . ЧпйиЬрЦшифЦ ntdbpp w^fuwinwGpo hwdujfudpnii}............117
§27 . 4hGbinhl| tGbpqhiu Upbbinpq tGbpqpwjp pbnpbdp...........120
§28 . ''HiutuyojinpU nidbp, GpwGg wpfuwinwGpo............... 122
§29 . !Л|ишЬрЦшЦшО tGbpqpwjp iqwhiqwGtJiuG opbGpp.............130
§30 . tyiGhui GhG^iGfiLn TtupdmdGbp: <wQwuwpwb2onipjmG L
UwjntGnipjniG....................................... „....133
§31 . ПЬцшлЬЩчллшЦшО tGbpqpw: Didp. рйщпцир L tGbpqpajfi
dLuitjinfunipjujG puiGwOGbpo................................. 135
§32 QiuGqQwdfi L tGbpqpiujp i|in|uujniupd фпГишЦЬрщшйОЬп......143
§33 . 3>ninnG Hncmbpfi t5>bG^D oiqinhGujjnid..................146
QLfldu V. btrnrhlllb UniTbLSb '’lUmUUTU'L ОГЬЪЯС
§34 . JndbGinGbph ЬшЦидлиршйо: bikqnquh OntibGinft
niwhiqiuGtkuG opbOpg....................................... 150
§35 иЬфшЦшО h&qnqub dndbGin...................................156
§36 Г)1ф L fidiqnquti liniibGinGbpG шОгшрс! июшОдрр ОЦцдлйшйр:
СшрдЦпц ubqpGujGbuip ОЦшслйшйр
dndbGinGbpfi ЬшЦшишргпйр...................................158
§37 UG^iupd шршОдрр zntpj hwikufudpp iqinni/mp................160
§38 . UGQjmGiJujhG dndbGuih mwhiijUjGihuG ophGuuGGbp..........164
К>Огфр.................................................. 17Q
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§39 РшдшрйсиЦ nj шпшйцшЦшО piufuniiJ...........................172
§40 . РшдшрдшЦ luoiudquil+mG pojfunuJ..........................176
§41 . Oj iur?uiflqwl|uj(i pwlund............................. 182
§42 . Г№[штЬЦМлшЦшО ObfuwGpliujjp фпрОшршршЦшБ
hf»5CJUjQnpnii5[i..................... „..................... 184
§43 . Фпфп^Цпр qwGqQiudnq diupOGp zujpdnuJc....................188
qinju vii. имл ингиър чгшитчи
§44 'Прйр йшрйОр zuupdikuG dbbpG m hw^uiuuipajltfompjruGQ..........195
§45 . 'Прйр iIiupdGh qGpwjpG 2wpdniil[i: hGbpgpiujp OndbGuip
₽bGqnpiuL|iuG pGnijpp......................................... 200
§46 . GinbjGbph pbnpbdp: hGbpgpiujh OmlbGinp ЬшгЦтйр...........205
§47 . 'ПрОр йшрф huipp 2wn<fr>ii5(i............................210
§48 . СфйшО mdbpo qinptkuG ЛийшйшЦ.............................215
§49 . 4приЦ: <приф Luqujin йпДи................................221
§50 . <гцш1|Ш)рЬ t3>bl|in: <npul|UJ|pG mdbp....................223
§51 . <гцшЦр ЬшрЦшрршЦшО Дпйду ЪтшшдршОЬр......................226
ЮйрЬпЫзр....................................................232
чщии vin. curdniuc гисчигчь по ьъьгагш.
гииичипмии
§52 . <Ш2Цшр1|Ь hbbpohwi ЬшйшЦшрцЬр .................... .234
§53 . <шйрЬршд гшрдЦпр <Л<-bp: hGbpgpwjti mdbp.................236
§54 . Сшрдйшй ЬшЦилюиргийо ИшгЦшрЦр 1|ujOujjujI|uuO fq pGbpgpwi
ЬшйшЦшрцтй......................................................240
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pGbpgpiut hwihuliujpqnii].......................................245
§56 . Ciupdmdo bpl|pwl|bOinpnQ huJ2Qujp4p huiOuJl|UjpqmiJ......247
§57 . ИшрОрййЬрЬ t|2tl|7D: U£il|2,7blhnLPJnLCl.................249
§58 . Llquin рОЦОпг] OujpiJGh 2bqnnjQ niqpwapq|ig..............252
§59 . bni^njp dndujGiul|D....................................... 254
luGqppQbp...................................................257
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§60 Ubuubpfi opbGpDbpp: SpbqbpiuUtuG dqnqnipjwG opbOpo...........260
§61 QncuilfiinujghnG rjwzin: nw^infi pQnipiuqpbpQ................264
§62 . 4Gq|i qpwQpiniugtinG qiuzinp L иЬфшЦшО qpiui|fiiriwgpnG
tObpqtiiuG: ОршфмшдГпО гшпшЦрр.................................268
"§63 Ubuiibpblutiqtipo............................................272
§64 . ЬрЦги diupdGfi ftj&qfip: bpbp JwpiiOh ишИОшОшфшЦ fuGqpp....276
§65 . LTn(npujl|Gbpti ЬршЦшО 2iupctnit5[i
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§67 . bCibpin L дршЦЬтшдрпО qiuGqi|uj6Gbp: ЬлЦЬгН фпрйд..........283
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§70 . Lnijub 6uji?ujqujjpp jbqmdo UpbquuUh дршфилшдрпО qu^innid .... 292
ЮйгфрйЬр.....................................................294
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§72 . 9qnidLubridrHiJ:<niUhopbGp[]...............................298
§73 . UmudqiuUujG pb$npi5wgfiwjb tGbpqhiuli......................303
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§78 . 2)hqpl|UJl|aJG L ОшрЬйидлЬЦшЦшй бпДшОшЦОЬр.................319
v§79. Uiupnq iniuuiwCiniiJGbp.....................................322
§80 . <шрЦшпршЦшС| тидлшОпиЮЬр ribqnGwGu.....................325
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шиллшйтйОЬро: ЭшрЦЬр...........................................329
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§82 . UihpuJjhO ZwpdikuG ЦЬОЫцдлЬЦш.............................335
§83 . UthfiUJjhG hwijaojupnid: Uih₽h i|inqwjpG ujpiuqnipjniG[i..339
§84 . Ujpep IGbpqtiiuG: (DnjpfiGqp ЦЬЦлпрр......................341
§85 . U|h₽Gbpp Qbpiuppnidp......................................343
§86 UiuGqniG lUifipGbp..........................................345
§87 Ul|niuinpl|W................................................347
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§88 <bqniqGbph и qujqbph huJinQnipjfliGGbpo.....................356
§89 . <nuujGph pGnipwqpbpo LjniptuUwG шдшйддид..................358
§90 . <nuwG₽p iuG|uqbi|inipjujG hwijwuujpnidQ...................359
§91 . tjifapfi hwi[iuuujpnnjQ...................................361
§92 . <pqpnuinujinhGiu)h hpilniGpGbpg.......................... 364
§93 . РшрпйнлршЦшО piuGiufiLbp..................................367
§94 . UujpiJtiGGbpti hwQiuuujpuj^onipjnLGc! hbqmljniii..........369
'§95. UimughnGiup hnuiuGp PbDGnqhh hmQujuiupnuJp.................371
§96 . СкидтдрЦ hfaqrnl|: LiuQib-Upnpuh ЬшЦшишртйр...............375
§97 . Mnitinti L'Tlniujqbjip hnuuGpGbp..........................379
§98 . PbjGniquh ppQ: LwiJhGujp L Lnnippnqbbin hnuiuGpGbp........384
§99 . UuJhiJiuGwjfiG jbpin......................................388
§100 . '’IhGq ihupOGh jwpdnuJp ЬЬптЦгнй.........................390
§101 . SmjGujjpG uitppGbp.......................................393
ihqhl|iAJl|tJuG Ь ши1ЛГ|шд|илшЦшО npn? hiuuniuinniGGbp....396
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difliqn] qm^mqpijq latfdq 7 piaqli q<3um dif qmtplqmnfq/]
:flqiukhunqin pmhBiuamh mdfi qmpdq iJlqUup qmpq
IqhdQi Uudmh Ц? qiufdiutnnrd dp ?u qmhmhdtnmpqdmp mhnrn 'Odqqqiufdiuh
-inmq qmhm} Iqhmam ddhuqdq "dtnhqfdo piuinfmqmmdm i|? Olqtiup qmh
•mhdbdt qdq Odqqqiuldiuhinmq qmhm} Iqhmum UnqBudhn l^nhqfdo qq
piudt] flqudu ‘fiudqqlqtiup pmbBmqmhmlmqUd Bqmdq ) piuqddmn|uij) Odqq
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; q¥m q infmqqm bqp Qnmp Zudu Bqmdq du ‘huampinmtn qfm qfmQp ?u 5 qi|d
г -mqqqm qpiuamtiZmq |n|dl Bqmdt, :OqiuWiuqmbmpbmd i|dqqqiuWiuhinmi|
} huiinmq i|inf]q(do qmqmqqbdt qmhmdd pmBmhqmB lidutlhdq :1mn|n
Iqqdl qq Uudmh ndiuti Bqdqqqmpqmn qmfdiuinZj? dpduQi q qq dqiufUdm
qmpBmdqmqdqi] ddqmnmQ) qmhmqpduib flqudu 'mdh i|dqqflqqdo qm^ni)
dbi|<t dhmZudu qq pmhqpdd OdqqqiufelHJinubminqq qmpq njmq ‘nqtnmhnq
BQqiulhqmnqin i|mt)dbd<t inni|n| Iqhdmpmq Uudmh Ц? nquqti ‘dpmWiuimnl
Uqqmdfmp qmhmhduimpqdmp ) pmhdminmh qfm hni|qfiuq qdq qiufdiULnub
-minqq qmhmnqin pmfimhqmg inqq ddqqnqBudbn qmhmqd q ddqqinhqldo
qmhmdd Un,u pdub Odu ‘dqmfdiucndto qmhmqd Ifm pmBmhqmB q nqhi?qd
Odfmtjdbdt qm^m^md Oqtu/dnjinnnJ tjmt)mt]d<^nnpqdmp rj/mi/jq
:dpmfdiuQm|idubmqpU4 ddqqdhunm mdq qd ?u q fiuuinmpd qmfd
-luinnnj qmhmqmdmpmdin ddqqpiubqmqmdbq qmhmhdinmpqdmp knqmh
-nmq 1 flinqhi Oqiufdiuinnnj qmhmhdinmpqdmp du nqhiqlq dpmtdiumZ?
dhmZudu inZQp Uiqq ddqqqdpdmp qmhmdd 1 piu|4imuimh Odu ‘huBuiqp
dpduih qfmdp q qfmdp lqhinn|p pmh Iqhmminnmq 1 Uudmh nqi|3dqb :0qmfd
-luqBmindmpZ? ddqqdhunm mdq 1 piubqmq OBdmq qmfdimndmpZp qfmhdm
-mpqdmfi :q¥m q piuhdmBmdqh qdlmtxnomp dnfml piud(m|nm5dp oqnmpmq
ilqdminmq Ufm L|rjv|T? dufimd
-mijq piu3tnqU ,yj/ = 77 .Sijqnm ‘Km qnd ‘inqt] qrrt|mdiUq nqhidu IqijiuUijO
q (ВЦ-7 ивиф 1 pmbrjm $ rjfmc|<i D- / qqd) Bqrputdiudmhdq qddiupmh 1Ииф
inmpqpmqqm Iqdmpmq Oqiufdiudmhdq i|lmqq3qpuinbm 1 dlqdmt] 40
. 1/2 ddq ‘3qqnm ‘piu3tnqb Цр 'бЦфт? 1 gmfdiuinZy ‘nqtnmhinmy *q Bqdqq
-qmpfmtn qdtJijnl ргтфп|гг>И ‘qpqdnj °i/i > 1/2 BqUqindu *1 > ei-i qdq "Bdqiuf
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-dq qfmr)q3qpuin[im piuqmrjQdo Uufihdminih.» Iqpiul Uik/br/nj / piuhfymq
•mtn pudu •mpmtofm rjmfehuisiZp } пфгтил Qqmn|nnHnmhn qBdmy Un 1» 2
Sqqdmpmq du •BqrpUdiudmhdq 7 Qddiupmq Orpuldiudmt]dq j dfmqqdqpuin
фт Цг)Ц1 1 3inqhi ОЗиф qmdTqq flqdqrjipufdiuinfmqmindm .йЗиф inmp
-qpmqqm. pmt] ..pqp inmpqpmqqm,, piufiirbo rjq njmymq рпКпфЦЪЦф
:6iJgiuWiudmhdq i|3diupmh qq 1Йиф inmpqpmqqm Odqfxfiin?
dfmqq3qpumbm qdq ,i)3r)dn(m 'jx> 2 4«<q ‘фи- ®> ^оф1тп|иф ij- 1 qaqQnfm)
dpmppdmZ duiqt] nmhmehu(f] ^оф1тп|иф 1 qiqdmf] Opiupdm? i|(moq3qp
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-mtiZmq quqrufim? qfmqqdqpuinhn V7 - ®J 3rjmr)nunnh dmpmq dhmrjmp
-mp UubSqmqrnhi inqh gmhmdiurg nqhndu omqqdqpuintim JuilqipuUiJO
:(dpm(duiin?571 Imqrrunn Oqmn|nminmhi) buSdpmh i)mldiudmt|dq 7 ilnBqmh
rjmqq3qpuinhm UuBqrjiu rpuldiudmhdq 2 duhpdmZ dpmfdiubmdm л piud
-BrndgO i)du ‘Ot|mt)mpmp 1 qfm SqqZudtj Odqqqmpfmhi rjm(diui|lqamdqh qmf
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:6doiufdiuinZy dfjmnJnrYHnmhn кфЗотч
•mtn q Bqilqrjrjmptmln ddUqnJ “Bdetfiuod qmppdmZ mdq qmddu ‘Bijqpdmp
ImQun отвдГт ?u 1 рлгфгЦтИ ?u qd ‘dpmppdmZ Qinqh qmhmdiufq IqqqdmnJ
-иф Opiupdm? dqpdmp BufUdm } qiqdmh :piuinqt] qml]nxhm?mdhdq рпфб
-mqudinijqh Ddiufq 5lu piugmdq fiulqdmpmq ‘Iqnqinom } i|lqdmt] QdqrMjwn?
qmhmpmdmin i|du ‘qi|pdmp hqtnuhnudhmp pmBmtiqmB piuJiZuti } nqtn
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q (hdqnmp pmlq) mqt) qmtjmelKifq .dqijijiufdiuBmtinmq ijmt]mBmdqb qml]
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dinr/qpup dnhutnpd dnhutnpq qfmdbdqq) ddqijdqqdo i/m/idpmqdti
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тфщ tubppnidbpuijcupctrudpрйтршдрпр РЬишЦпртр/п^ЬЬррд
РшдшрдшЬ tpfibp ikupilpOp й|ш₽ш1|шО Gbmbph hujduj|uniGp t, npp
2iupcti5wG дОршдргий diuu£ihl|Gbph dh?L hbnwQnpmpjni&Obpfi JOniiJ bO
шйфпфп|и. lujupGpG hLutku|uniiipo pb^npduugpujjh ф ЬЬршрЦЦшй: Рпрпр
ЬршЦшй diupdfiGCibpo шртшррО nidfi mqpbgntpjujO шш1| рЬ^прйшдЦшй
bCi: Uuul|UJjG bpb pb$npGiLigtiuj|h ^шфр ikupGGh иЬфшЦшО ^шфиЬрЬ
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pb[ ршдшрбшЦ u|pGp L ?шр<1йшЬ гфтшрЦЛшЬ сГшйшЬшЦ шрЬшйшрЬЬ[
Gpiu рЬфлрйшдЬшЬЬрр:
Jqqpmqmbq qmpmqd 7 qdfminmqQbduut} qmpmduinpqti
aqdq qmfdiudtxndmdq qmppdmZ qmqt) qmhmdiuiq qqqiu qiuldiuluta
:6t/mqdqmnjqp dmqt] qm^md
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-pdmZ qdpn|mpmd qdquiqt] qm^meliulq Uutibmnjmp 4 piuhBqbqmq Opiup
-dmZ Qbdmtimpmq qmhmfmpmh du nqfnqfn uiqh qmt]mdiu(q nqfndu IquiQU
1 dlqdmt] nmp qndhiUm diuRqmdmdiug :ddqnmp tidtnuhnudhrnp dduQi btrtj
-Ьтп|иф inqq Bqmlpdp Iqqudin dbuinp } dlqdmf] qdpdmp pmBmhqmg
:Oqiu(diuqmbmpbmd dub
члф ddqqpiupdmZ lulqduimBmd piuhdb } Bdmq ddq ‘dqqqiuldiudqddmui
ijdfmaoiudbhn Odun| qq piuqm3mam q3dp ddqbdmhmpmq dhdmtiZm>
:rjq dqpdmpmq r)qdut)Qmm(iqr)dh Odqbdmtyripmq duhjd ifridmtiZm?
:pmhdinqi] 1 bdm^mpmq dhdmNmq ?qd
qd ‘mh? qmfdiudqddmui qdfmSqiudbqn }qdu piuBdmq qmphdrmndd qm^rrt)
-duwnpqqdh qmppdmZ qfmqmn :dqddmin nqtnrn} Iqqdl 1 Uidmf] piudqbdmt)
-mpmq dhdmhZmq dqddmin OpiupdmZ dqpdmp qduqqdP BdtxJmhmpmq
pm6mhqm6 dhdmtiZmq Iqhinbo } d'ddmh ndlqddnmqpiuniu piupdmq
:dqtjdqqdo qmppdmZ qq piufiZut] Odqqqiufdiuinlmqmindm qmt]
-mhdtnmpqdmp qmpQ qdqmhi pmBmhqmB dhmqmpmp Sqp qmldiuQmdmin
aaddtl ddqqqdNmp Iqinlmqmindm qqduqdmmpqdmp JiuBqmdq qdqQn
4m ‘ddqqpiupdmZ ddqqqdpdmp Iqdbmdmliq Zd^mhin dqd' dujimdmqq fiu6
-uddp Bqudu 'dqqgiufdKJQqp qmqmtiquimpqqQt) Uudbmdiuqd dqqqiuldiudqd
-mUmq qdfmhmqmpmpmomdmin qq pxjfipiupdqq piufmt]duimpqqdh
:Odqqcimyinmtn
qmpBmdmam ddqqpiupdmZ lulqibmZuZ Bqmam ddqoqmqmbq qmteiudb
-mdmt)rj qmppdmZ ddqqqdpdmp qq piuptynZp piuqpmd mpd^rrCQddh
пнчтпапян usqn тпнп-ениеч
1ШЧи*1Ъ
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Ц|и Ьг[шйш1|пи5 РшгЦшрЦр йшрйОр ^bin ЦилцЦпр L/nnpqpljuJLnuJjqCi
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qpQtud шой^пщгийОЬрй nitibCi ЦшрЬлр ш-
oiuGiGujhiuinqnipjniG. шйЦш^и ЬО l/nnprtft-
(jujtnujjfitj hajtkuQujpqti рйтртр/тйЬд:
ЧЬЦтпршЦшй Ьрш&шЦгнй ОшиОрЦр гур»Р-
РС inwpiudnipjiuG ОЬ? inpQmd t г гииош-
Qpq-QbQinnpnQ, npg hu^QwPUt1 ИшйшЦшр-
qp О иЦдрйшЦЬшр "Циищпий” t йшибрЦрО
(ОЦ.1.1): СшрЬйшй оОршдртй гцюшЦЬп-
ЦЫцлпрр Цргий t uj&cOnhuiin ipnipntunip-
jniGGbp
г-40 (3.1)
ЪЦ.1.1 Uju iuo(iinipjni(io inuJihu t йшийрЦр
qpppp uTiupuidnipjiuO йь? дшйшйшЦр дшйЦшдшд iqiuhpG U Цп^Цшй t
i5wuGpl|p jcupdihub opbOp.
Сшрдйшй Qbpwgpnid гшгтшЦЬр-ЦЬЦиппрр dwjpwlfbinQ qAruiS t
7> ппп2шЦр упшрц|Ош(41иС| Unn. npg Цл^Цтй t гшр^шй hbmtuqtf Cum hb-
® inujqdp икиррЬрЦгий bG mpqujq/тд U Qnpwqfrt2UjpdnnJGbp: CiupchJwG mq-
qwqpb qiuiJ Цпрцдфд (ЬЩО РшршрЬршЦшй t: Up ЬшгЦшрЦр ГиийшЦшр-
qniil йшийрЦр niqqiuqpd гшрсйийо Mwpnq t шд ЬшгЦшрЦр ЬшйшЦшрцпц]
lpGb< Цпршдрд: <baKuqd^ ЬрЦшртр/тйр (щЦтй t шйдшд АшОшицшрЬ:
bpb ЛийшйшЦр / ицшИрО йшийрЦр дшОЦЬ[ t hbinujqdp A l|buinid, риЦ
iqwhpG В ЦЬттй, шщш At ЬшйшОшЦгий Gpiu иийдшд бшОшсцшрЬо l#pGp
АВ uiqbqp bpl|iupnipjniGQ (ОЦ. 1.1): UGgiud бшОшщшрЬр иЦшцир фрсф-
ЦшЦшй JbdnipjmG t Ь гшфЦли! t bpqwpmpjuuG йршЦпрйЬрпЦ: hdwGuqnq
t iqoJhpG ikuuGpqp qpp₽O inwpujdnipjwO Ob? G At ^шйшПшЦтй шОдшд AB
бшйшщшрРр, hGwpuuQnp g JpiupdbpnpbG npnafai йрш ЦЬря&шЦшО qpp-
pp, bpb hwjinGp jt гшрсЮшй hbinajqpdp: Ujq рйшилпЦ hwpiJwp ilbdni-
pjniG t (лЬршфп/итр/шй ЦЬЦтпрр йшийрф uLjqpGujqujG L QbpjGiuqiuG
qpppbpp CpwgOnq niqqnpnQujd hiuinQuidp: bpb t iqwhpti йииийрЦр qpppo
pGnipwqpi|bi t KrX риЦ t+At ицшЬрО r{t^At) гшош^рр-ЦЬ^шпрйЬрпЦ
(0Ц.1.1Х ujiquj At диийшйииЦгий йшийрЦр qpppP ipntpnlumpjniGo Црйпь
ршдрЦр 2wnwi[pq-Ubl|innpp шйпЦ
Дг - qr+dr) - X (3.2)
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dufimdp q OqwfeiiuUUiu qmlehunjuibuib pmdh qmldiutomdm dqiu rjlm 7 duui
tytf) OpiuGmbmdn pupHjBmbmdm 1 piujidbmdiuqd OQiuldiunJuibuih odfmh
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hiriQmrjmd (л-л)д л
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Xrrhn)ndMimZuZ
Qmhdmui ijdduh piuuiqh 1тфт 1 piuhpmdqb qlm nijlqqBquibp dfudb Oqiiid
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qdq Btlpiuqmpqmn (p £)) piuqinqq mt
/ фиЪифтги? !| рпфШли piuinqh ртб
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__-- -mp LnnJ ) qlm/Bqmpm QtxJmt] qi/dmam
ddumW-lAjfimumZ dqiufdiubmdn
IP o~,v
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dnjbmdm qdfmddmdqtyn rjq piuqiupdqrj buampinmhi bin :dqddmin dodt]
pmnm nqhrimdomuljqQ •Qrpulehubmdm fjd^dP piudqnmp ЬЗиф dlQb™ .rjd^
-dqq mdq pmt| ndiuti Bdnmpmbqin bln 4 QmbbZmq fjlm piudu dmpmq dn
-mpmbqui qlm dpbminqq 5 d'domddh Oqiuldiubmdm rjd&IP qlmhmn Oqmld
-lunlubmbqin qd^dP Qmdminmh dhdonmp piuhmrjmpmp dufimdp } dmnmfi
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tfmhmn :piirtxJmhmpmq qi|fminmqi|tjduuh qiulhqmUUiu ‘hmqqdo ‘Iqdbrnd
mho 1 Mlqdmh piupdmZ pmBmhqmB qhUonmp qqduBqiudbhn :6qdqqpiua
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lOhmqmUq qqTminmqdbduuh) qmhmamdqh
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8qmam ‘piudqqhmqmddZ dhmqmUq qmhmduinhqh IqqBmqmhmdil ) du^md
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ip о-a?
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ЦплрпЬйиллшЦииО ЬсийшЦшрф hwpnq pGinpnipjiudp ЦшрЬф t |шнишфЬ(
шЦЫпрр йшрЬЛхллрЦшЦшЬ qdMiupnipjniGGbphg L uintuGiui ЦЬррйшЦиЮ
lupqjruGpQ ицшрч, шЦОшоти ршйшдЬЬрпЦ: ОррОшЦ qiuiGp йшЦЬркпцрпЦ
ЛиийрЦр гшрсйийо hwpdiup t GQwpwqpbi qiiuGiujpG ЦппргфОцклшЦшО
huiikul|iupqntiJ: UnnpnpGwinGbpp ш| hwriwliwpqbpnid йшиЬрЦр b?i[iud
2tupdnii5o Цшрпп t Lupuiwbwjini|b[ piupq. qdQuup dbljGujptu&bip йшрЬйш-
ршйшдЬЬрпЦ:
Uju Lfiud ujjG t|nnpppGiuiniul|uiG ЬшйшЦшрцтй GpipwliwG l|binp Ц|>
(jb<kuinpL|LuG Giuonigbtni huiduip wGhpwcft^cn t 2шрсМшй ЦрЬЬйиялрЦш-
GwG JbdmpjniGGbpG ni uunGjnipjniGGbpG Lupimuhuijinti[ Ьшйшщиллши-
IuujG l|nnpopGiuinGbpni| L GpwGg <ЗшйшЬшЦш)рЬ wdiuGgjiutGbpnQ:
UnnpqpGujinujjnG ЬршЬшЦр tnipjniGp [nwujpujGbGp nirwuGQiniG L
pLtnujjpG QnnpnpGuuinujQujG РшЬшЦшрцЬрр рйЬшрЦтйпЦ:
I. ЛщцшЫцтЬ Ijnnfutfitiuiuiwljuili hunfailfuipq
Сшршфч-ЦЬЦклпрр L l|nnpqpGujinGbpp l|UJii|G tujucnbq трЦтй t
r lx+jy + iz (4.1)
inbupm|: U|p qbmpnui (3 1) jtupdtiujli о/тйб^Ишйшpetti₽ t
x = x(t}, y=y(t), z = z(t) (42)
uiDGpipjniGGbppG, npnGp ilfHudiuduiliu^ CiwpQujjwgOniilЬО йшийЩ) jajp-
dikuCi hbimuq^' щшрилЗЬспршЦшО спЬирпЦ Upinujpub(ni| (42) hujQiu-
uiupniiSGbppg i ецшршйЬтрр. l|uinuiGujGp htiniuqdp z - z(x,y) ЬеиЦш-
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qd rjfm ] pnjfipdm? . Iqbdmtn )f dupmdmqq rndp qmpdq c/dqrrf/pulUUm
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ddnmqpiuniu piudu •hmtrjqrunqduip VrMjmhnmy } Sinqfri fiulqnm hnifrjqnmpdiMb «hm©» ,
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piudq-^q^ dqddmin piuqmdqUqq
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4]0 ddqrjeMiuqdq ijmhmhdqmnjqp UuBmdqd piudqqqmtijqnmQduip Bqmdq
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•uimhq Bqmfpdp i|dq->q> du '} piubijhi iJdgiudbiJhn qnrtfeliunmhmdqdmdmq
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iliuHijmamdiuf qd 'Qdqqpiudmnmhmu iu qdqqdqqdo Ufm qq pjuqhqOpmu
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-тц r)ddq->q> BqqdiJ Imijminn qq Uudmh OdqqUmnubminqu piuBqmdq
mhim 'hudqddmn iulqdi|nmqpiuniu q lulqubdb diuqdq qmhmhi|qmnjqp
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-mqinfmq 3q? 9iub piudqqdhuqdq dutud pm^q mlnm 'i/dqqpiuyup Bqrrwm
'] ipmtmdmnmpmq ilpiupdm? qdq dpmfdiubmdm gmhmfmpmq ktfipdmt
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•qm qfimq aqb qqmd du 'piupmtjnmh qt cfu Ju qqd 'qqdutud nfm dqqinqq
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-qqp dqdmuimtjt] Biud qiutmu lutjdq hu!qhd> mdfr qm/diudubmaqq qfiuq
q piujHnqq ddq qdq ‘dpmfdiubbiu Km qmd dpmfdiublnu qp rulqmqq qfm
qfidqmqmtn qj bq? qiqfim Bdqbqp 'dq qqdu pqpdquip dqp hulquiqr] :ndqq
6qd6qm Uqq qduqm pmpdti piuqddqt) gqqtiqdq Jdqnkjdmq duluj :f)ud
-qqqiu/dwbbw dulud qmbult] dqddminqm ‘dqqnqint] nqtnfqq Odqqqqqljc
fiudqqqiufdiuUbiu dqddmin qqmfgqn qqfadt] qmnqinmqp Odqqt]mq buJad
dqmp nqtnJqq qd dqqtnqu di/bmZiu 'q pmqbqml] pdmZqm otimq aqb qqmgf
ndqq /ludBrjm bqrj qdugm pmpdti qdbminmq qpqimd li/dmf] am iqdmt)
Sqqmdg Odiud du 'nqfnqfm dqnjmt] ¥iub Bqbrmnnman dqqtidqhp qq pnjb
.Я q М ‘OpiupdmZ 1тфщ ф
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qdqqdqiup6iu6 qdqgflfiuBmp
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1 Uquidu budqrjinmgQtjijui/)
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:(|‘£ hO) OquifefiuliUiu rjmp
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BqBrjudu 6ddq ->q> ,x q x dqq piuquiqq OqmppdmZ dhdqnmp diuBQt,
Odnqtn qmi)mtyjmmpqtimp qfiuqqijp qmqqqiu ) dmqtn xkJqq
fuudmnmhmq lrrn/6qqdq<tQti qmfipdmt qmqQdo ddqqdqqdo rijmtyjm ttyd
qqrjmp/mtn qmtjmqdbtjn bnd 'hudqqqmplmtTi qmqmqdbqn qq qiubdqddmcn
(k/dmdd qdqqdqqdo (i)j - j qmppdmZ ijtjijqnmp piudq-^ф dqddm$
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d? knqqqiu qpdbminqq .Mnqin ghuqqdp dpmpinmhg Bqmdi) UmdmijinqM
“q hudqoqmprmfn rjmqmqdbqn dqddmui } piubdbmehuqd OpiupdmZ Imlfiin
dhdqnmp dpmpinmqq t|dq->q> dqddmui opqdijj qiutehutxndm qmqmijdbhn
dmnmhmq Oqmrefiubmdm qdBmqb dqiu dpmpinmho dbfiuinmpmumh OijiJp
-dmp Uiqt]i)O qmfdiubmdm gmhmqdbqn Bgmam dpmpuimf]O ddBmqtj :(l l§
n.qwi) fkKlqqqmpfrnfn qmhmqdbqn qmppdmZ 1 pmfinjmq Odqqdo rjmppdmZ
dqpdmp Uudmuimt) piuqqm uimbm du dqmd ‘dpmpinmhq d~>U> pnri|ihimh
uiqq dBfiunmpmamh piuhpdmZ } fiupbmuiqq qmhmludmdmhi OqdpdnH1
UuqhqO bdpmUUiu piu~>q> pmtihimh inqq i|d6mqb )?Ln?dymt, dmpmil iW
-qqUicniltJ 60dq->q> dqddmui Црю qdnqcn qfiuq Odfiuqdq qmqm0dOn,nltK’
qddd Qqiuldiuqmdmqhqp lmn)n Imfquiqu 1 piuhdui nlmpmy OqmfdnjtJub
-mdmnmhmq ddq->q> q&|p Bqmdq mq himf] ?q*d mhnm ‘?u qdq hq :Odqq
-dqiuflidm qmWiudqnmqpiuniu Bqmdq qq p.iuqhqOpmq dufbdn epdqqhfrt
-qqnmpdmji «6md» dOq->q> dqddmui qq piuddnmqpiumu qdu tpmbtnqn }
<h<4ipp hbinmqninnqGbpo ЦшлшОшЬ гшр^йшО opbbpObpG nt ПшЦшиш-
pniiJGbpQ гфшОр прпгшЦр ЦшицЬр ЬО hwdoJiqwinujuftjujG <h<-p тшрш-
дшдид5ш0ш1|шф(| L|nnpppGuJinGbpp Ь CipiuGg дил5шЬшЦш|рО wdiuOgjun-
Gbpp dfrgb
К-гнй )=О, (123)
K’-nui )=О;
(12.4)
h*[Q Цшиц Цш luju фгиОЦдрпОид lunGjnipjniOGbpp (Jpjk
РОшЦшО ( К L К' <ГЧ -Ьрр (12.1) U (12.2) qnnpppGwinGbpp йЬ?й
щЬтр t qnjmpjniG niGbGiuG прпгшЦр l|iuu|bp
x = x(x',y',z'.f'),
y=y(x',y',2'J'),
x'=x'(x, у, z,f),
y' = y'(x,y,z,t),
z=z(x',.v',z',/')
t=t(x,,y',z',t')
z' = z'(x,y,zjY
►
t'=l'(x,y,z,t)
(12.5)
(12.6)
,K'^K:
UpiuGp UnjQnid bG 1ЛшпшдшЛийшйшЦш/)С1 QnnpppCiujmCibpp dhiu-
фп/ипщтййЬр. npnGg piugiuhiujin inbupg biupbip t uintuGiui dpwjG inuj-
piudnipjiuG b dwikuGujMh i|bpijupbpjiui npn^wQp щидлЦЬршдтйЬЬрр hh-
OiuG 4pui: Uq щштЦЬршдтйЬЬро дкшЦпрЦтй bG Gnppg фпрйрд uiniug-
Qnq inQjuJiGbph hpdujG Црш b 5>hqhGiujniil mGbG ЦшрЬлр G2UjGuul|nipjruG:
<iupwpbpiul|ujGnipjujG utiqpniGpp щйдтй t, np libfuujC^Liiujti hu/Quj-
ишртйШзрй nt opbQpbbpp щЬтр t Цп^шрршСнл ifiObO (12.5), (12.6) dhw-
ipnlump/niQQbpp ОЬиллйшйр. LUjUpGpG тЬршпрЦпЦ K-p (123) opbGpoiil
dUajipnlunipjujG (12.5) pwGwflLbpo, iqbirp t uinwGwGp K'-fr (12.4) ziupd-
i)iuG opbGpo l|wd huiQuJUiupnidQ L оОпРшЦшпшЦр (12.6) fiUupnlunipjruG-
Gbpg (12.4) ЬшЦшишрйшйр iqbinp t pbpbG (123) inbuppG: Ujq u|Win&ui?ni|
(12.5Ю ЦгцЦгнй t К - К', риЦ (12.6)-o К' —• К wGgikuG йкшфп|итр)ш6
pujGujfllJbp:
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GpuuGp ppiuppg флшррЬрЦЬО 2wp<NwD ul|qpbuJl|UjO iqtujdiuGGbpnQ: BpC
2tupdi5ujG uGqpGtuliiuG iqwjdwGGbppg ujGL|uj|u opbGpGbp bG. pGjiqpupp bG
2iupdiku0 hujQiuuujpntdGbpQ. шщш GpuuGp qiniuppbpi|bG tipwjG GpwGnQ.
np йЬЦр ЦшрслшГхцспЦр 2шрр|иЦшд. риЦ iljniup ^PbMwd Цппргф-
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-qO dgmdtj gfmhmn :lqbqq>mqmd qq? giuinmq hnQqfiuq q «Qlmqmhnmq qQ]
-dqQ» qq Iqhdmpmq du ‘qmt]mdu|iun gmdgfm qq IqUq Odqqpiu6mdqf)uwnh
rtfm Imfdqdmdqh qmfeiiuhmpdm6md Uhmqmpmp q qmfefiuqmdms
(ГЕ1)
;piupmqmZq DqiuldiupmpdmSfndL/hmijmpmp mhim
qddqqmhi *j q Ц piu-.x hN ‘qddqumhn 4 q 4 Qhmqmpmp qq 1qqmn|nmui
-mhnmpmq рю-х Duidmhm iu qdbdhn ddu 'nqfiudtn 1 Iqbubdb qeiq
(1П) '
nqhinim
itfnnfmqmuidmt] qqdutidinmpqdmp
OqKifdnjt]mpdm6md qmfdiupmdmin
‘dmdmquiq> :(rc h1)) Э qqiufdiud
-qddmin ddqqduinhqb-UflimamZ
ddqinqhmdfmQ mdq Oqiufehudmqdq
ЦЪир |qd(j dpmfdiubmdm n dpmp
чптГу) Ц-x | piuhpdmZ OtxJmh
-mpmu QhdmhZmu diuBQb
.piudqbdmhmpmq QhdmbZmy
dqddmui OlqqQI DqhugqQp qrrtfehuUuqin QdqqnqBudtn OqiuldiuhmQdmBmd
qqmqmpmp Г]™4 ‘(Ц^рфт? qQlmqb Qqpdmp | qqfiuq du pm^) qmfdiudub
-maqu qdQp Qdquiqh iul]dq |qdu 1 piudbmelqq OqiuWiuqmpdmbmd qmfdiuQ
-mdmg :i]piu6mdqhinmhi !jmTdiut]mpdm6md dhmr)mPmP 4 omfdiupmdmu)
qq Iqduhmqp OdqpduQi Uudqdmdqb qQdqqpiupdm? UmUqmti i|dqqqi|pdmp
qqhlUb|nudtimf| nhjiMiatimydmdmd tftimqmjimp q qmfthaifmdms "1
□JQ'Y’VW&eHUniUOnhQC 49Ч*1‘ППЪ Tl§
:dpmpmmhq ddQOnjfdiurdudvnqp (9 z/> '(SZ 1)^00
inmqd^duut) qqQdl tngmddmtnd] ddqqpiudmnmpmq hj rjdqrjdrjqdo i/mt]
•dgmnjqp du piuSqmqmfn Odqiudbhn gmWiuqmhmdqdmdmu ‘qpqdij
:dmpmpcnmt]q ddqqp^fdiurdudvnqp
qq Lnqmddmfiqd OdqQpKidmnmpmq du qq piunm mtnm tJdqqpiudmnmhmq
piuqbud qq njuipuipqm ddqqqiufdHjrduipmqp ddqqtnmqddduup qdq
(миЦ, 0Ц1пЦЬ[пЦ Gl|.3.2-nid щцллЦЬрЦшд ЦЫцллршЦшО boiuGluniGGbppg,
L|iupnq bGp qpb[
Г|»гв+<, r = 'b+rj« (,3J)
npinbq r9 -G К L К ЬшйшЦшрдЬрр ut|qpGajqbinbpp ЬшршрЬршЦшй qpppg
pGnipujqpnq гшошЦрр-ЦЬЦтпрО t: UinwgUwd uioGinipfxGGbpG рршррд
hiuObinQ, L|uimiOujQ₽ iniupwdnipjiuG ptugnip6wl|nip)UjG (13.1) щшдЗшЬр:
StupiudnipjujCi U (huiJujbujQp ршдшрдиЛ/гнр/шЬ ш/и ^шрсирршйртй
JbOp fitip щшЬшЬрЬ) ГнигЦшрЦ К L К' hiudtul/ujpqbpp pObpgpiuimpjnibp.
U/O № t hLUjL/ujpqp дшЫридшд htudiuQujpqbpp huriujp npnbp рршр
ЬС/илпЬсийр pup&L/ntd bb inijupg jwin фпрр ujpujqntp/nbbbpnip
2. Чиц/цк]/] ЛЬшфп[итр}П1ЬЬкрр: Ujdd одшЦЦлЦ inwpujdnipjuiG ni
dunJwGwljp pwgujpdwUnipjniCihg. итиЛлиОр дЬил/infuntp/iub (V2.5), (12.6)
ршЬшдЬЬрр ршдшЬш/т Lnbupp Cijniinnbflub йЬ[ишЬр1/ш/П1й: '’Iwjikubm-
ЦлрЦЬОр bpl|ni ИшйшЦшрдЬрпи)
dujiiuLiGuLilip uQhqp hiut)upb( ujjG
iqujhQ. bpp К U K- h ИшршрЬрш-
ЦшО гшрдйшО (iGpujgpnii) Оршйд О
Q О’ иЩрОшЦЬитЬрр hwdQGpbntd
b£i. х - х‘» О, bpp t /’ -О. dwiJujfku-
Цр pwguipduj^nipjujG (13.2) iqwjdui-
Gpg wjq qbiqpnti) l(p|uh. np hbuw-
quj pnpp iqiuhbppG К L K' hwiku-
Ijujpqtjph ctwdiugnijgGbpp QmGb-
(13.4)
(fiudiubujltfi pbpwgpQ МшспЬишЦ t huu^Qiupl/i pp/np Ьил)ш(/шрдЬртй
Ujcft) npn^bGp K' -at) wOjwpd A pujGnGp bp^upnipjniGo Цшйш)шЦшО
t • t' iqiuhfiG: K' -nil) ujjG aiwpquJUjbu r‘ t |mjQ К -пи) r - rv (Gl|. 3.3): Oqin-
Qbbp iniupLuOnipjiuO piugiupdwliripjniGpg
r-re = r', 1|uji) r=r0+r': (13.5)
₽ujGb np r0 -G K' -p inbquflpnftjnipjniGG 11 (huikuGiulpid, шицш r0 ” ut:
Qbpgpbpu U (13.4) -p hu^QwntoJiJp (13.5) -Q liDGqniGp hbinLjwi inbupQ
r = «/' + r’: (13.6)
62
(13.6) L (I3.4J (риицЬрр мшршди&шйшЬш1)ифЬ 1)ппрг)/)йш1ЛйЬрр биилрп-
(итр/шйршйшдЬЬрй Ьй (ijnicnnCifujCi йЬ^ишйрЦицтй^ Цп^Цгнй bG Qcuipitjjp
iUm/mfunipjnt ййЬр
niqqiuGQjniG ЦппррЬОидлшЦшО ЬшйшЦсирцли) (ОЦ.3.3) Quqhibjp
aUuipn|unippiGGbpG niGbG hbinGjiui inbupo
x=x' + w/',y«y, z =z'j-t'i K-+K\ (13.7)
fiuU ЬшЦшршрй aidDipn|unipjniGGbpo
x'^x-ut',y'-y, z' =z,t'*r, K'-^K: (13.7*)
LlpjinbGp, np fiUuipnfunipjuiG t bGpujpliQnid dpuj)G К L K' huiikul|uip-
qbpfi ЬшршрЬршЦшО zujpctiSujO niqqnipjwdp ЛшиОрЦр ЦппррЬОшто (bp-
ЦщОшЦшО IjnnpqpGuJin): CwpttowGG niqqwhiujug GnpqpGunnObpo (iwj-
йшЦшО GnnpqpGuJinGbp) dlduQinfunipjiuG jbG ЬОршрЦЦгнй;
ИдшйдЦпЦ (13.6)—G gum ЛийшйшЦЬ. ЬшгФ шг?йЬ(пЦ (13.4)-q, Цшпш-
(jiuQp
v^v' + u, (13.8)
(13.9)
(1310)
Цшй
V, = v’ + U,, s vj» V, = Vj.
npinbq
dr , dr'
v=—, v =—,
dt di'
duiuGhMb lupajqnipjniGGtpG bG hajdwiqiuinijuuhJUjGiupiup К U K‘ hwdw-
'+unqbnni.d: UinajgQiud (13.9) ршОшдкЬ Lupinuuhwjinnid t шршргир]гиОйЬ-
It dbljtnnpu/QwCi qnidiupdujQ L/wCmOp про Gbpl|UijwgGnii) t wpiuqnipjntG-
Qbph iGuJifinfunLpjniGo GjniinnGjwG i)b|uiuGhUwjnii]: UdujGgbinQ (I3.6)-G
Quin ftuikuGuilip bplipnpq wGquii], (jniGbGiuGp
(13.11)
dt
вшйЬ np К G К' ЬилЗшЦшрдЬро hGfcngfM bG, шицш u= const, npfi ^GnphhQ
a = a', (13.12)
npjibq
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itouG Qbl|innpujl|iuG (13.9) ЦшОпОр'
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Av = Vj - v2 = v{ - vj - Av':
ClipbdG
Av=Av', (13.13)
tujupGpG' hwpiupbpiul|wG шрих}шр]П1Бр dpLGntjGG t pn(np «-bpntd:
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m — = F(l^r,^v)‘, (13.14)
m — = F'(Ar',Av'); (13.15)
dt '
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^iqnmp mufp ddpnjmpmq 1 Iqjidnunmh mb mhim Iqpm Dnliuhipd piunmp
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fd bddl ddpnjmpmq du ‘nqhnqfm qq piu|idminmb DdqqgluWlunJuфuф nlm
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bG dttmipfiudp. bpb diuuGpqGbpp qojGqqwdGbpp hmdwpbGp iu(il|tufu ОршОд jujfW-
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шриЛадпф: U,uinbqhg htanLntd t, np K. -fi Y LunwGqpnq hdtqnipt щшРсцшШ^
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llpGnmGh hbinLjiq inbupo
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ЗшйдЦшдЬ ОйрГивйршдйшйр испшдЦпц йший^ЦОЬп^
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106
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dqqp dqddmui qmidiuBqbbmnjudi hqmmhiqnqb dgqqdmqqa
Odqqqiufeiiunluqimqp *s - ‘s .,« dfqiqimt) hulqqum
iftiZmn piu- (g 83) dqhbupmyh piuqmdv : ' = У qq qqfiuq Odqqdqmui
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(883) =
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qpiu qmpQiZ Uutibm md|i mdq dmdmquiq> q pdmZqm qhmuirqmin piu
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rjliutxnlqfimam ddmlimU du Iqhui qq 6hu6 Ddqpduifi pmbdminmh fidpbuh
dquliuh (d'miz f hq) 6dQiu(diupqp dpiu uj > j rjdammdm pmhn|mh Sqp
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°j 1 p»uo6mrmhdqf] Ohd<tmdb piudhfiqU o= л :Orpu(diUQmhnjmh ijmhmdbnd
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Bdrjiufdiubmdm л ijiundu? q pmbn|mh
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lubmdm л hudfiiF|dqhmp dQmUqn q piuqmn rpundu? drqqdUmdqq ppfp
ipiudminmh d? aominmnjZm gpiu дтрф? ddmtimU
du 'rymhmn ‘dijquimhQ tfijqdo фшлрирп) Oqiuom mdrjq piudhh (e*669l)
ilrjuuiQupn lq6muin rjqdurjmhmqpdiKb Dr)iufdiu?gam (OI 8Z) ЗДт?
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mom ddmdmb q piuh?uh ‘hudhuqdqhmp dqmUqn Odqmn diundu? q piufinhn
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nd. npp GnqGiqbu ujpqbpuQnu) t dwpi)G|i гшрдтйр Lfbd tupmqnipjiuiJp
гшрсЩг»! ikupdGp Qpiu dhjwQiujpb qpiJiuQpnLpjujG nidp Qiupnq t pQwiqbu
цЮЬшйЬйцдл qbpwqiubgbi i)ujdnighl|nipjiuG mdpG: ФпрйЬшЦиЖ 6uuGw-
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t wpwqntpjniGGbpp OA dpgujQiUjpniil
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mUqcn q 5qp qmfeliu?qam (16Z) Uuinfmqmtndm qpqduqd qfmqbdqgl hdinqq
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uit/qL/fqilq piub?uh OpiupdmZ Qmpq dhdOnmD «днЛ
diuddqbgm» piugb q } piugamdmdqb ‘gdmqh gmpddZ 3 bulqgnmd mfrim
n|mp dtnqtj 1 piubpdmZ q piuetfiudQui м } piubgmb Ohdgnmp qdq
qq qdqqpiuQiulqmpdmnmhmq fxjfj.3ddqtnqq
tjmpidQ dqtnqq qmp&J? gq piub?uh Odquiqh 3 ‘g ‘V :mq IqbpdmZ 1 piunhn
Otnlgnmp mfnm ‘piu pmbbbiu ginqh w d^qti } piubbm mdb mdg piuin
qh trfm du i|gmj :piugam } bgmh gfm piumqh 8 h ‘(piupm rjmutbdqgq 1mi|6
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'Oinqh hi) piuhmuimq dduq Imdegqinuu, :piupm Ohdinqgdh hN ') piubmbo
imdbdqgi lmi|6Qqinuln dhdgnmp ‘dm bulqbpdmQ Ьивбдтат x 1 pmb
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°XQ Imdegquiuhr) 77 7 pmbmpo OhdO™np piumqh a ‘hmgi|do budqggiuld
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effiuqdq Qambqmp } piu|i?uh гтц_, :hupiu qmpqtf QdmbmL piuqmdq
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} budmh Qhdonmfi dqddmin OqmpiJh piudhiqb Qdqpiu qmpQi? due
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:(piu- W fr'hO iXnqhN)
qq qdqinqh QpiupQnamp QlmQtxJqq, ImQBqqinuhn OdqddQtJ qmfehuuZhmdmn
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nQlqdqt 6ddu Oddc/b qfm qmfehua^mdmnmpmq piufifut) ) Qiufmqqn
:dqqpiuqminmin Qdminmhh OqQpdmp nQlqliqZ eqaUQb nfn :(pw
Wt hO Oinqh M) Odqinqh Uuqmn|nminmhimpmy oQpiupQqdp qfmqbdqq?
1mi|6qqtnuhi piuinZmtimpiu qq piudmdmhmd qi|qmp(mhn riyy^iu paifibUnj
qddQh QmfdiuaZqmdmnmpmq qtnqti) piuqmimum piu&hnqti ijmpbq? Миф
idq/irjm dhdqnmp BQdu Offddh rj(m qmfdiuatpmdmnmpmq ) tpulmt)
. dqddmuiqm q q njfmpqm q lufmp ) p iuqd/ dq iuteiuutymdmnrr>fvri>
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piu6qnxJi]
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-bm Q? piu mdb Qhdqnmp piuBqudu ’Odqunqh qfm qinZmtimpnj :hmqmpmp
dmhdq nqnm qmddu mqph piuadQti tifm q piuinqh Wjf UuqmrQnminmhimpmq
qqpiupdqdp Qduq lmQ6qqinuhi Qqamh bqmh tlhdOnmr> :iJdb mqumUh uidqh
q hulqbmhq Odhuqfml qdqqpiuqmtnmin Qhqqnmp Uuhpdm? piurfiudqm ll
mhim ‘OpiuQi? Qdmtimb } piutmhmBmd piudtnqti qmpQiZ 6md du Qqma
dpmWiueqtibm qdqpiu qmpQi? du? q 6m«J 1 piuh
innipjniGQ: Ujn Giqiuinuul|ni( oqinQbGp пЩиклЬЦЬишшЦшО qiuGqQiudh
m(v) = m/ v2/c2 (312)
ptuGiuflLhg: SbqwqptHnQ ujjuinbq v= p/m(v) L ptupdpiugGb(nq piuptuqm-
ufi, qumiuGujGp
p1 + m>cl = m2(v)c2: (313)
ПрфЬрЬОд^пЦ ujju iupuuuhiujuinip)niG[], ЬшгФ шпЩпЦ, np m
htuGquinp qiuGqqudQ hwuinwirniG JbdnipjniG t, GniGbGuuGp.
pdp = m(v)c'dm(y).
nph <5ш|и duiunid p - m(v)v wnGjntpjiiiG huizMuroniiiQ l|inw
vdp = cldm(y): (31.4)
Jjntu linqrihg, uuzfuiuinLuGpb piuGuudLfig niGbGp.
A = (Fdr = vdt = fvfljp, (31.5)
। \ dt ।
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dt
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U2fuujiniLiG₽b hwOuup ишшдЦшд (31.5) piuGiudlp 6h2^n t r)iu-
ишЦшО, lujGiqbu Ц nbiwmbQbuinujl|iuG dbftjiuGhl|uJjni.il LljG IxujQbini hui-
tkup iuGhpwdb2ir t niGbGiui tupiuqnipjLuG L hjL4nLL|Jh Цши|0‘ ПЬршлЬфн
inwl|UiG ObtuwGhllUJjniiJ (31.5) hOinbqpuJinuJ (31.4) ршОшй(ф hiu2<|uJDnnJ[!
qmui.
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qwG L Qbp2Gujl|UjG ЦИЙшЦЬЬргш! DipbOG, о^шспЩриспшЦшй Obfuuilft-
l/ujjnid ntdft Цштшри/д ш^шспшОрр npnfQntd t dpujjCi U lifnujb OujuW
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niuquinb UJuScuLihQ, unqui wu|iu ОгшйшЦЬ[пЦ ЦЬр^ОшЦшО wpw-
qnipjmGo v, (31.7) iu2|uujinujGpb huuihup qniGbGwGp.
Л = m(v)c2-me2 =/^(v)-K(O), (314
qiuinmtnnmq rjq piuhdqddmin Bi/dmdi/ qdqqm/bdqqq tpjuiqqtfi] q qmt)
muvuttHjinmlqa dhdnnmp du dqmg
:Bddqf)<]ml
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Qdqqqiufehubmdm cnup qQnftul ] qmijnq
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ФП1ииЧЬГПШ1иЪЬГ
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ршд GpnqGbGp).
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c^yjy-v^/c2 Jl-yffc2
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(he) чтоз=’п^)1~ и
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W piughgOpmq inqdbZ? Odqgpmgmd (£ Z£) dfmdbdqg} g qnhutnpQ hQdl
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г)ШРП qwDqQwd: Ujq щштйшапЦ К <b<-nid hiuiliu|udpp (ррЦ pdiqnquQ
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I] - v2 /с2 fi-v* !c2
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= - Hlc2, (32.13)
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(й^ПкЦр piujpujjb(ni Ршйшр ujGhpiudt^in GQmqiuqnijG uj2|uwinujGp(i).
AE = Am c2 = -H : (32.14)
(JTigniLiti Цапф (Gbpqfiujjti L quuGqQujdh qb$bl|inh db?b uiju wnGgitp-
jniGQ, npp qujGqQiudh L tGfapqtiujjh (31.10) QGqhujGnip 1цииф OujuGwQnp
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-ifomnjqp i]mt]muinqhi)uimlqd I) nqtngfm •qmfrjuuwrrj nqhi?qi| ‘rjpqdiQ
(6Г6Е)
dr)mq
•muinl) 0- (tret) bulqrjom qjiZmq q 0г)1и1«Ьип|ифиф qfmqtxJqq)
hi|dl qdqrjqqqnmp piutxJmhmpmq v uinqq q imam 6qpiun|md bulqfiZrri)
qijiJqqdo rjmpqmfnqmhi i|(mi|txJqr)) ) piuqmnjnmuimhimpmq r)i|huijl Odu
(8Г6Е) tq II II J t J %
arjmqqrjiut) dmpmq ijfmi|bdqq) dhUonmp piu- v mnqq 6<JpiuR|mo
•.dpmfibrjmb j/drjmtjmuTntfH^mlqa dqpdmpmn
rfLfimJbdQq) rpjfmpdqd pmdbmlqfim rjddmpiub ddpfjpmlibrjmb d^nbqm^
ddQtjhdfjnmp imam Bdpiunjmd J dmnm/imy dpm/ibqmb dcnnbqmq
•nmpртбтбтат umqq6<Jp)un/ma *z *.ш piuahnqlj omh)minni|hi|inm)qa
*} ЬфлЦЬт орпфЬртЬ piudu tjahiqb qmfguuiiufq qiuldiudqddmui q
(1Г6Е) : гэ/д + шг = £э/у dqmqrrHnnh ‘Odqr)
-nliuhnpd (91 6C)q (tl 6E) MiA ddqqhqqnmp ixnqq q dmom ajpiunjmd buhO
-Oqdmnmtimq q 6i|aqqdo qmpqmtnqmln Qnhu(npi| i|dpn|mpmq hulqfiuibo
7 qpmfibqmb i|dmUmli qtjqqnmp ртбтдтат й- ,ш bquidu ‘fiunliuhipil
(9Г6Е) г 1 = d л,ш • 1||]Ц1(] pmfiuipo q rpufehubmdm л mg
-qqiut] piubdmlynpmq v OhQonmp pmBmdmum dur) uinqq &Jpiun|md
(5Г6Е) X +1~ 3
(»l 6£) z9/zA-^ _ dqmqqrpuh dmpmq i|fmijbdqn) q ЦпЬиИтрЦ fiijdl
ipOntd qnpd nt&bGiq 6wuGpl|Gbpp рщ.
Pt a X A> _ дшрбшЦ nt шошддшЦшС pwfudwC
"* * * * ПшЦшпшрй щрпдЬир hbin Пш OuXip
Ы| 6 2 6p?nil)p pbpOtuQwi) inpnhntJb t ЬрЦт
i)p?ntl|Gbpp 'Зрдтр Л РшйшЦшрдп1й
ршПШПР Црйш1г*й qinOUnq m ршйрЦшбпЦ йшийрЦр mpnhqb( ( и, Ln. ЬшЬрццф
диКкЩшМЬрпЦ рЬЦпрОЬрр (ЬЦ 62) ₽w(ip np шрпЬЦЦр pi5u|ni|uc bqb( t qpn
шщш lumujwgwd рЬЦпрОЬрр ЦшОЫний dbdmpjujJp ПшЦсиишр U (хиЦиюиЛ| mqq.
Quid pt)mnt|u(ibp
Pi " ~P< Pi • Pj 3 P- (39 20)
OiuuinnpbG. inqjm qbmpnid (шрпрцдлпр РшйшЦш[Чр С ПшйиЛдирц t (Gbp-
qpmjp ujujhutuiWujG opfabpp спицри t
me’ « E. ♦ £„ (3921)
E’ = m3cl <• A’c‘; e; = m3c* + p\c' (3922)
4шгЦр шрОЬ|Ш| (39.2O)-q. (39 22) -pg ЦолшйшСр
£;’ - mfc* - E,1 - nic* * p3^ ’ (3923)
UinwgQmd (39.21) L (39.23) wtrtijmpiniUGfappg Цпрп^ЬОр рЬЦпрЬЬрр t CibpqpuulibpQ
_ > m,1 - m3 t m3 + m3, - m3 ,. (3924l
2m ' 1 2m
риЦ (39.23)-pg рйщпциЬЬрр
₽шйр np (39.22l-pg E, > m(c*. E2 • m<’. ишци (392lbpg hbmbntd t. np dpjm-
l|p рйрОшОшй inpnhntip Ылири^пр t. bpb Ьрш hwl/qucnp quAqtjujdQ йЫ t pbl/p-
bbpf hiuOquinp quibqQuMbpp цгчйшррд m > m, + mj: ОдитЦЦпЦ E » mcJ + К
pmGwdLpg. йимЛр^йЬрр hwtiqunp qiuGqQiDdGfanp йррЬ ЦилиЖшйр (39.17) -Wi
РилЗиЛйшй Цили m = пр ♦ m2 *K/c2. npinbq К -(i рЬЦпрЫзрр |ррЦ ЦрйЬшрЦ ((Лр-
qpujGt
§40. ризигаич ипиа^ичиъ риюти
Ujuu|bu Ьй Цп^Цгнй ЬрЦт йшибрЦЫзрр ilpfL pw|uniiJGbpo. прпйд рЬ-
ршдртй йЬрр№ гфиГпцилпМ nidtp }Ьй штиршйпй ChpbiJCi. luju рш-
lunidCibnh ОшйшйшЦ ajwhujUJGQrnij t nj й1иийЬЦ0Ьр|з inhU
uq. ujji U ipfH] IfiObinM tlibpqtnuCi
Swppbpqnid bG JuJuGhl|Gbpb ршдшп<5ш1| шг?ш<5цш1|шй ЛшЦилпифЬ
L ry pw|unu5Gbp: РООшпЦЬОр i5uuuGhl|Gbr»h ршригийо Ouj!l
GjntinnGjuiG йЬ|ишйЬЬш)П1й:
1. PuiguipAiul] umuiAquiljuib Siul^uiuiiujfibpw/uniif:\Jtll ЬрЦт dlUllOhl'
Qbnh ujjG ptufunidG t. bpp рш|итйрд wniu? к hbinn йшикрЦОЬрр гшр^Цпц]
bG nr/?7/7bpl|wjGpnQ
n|iinujpqbGp Л <h<-niiJ m, к m: qu>GqquidQbpni| йшикрЦОЬр. npnGp
pwluntdpg шпш? гшрбЦгай bG v, к v, luptuqnipjniGGbpnq: Прп^Ькр 6ш1|ш-
inwjhG pw|unidpg hbinn GpiuGg lupmqnipjniGGbpQ:
luGppp jnidnidp twiqbu iqujpqbgqniiJ t, bpp oqinqnid bGp C hwiku-
Gwpqpg. npnu) dajuGpqGbpp рш- m.
lundpg turnup L hbinn nibbb tib- •---—-----► ~<
tmtMudp ЬшЦшишп L htuQtuniuQ
пимЦшд №и/пцибЬр (Ы4.6.3). л Р: • Pt' г
А=-^;А' = -Рг Lq.e.3
*• (40.1)
Uju pi)iqnt[uGbpp ObdnipjniGObpb йр?к Цилцр uimukwtni hujJtup oq-
inqtGp qpGbinpq tGbpqpiuip щшРщшкйшО uiujjdwGpg
2m, 2тг 2m, 2m3
(40.2)
npQ. (40 I) ИшгМшпОшйр l|uuu
a* ->2
k^P-.P-
1ц
(403)
Ujuinbqpg uiniuGrxd bGp
A = Pzs P= Я = Pze p'> (40.4)
U/upGpG. C hwdujqiupqnid ikuuOpGGbpp pOiqnquGbpp ObdnipjniGGbpo
1ЬЬфп|иЦп1й, iJpujjG фп|иЦпи5 bG GpiuGg ninqmpjniGGbpc (Gl|. 63).
p' = -A; p2 = -рг‘ (403)
Pwjg ршйр np
A P', = m,(/ = I; 2), (40.6)
шц|ш C hiudijuGiupqnii) (40 5) iunGj>nipjniGGbpp 6h2in bG Guik uipiuqntpjniG-
(ibpti hiudiup
Y'l*-»»; (40.7)
UjdiJ liujpbih t wOgGb[ ЬшгЦшрЦр л hiuOujl|iJupqpG к npn^fai puj|umOpg
hbinn dajuGpl|Gbpp LupujqnipjniGGbpp
< = * + = К -(*’.-»’J=2v -v,,
v; = vr+v; = v,-v; = v-(vI-v,)=2vi -v,,
npinfaq oquii(bghGp A-hg C, U ЬшЦшпшЦ LuGgriuiG ujpujqnipjniOGbph <JGw.
ipnfuOuuG l|iuGnGpg G(40 7)iuoG}nipjniGGbppg flipbiJG
ту. *лг(2у,-к)
v,’ = 2v - v, = ——---(40.8)
mt + m,
_ m,v, + m.(2v. -*1) ...
< = 2v - y. = ——-----Li—1----U, (40.9)
m, ♦ m2
npnGp L inuj|hu bG |uGqpfi tni<yni.i5p ишшдЦшбрд йшиОшЦпршщЬи
hbunbnul t, np bpb трчк}. шщш »2'" v, b < - vj. lUjufiGpG hujQujutup qcubq
Цшд-ЬЬрпс/ bujubpL/bbpp АшЦинлш/рЬ pwfuihub ЛийшйшС) i/mfuujbuibnul
bb pptjbg шршдтр/тЬЬЬрр ^^. орЬОшЦ, pwfunidfa wmu? ikuuGhl|(i bqb(
t qwqiijpb ЦЬЛшЦтй, опции puj|unii5hg htinn ЬшрЦшдпр OiuuGhbo GiuOq
GujoGh. hut) djniuo bzojpdiJh huupi|ujdnq OwuGhbh mpiuqnipjUJiJp
Qfcppnid GbuuinbGp htjinbjW) hb^ir hhzbnq ujr?b)nipjnibQ
v, + v', = Fj+v'2 = 2v€,
(40.10)
npG итшдЦпи! t (40 8) L (40 9) [nidnidGbphg'
2 PtuguipAuil] umuiAquiljuib nj Swlpuuiwjfib puifuntif. UniuGg uuihOw-
Gw4xul|b[ni |uGqph oGnhajGpnipjrKGo. nhuxupbbGp lujG nbiqpp. bpp pu>
luntiJhg wmu? m2 qwGqbiudnQ ikuuGhQG wGzwpc) t Ow dhjui bwpb(h t Uu>
iniupb(, nhiniupbbinb piufudiuG LLipngbup ptufuniObg ujoui? m> qwGqt|wdn(
ikuuGhbh tuptuqntpjLudp ;ujpdi|nr| Ьш?1|шрЦЬ hcuduibtupqnid:
ЪЦ.64ш Lb.6.4p
'Ihgnip л hwdiubujpqnuJ m, qwbqi[ujdnQ bmubpbP v, ajpuiqnifijuril
pcufUL/bi t ujbjujpctrm qujbqLliudnil btuubpltfib (Gb.6.4uj) Прп^ЬЬр шу] йил>
bpL/bbpp ЬОшрш^пр tibLqntiubbpp piufuni йрд hbinn
niuniiJGujuhpnipjniGG uliubGp C hujiJuubujpqhg, npntil bfiQni iJunjOhV
(ibpo piufunidpg uiouj2 G hbinn niGbG dbdnipjujdp hwQwuujp G ИтЦшошЬ
пщпЦшд hduinquCibri (Ql|6.4p) Pujgp ujjq. hwdwdiujG L|pGbinpq tGbpqpwjp
щшНщшООшО. C hiudwl|ujpqnuJ hiitqnquGbpp dbdnipjniGGbpo OGnid bG
швфП1рп(и
P= P- (40.11)
UGqpOwQujG гшрдйшй niqqntpjniGGbpbg OiuuGhqGbph ^bqduuG 0, G 6,
wGQjniGGbpo (Gq.6.4uj) ЦшЩшд bG diuuGpqGbpb iMuujqnbgrupjujG QnGli
pbm mwjdwGGbppg (hwinqwiqbu. Огшйиши^О b hbpmQnpnipjniGbQ)
OprvbGp pwlumJpg hbinn dwuGhqObph ЬйщпциОЬро Л ЬшйшЦшрдпи)
Lnppg oqinqbinq С— Л шОдйшО wpiuqntpjniGGbph OGwibnhjnipjwG ЬшОп-
Gpg. UuinujGujGp'
P' ~ m.v> = w,(* + $') = -г Д', (40. ]2)
P: = mzv': = «:(». + i’j) = m:v + p', (40.13)
nfitnbq, pwG|i np v2 = 0
апп5шрЬ|пЦ (40 12), (40 13уф дш|и L luj ОшиЬро G hiujQb iur?Gb(ni| C
nwdiuqupqmi) [phi| ЬОирциГ) qpn фОЬ(т imujjOujGq, quimuGioGp
A + /»: = (m, + m2)vi = mv, = pt, (40.15)
про ibnqhG Ьшйши|Ш1Лши|иш0п1й t ЬйсцпциЬ opbGppG
ОцшЦЬ[пЦ ишшдЦшд шой^тррсОйЬгфд, ЦшрЬф t l|wi?nigb( uijuiqbu Цп^-
Quid, MajmiuGbnti QbQumpiuQujli гфшдршйр({Л\. 6.5X
PwAuGbGpp, ЦЬЦшпро W/v„ w?v. duiubpb bwihudiujG (40.15) uif?G)ni-
PUJb: OOtnpbGp LjwiJujjwqiuG 9 tuGluniG G uxuGb[m| O^btnpg д' = _ д До-
щпцийЬро. hwdujdiujG (40 12), (40.13) pajGiuOGbph Uwonigblipp,' G/ъ ЦЬЬ
innpGbpc AO G OB niqqnpqi[iud htuin-
4u*6Gbph inbupnij: QGq npnid GlfwinbOp.
np wGQwfu «9-p lupdbpfig OD = OB;
МжцЬи, hujdujdujjG (40.11) G(39.6)-h.
OD = p' = p = ^|Vi _V,| = /A., (40.16)
Bw«i np nhmujpqqnq qbiqpnid v>j = 0,
1ШЦ
A
VU 6 5
5mfmqrnUUiu ,qdqi|n(m ipultyjm м rjq piupbmt] inZift Odqijnliutnpil uinqq
Jxjpiunjmd qillminmhm? ?u i|dqqbi|nnmp hudqqpmbbqmb dmnmhm>
(6l0f) •*>'б’>0
0-o061 piubqmbmdqb inZqp Oqiulhqm ff pmpbmt) qdi|p i|dqqnliutn
pd ddqqr|i|qnmp qdqel iu dqmp uinqq Bdpiurdmd piudu UqC hudqqqiufriqm
dubmdmqq du kid к}п)иф} Uudmt] OqiuldiuUUiu qmppdmZ dt| qhQqnmp qdqd
mjlqhnlmd inqq i|hi|qnmp dqmp du q piuqinqq 6qpmdt>mdb nri9 9 ty~l
qddqdhiqti dqddmin qmWiudqdmdmq i|dqqpmbbqmb
ijdqqhUonmp Uuhnjmd qq piuqmnjnminmhimpmq OdqqpmdbmQtj qmh
mduinqqb dqdq Qmbdqtiinmhn piu-99 hQ Oqiulbjqm %> ♦ # = p pmpbmh
ijdqqnhutnpi| QdqrjhUonmp uinqq fidpiur^md q iqiultyjm qmpd6) Oqiulhqm
# дтрффиф qmfdiublnu i|nbuhnpd dhUO^mp 3mum 6ijpiun|md ) duqdmh
bqinnln ллптрЦ }qdu l|qiu? Oqiulhqm 6 i|bdml]mpmq duinmdudmi
WlOt) -*>6>0
Odqqdqpdm Imhinqq IqqiutiqD } Uudmt] Oqxjftiqm 6* piudqatnqti
dulud piudu bqo piundb pmf] mdh mdq ‘piundqq dpbmqmidZ Iqfiqinb} bud
mq iknqh v ‘fkldqqqiulehudqdmdmq 'ш >ш qdqqpmlibqmb pmjinlmi-i
Qdqqnhulnpil dufimdmqq
ddqqlidqnmp uinqq Bdpiunjmd piubdmqmpmq duinmdudml qq piuqbmlmh
•dqq Odqpbuh G0 Л QV } qbqui qmhnutim?mdhdq ddqddifti duhmdmqq Qd
•mbmb a qmfriqmoq Qgy i|dqqnhulnpi| Opi|bmqmddZmndh рпгфбттп
гш.'ш ж go:OV L/Uqnmq qmt)
rmnmpqpmq rjL/dqrjQfrmbqmb LfdqgtiQrjnmp bufrnjmd L/qmpmd йрггфттц
ffK OrjudtnoQt] о № pijbmqmddcmnijt) Ьи1лЦ1тйГГ^ (n oh !qf>b-
0(>mb
tnmq gy budqbLnmtr) Unliulnpq1 dQbdonmp imam 6iJ[iiunjmd Iqqmn-
) inZqpmdq
•f)m dmpmq lulqbiuumh Opmdbmi|U qmnmduinhqti qdqqnliuhipd } pdmZqm
imam 6i|piurdmd Ot]qp 6i|dqqhi|qnmp ddq dmpmq qmpnjmd qqfminmqmy
?u qmt]mbpmam hmpdmbmd dmdmqinq} .OdqrjijiulehulilJHJ hj ijdqijijHjfel
tuqqp du/imdmrjq QdqqnhuhipiJ c/dqi)t)Lli)nmp uinqq fkjpiun/md <Jr)mqminnt]
'mdti ifobmtjmdd? Xik/b Qinqt) a fiutqn/ифиф mdb dpbmqmddZ ЬиЬфт<1
•mZ 'лЯ = QO П huqudinqqho Iqbqinb qlmdp } Uudml] Oinqt] о QPq^HJ
1ш -t- 'ш
aГМ-) : = 'л'ш = 80
Й рршр. hull prjjnq ikuuGplih hduini|uh фпфпМшО wGqjniGp gi l|ujpnq
qbpwqujGgb[ 9O'--q (C1I4.6 6p).
Ошйр iliuuGhllO wliawnd pbpL OwiiGhGhG hwpqujdb|nig hfauin qujpnq
t "Дг«/6/ tifiujjb шпиц» UjupGpG qnjnipjmG niGp дрйшО u/muijbtujqnijCi
Л™. wGLuniG, прпЦ ишР0ш0шфш1|Цшд t piupjdujG hbinbwGpnq diuGp
ikuuGpl|p gpduiG jiuipp
m,>m2; 0<J, 9<K/2: (40.21)
Ujuinbq шЦЬцидррйр GiuL Gq.6 6g -pg hbinGnq wjO фсииитр. np pui-
lunidhg hbinn йшиОрЦОЬрр htkqni[ijGbp[i Цшдйпи) bG unip wGl^niG:
BpOiuG шошс/Ьцицпуй ujGl(jniGQ Цш|иЦшд t dpaJjC йшийр^ОЬрр
(цийя^шдОЬпЬ hiunujpbpnipjniOfig hpn₽. OD A bobuG^niGntg (GQ. 66q)
sinJ'l-.=^ = —= —. (4022^
04 m,v m,
npinbq oqtnQbi bG₽ GiuL (40.16), (40.14) ajpGjnipjniGGbphg:
npUjqpiuiiGbph oqGnipjiudp ЦшрЬф t uinwGua GwL 9 L 5, wGlflniG-
Ujpp l|UJU|p: hul|wu|bu, (Gl|,6 6q) Цшрпп bGp qpb(
,гв,—"£—--£*? ____________________”21 ..... (4013)
AO + ON -r p cos <9 m, /w,+cos<9
TO dfain t m Jm~ hwpwpbpnipjujG дшОЦшдшд шрбЬрр пЬщршй:
UpwGp bG. ipmutnnpbG. wjG inbqbt|nipjniGGbpo, np ЦшрЬф tp uiniu-
M pwfuOujG qbpujpbp|uj(, oquiqbinq lyiuhuiiuGiJujG opbGpGbppg: OpuiGp
lupuin шрЛзршЦпр bG. pcuGqh wpinwhwjinniiJ bG pGGwpqqnq bpLnijpp
шошфЧ pGqhiuGnip ophGuqiuittfupjniGGbpQ L uuGliujftj bG йшиОрЦОЬрр
ilbjUqnpdnq nidbph ЦпОЦрЬш inbupfig, pGnijppg:
Э0ш)шд (40.I9M40-23) pGnhiuGntp ophGuqujihnipjniGGbnh ЦшрЬпрт-
B^Lqindu
iri>)
mhim tjqqiufdiudinqD qbdmhmpmq
4l]iJmbZrni_| 1 n|mhqm фрш«Кип|ифиф ijmdbdqq} h^qqdh du Qqm^
piubdmhmpmq j njmq Odi|bqnJ dqqhdmindt, :Odqqnlkjhnpd
Juhmdmqq ddqqNhnmp uinqq Odpiunjmd IqZudu } qhnunmbiq dq/q
piubmhq piudhnqb Ududhdq hN ‘(qmpbmhq
qjqqmqbdqqi qi|ddqq ddqqhdqnmp hd?mq ф 1 puiym uinqq 6t|piun|md
lyniJtxJqq} hUtnqqdh ddpnjmpmq piudhnqti qdiman \o>Q}tiL/uiqbdqq^ubq^
pnt] (0<d) t]QuiQt*Jqt))ubt]) qq piuqql Odqqpiunjmd qmhmb^mam ?□
UI0 :д = У-Л
5 Ортп ijmqbdqq} hU^QOUh
idqqqqqnmp bueoniqinqq qmpnjmd dqqhmqmZq. qmijbdqq} ЬФпЧОФ ЬМФ
Bqmdq qmq dmdmqinqq Odqqmdbdqq} qijddqq (UhQP BUBqmdq pmh) ijdqq
4|ijtjnmp bufinjmd qq рш^фф hmqmpmp qmpojmd qmhmbQmam ?□
принта чпьпъстнт cu i r§
:01ЛптфЫт } piuhinminnmu ndlqpiul dpmldiuqbo
iWqqpiudmnmhmu qmppdm? Oddbqrq dqdddb dqddmin iuhdq i|dmbmb
fl qrnfhqmaq qmhmduinhqb ddqqnhufripd qq piuqmnjnminmlrimpmu qij-
eqhuqqqp du i|qmd 6q-b9 9 h|] 1 рифЧ ?udubdmhi mt, dqqnliulnpd bliub
dqddmin iuhdq ddqqhdqnmp uinqq 6qpiun|md qq piuqmn|nminmhnmpmq
ifiQahnqti qmpdB dpmlhqm qbmd) qqdqpdm qhuqqqp qnihpm ft qmpdb
(nirttnqu ‘ш<<ш du *qqdqmpmbqmq q(m dqdpdmb qiuWiudbrnZiQ
;dpmpinmhq dhUrpnip pdm?qm } qhiubmd ijnliuhi
-W dhUrjnmp UuhpdmZ imam fk|piunjmd Odu ‘Oqmldiuduhmoqq q qijfmu
«nqmZq qmpn|md 'pm|i?uh nqlnnfm q Odqpiu bupdub qi^p qdqqhdqnmp
И Qqinfmq qdq ЬибидЦр qmppiul i|dqqpiudmnm|imq qmppdmZ qfmdp
Inwyrunn ] qiqdmh Oqmnjnminmtn mdt, budmh Ц7 lqqmn|nminmln Obudqp
JUqqdqqdo qmpqmhiqmhn - ‘Od.u qd hnq :6qqiu(diupbmd Qdqdlq Uuhdin hu
(iZ Ofr) 1 OhhP qmpnlmd Uuddddminqq bqp du ‘qq piuUqhi Odqqdqqdo
Qmpqmhuimij, :Mlq inqdhqut] qmpnjmd ddqqhdqnmp (piudhiqb !ш<'ш hmq
4Jo) iuhdq pmhin Iqbdmtn dpmfdiuqbo Bqmdq budmh 3qq? dqqp Oqmld
p' = y]2p(K +@) ж p:
HtpbdG. nj LupiDdqujUiuG piDfuduiG diu-
ikubujU C hiDdiul|Lupqnid diuuGpqp pdiqnqup
ttdnipjniGQ ipnfuQnid t: QGq npnid pwfuni-
dng hbinn dwuGpUp Мщпций wAntd t
tljqntlibnqbintiQ Qbujpntti L (iQmqnuT ttiqn- д
tbbpqbtnfilj rtbujpnid:
Ujdd pojlunidp qpinujplibGp Ьц^ЦшрЦГ!
(41.3)
mjV,. m2vc В
Ц.67
iwpnpwtnnp hwdiuGiupqntd. npinbq pwfunidhg lurid? m. qwGqqiudnQ
(JwutiNO bqbi t шЬгшгк): Lnppg hojpdwp t гфйЫ ЦЫ^шпрщЦшО qhwq-
pujdtibpfi dbpnqpG. npp hojdiuGdiuG t Guj|unpq iquupiuqpiu^nuJ qpuuupQm-
dh& Lnphg lufihpiudtjjin t ptu|untdhg wow? OuuuGpGp Pt ' AB hd<qni|UQ О
ЦбшпЦ piudvuCibi diuuGpUGbph qLuGqt|iudGbppG ЬшбЬйиллшЦшО diDubpp,
ewQb np wju qbiqpnid Gnppg йр?1Л bti (40.12) - (40.15) iD0G)nipjniGGbp(i:
SwGb(nq О ЦЫлр 2П1р? (40 16) гшпшфрпЦ GpUQJ2p2iDGiuqhd (Glj 6.7),
UuuuuGidGe UJjG Qbinbph ЬрЦрш^фшЦшО inbqQ. npnGgntd l|ujpnq t
дитйЦЬц hCiqnquGbph Qbl|innpujl(ujG bPwGGjniGm D qiuqiupQ: ₽iuG|i np nj
iuoujdqwl|LuO pwfudwG qbiqpnid p x p, ц*цщ p' ж m,v , wjGiqbu пр В
IjbuiL lupqbb qinGQti 2P2tuGwqdh Црш OGq npmd Q < 0 qtxqpnid В
l&np GqtnGQh 2P?iuGuK|dh Gbpunid. Mj Q > 0 qbuipnid' qpuntd
UnGinul|tnujjpG nj Lur?iu<5qiuUuiG pw|tinidGbpo (ЬшрЦшд) QGqntGQiDd
tptmipcuqpbi ^ЬршЦшОдййшйqnpdcuQt)g\xni\\n\ dbdnipjujdp: Dpb diupdp-
йО 2iupdi|btf>Q v, lupujqnipjtudp pwfuqnid t r, wptDqmpjujdp 2iupdi|r¥]
tXupdt4)G. LUiqiu
к =
Osk£\
(41.4)
JMnipimGp GnjQnid t ЦЬршЦшЬдЬйшй дпрЬшС/рд. npinbq n -Q ptufuQnq
tapdpOGbpp hiqdiuG pGqhujGnip dwl|bpLnijpp Gnpdiu|G t tpb bpQpnpq
liupdfiGG iuG2iupd uquiin t. wiqiu
’’luipq t, np к = I qbuipnid ntGbGp ршдшрйшЦ wr?ujdqiul|iuG. |>иЦ
t = 0 qbiqpnid - ршдшрдшЦ nj iuf?LudquJl|LuG puulunidGbp:
§42. ftblUShUMJSUMUL UbIuULb4U3b ФПГЗЦГЦГиЧЦЪ
2МГЪиЧПСПк1ГС
I. lytljinpnb-tjklfinpnb ршfunit/p: Obgritp m huiGquinp qwGqqwdnq
tlbl|tnpnGp V, wpwqnipjiuiJp zinptjqbtnq рш|иЦпи) t piuniupb ЦЬДшЦшй
qinGQnq hunJuiGOiuG йшийрЦрй: Рш|ишйрд hbinn pdiqnquCibpQ Cj^uiCuju-
L|bGppC Lp-. hull GpiuGg qiuqtkud wGtjjniGGbpo piufunidhg шош? йший^Ь
2tupddwG niqqmpjiuG hbin A.iSfe (GL| 6.8): ПЬ|1итЬЦЬитшЦшй JbfuuiGp.
Quijh iqujhiqwGdujG opbGpGbph oqGntpjwdp l|iupb|h t npn?b( ДЦ шЫдщ.
Go. npp Циирпр t mnmqQbi фпрдпиЗ:
OGinpbGp pb^iupinjiuG X. Y cuoiuGgpGbpp GL| 6.8-шй inpi|wd GLnQ
UwuGhGGbnh C hwi5wl|ujpqnid piufejniiihg wixu? U hbinn hdiqnquGbpb hiu-
йшр Guipnq bG₽ qpb(
Р = Д+Д=0. Р' = А + Л=°: (42.1)
Lwpnpwinnp hwtJwUujpqnii) pwfunidhg шошг hunku|ui)pp iphU N-
iqnqiio. piuGh np ЬрЦрпрр йшиЬрЦр wGzwpd t Mih(*h
p = P+P2xPv (422)
hul| рш|ипи5рд hbinn
/” = д’+р:
(42.3)
4iuiku<5wjG hduinquh iqiuhuiwGiiiuG opbGph' P' = P: Oqim|bint[ C
—>A uuGgikuG рйщпцир dLuiihn(unipjwG puuGuudLipg
P P'~V'E/cl
(42.4)
Щ.6.8 ! '
li hwjqh wr?Gb|ni| Pt = о щш)йшЬо, h(ib|>
ghwjh GbGinpnGp vt iupujqnip)uiG hwiJwp
lluimuGiuGp hbinLjtut lupiniuhiujinnip
jniGg.
vc=c’P,/£. (42 5)
npinfaq £ -G pwfumdhg ujouj? hujdujhJiJpb
LPhU IGbpqhwG t <iU24h woGb|nq (42.5)-nid рйц|пциЬ L tGbpqbiujb
(42.6)
ршйшбЬЬрр, pObpgpujjh t|bGinpnGp lupiuqnipjiuG hiuOiup ЦшпшОшОр.
v. =
(42.7)
'’hupq t, C htudiuGujpqnn) О^шшЬишЦ ikuuGpqGbpo tqbinp t niGbGiuG
ilbdnipjwdp hwQwuiup L ИшЦшошЦ niqqQiub wpwqnipjniGGfap PuuGp np
pwlunnJpg luolu? ЬрЦрпрр dujuGhUo [wpnpiuinnp hujdiul|ujpqnid qinGQbi t
qiuqiupb фйшЦшй, uuiquu C hwikuGiupqniiJ cujG Itfwpftlh v. wpujqnipjiudp
ГИпЬйй
*»*! = К» (418)
£ £• W£’' A,-.
A = . = £/2. (42.9)
yjl-v4cl
nptnbq E -G C hwikuGujpqnid ikuuGpGGbpfi [ppi| tGbpqpoiG t:
OqinQbinq C hwikuQiupqntd tGbpq|uujh L pdiqnqup iqwhujujGdwG
OfibbpGtphg, l|uinujGwGp ikuuGpljGbph hdtqnnuGbpp U tGbpqbiuGbnh шр-
dbpObpo puitiiniOpg hbinn.
Д' = p\ = ^E^/c1 -me2 = - mV\ , (42.)0)
Et = Ei=—m(\ ^Г/2: (42.11)
Vl-vf2/c2
riipbOG, puj|uiJiuG hbinLujGpni| liujuGpljGbpQ C hLui5uul|iupqnn5 фп-
funnJ bG OhuJjG hpbGg wpwqnipjniGGbph GziuGq. puq iut?ujGdhG liiuuGhljGbpO
hikqnquGbph ObdnipjntGGbpG m tGbpqpwGbpQ GnijOG bG. pwfunidpg
wow? Glju рйилллпЦ ujjumbq рриифйш1|0 huudiuGGiuG t GjTHinnGjwGpG:
(42.10) L (42.11) LUPGjnipjniGGbpfig hbinbniil t (42.5 H1G huuiiinGOiuG
l|WU|.
vr£,7c2 = A‘: (42.12)
Ul 6 8-pg uinwGnid bGp
= p’„ / p'„, tg#} = - A, / Р'г, • (4213)
OqinQb(ni[ piufunidhg hbinn pdiqnquf) X l> Y pwqwqppiGbpfi ЙЬшфп-
MxpjwG (31.16) piuGiudlibphg L htuzQh шпОЬфЦ (42.IOH42.I3) lunGynp-
qmpn|md pmbhdmmdd BdpUuh dqp ‘tnqU q (Mqiufbdm (izot) nqin) inqq
JhMnnmp pdmZgm nqtnmrymg } piubnjmd диоптр dijmp ddq ‘drjq piuhn
-0jqmq dhmydbrndd qmpq piufmt]d<jmn|qp rjmfguiniuft] du dqqinmhq
Й1») 4< / bdq‘£/if >1€ + 'б = 6
1 diun Oqiufhqm pmpbmh qdqgnhufnpd qdqqhdQomp uinqq fiqpiunjmd
qdrjdnfm вдтдттпЬ ОЦ-($Г») П (<Л mhnrri dpmfdiubmdm j -
'4 mup rjdnhul} piubpdmZ OhdOnmp imam 6i|piunjmd qdq :qdlmt|UQmnJqp
tjdiquimulr] gq piubhdmdqq gilb^d' Odqrjpiunfmd nfm gmfdiudduib rjmfdiub
mdm ddqghilonmp о bddduijQ piudqpdmh ijmpnfmd i|dqghqgnmp n inqq
i|Jqi)f]iu<k|p qpiuijlqq piuhdbnf drjunlifr> gqduijmbmqpduib 1 Iqbinmuinmq
qfp piudqgpiun|md qqiminmhm? ?u ddqghdbgb qtidmqkjd Iqinqb } qiqdmt]
inZu|p CdgiuRjdm nfm dqinfmq piufmhdomnjqp gmhmnmv, ;dqgnliulnpd 6mf
•mqmUUiu dmdd gqgiu gdqohdonmp hmnqinmi|p uinqq bdpiunjmd gdgqnfm
(41») 'Z/U = :6,+ ‘6, = 6'
(xjbqindu
‘oo = (^ + 'ff)8j ‘| =
Oarpufbdm Q-oH 1 ртЬбггмлп 6i|dqqpmqmd (9|J>)
tSI ») <l--0 piugmpqmn dfmhdomrilqp gmhmnmfj du 'dQqinmtiQ
bdgiufdiubmdm dhdonmp
bubpdmZ <Jmum 6qpiun|md qfmdp i Qmhnjmh q (dmpmq ddqghdqnmp bmn
-qinmdp) Bdpmbbgmb Qmnbqmq ddqqbdonmp } njmlqqm Qlmfdbmindm Qd
•qqnrjqbrjmin ddqgqmfbom UubhdminiJU dqiufbdm duqdmt] BqbBminn
(91») И?
Uqindu
(5Г») *|5(>Z + i)/Z =
.drqmgminnh nqfn
-fnddqb 'Ogiufdiuinfmqmindm (z. jfr) dmpmq d > Uqinnfm bulqdbmUqg
(frl»)
: i^l > - I =
dgmgqqiut] (Hcrzt) bulqrjum db?mq 'BqUqindu
agmqminnh ‘iJdqiqrjiuf
(irct)
(оггн
ЭШ
•pn„ oi ггг = у = *r
bqtnnfn LkntyMl Q/jumhipu^ } piuhmbqmhud q Odu
l эш °л 4
•- ,uis— = °v - у =-----
в 41 a 3
dqmqqqiuh 'q-n hulqnamindm fxJfiquiJu
‘(Л - °Л)гЭШЧ£ + >(4’42-^ + ^)t4 = 1
‘(0SO3 4°4Z - > )— = — - 1
:V r”:»
dijq piuqmum 6t| - (erztO Ddqqqiufeliubbiu qmpipmdmin Uinqmhd umqq
q dmam 6i|piud6 nqimm gq 6hu6 Odqqducnhqh dufirndp и q "u bqinnln
+ 41/ = °4«/ + гэш
<6IW /."-1Д i s
‘ ' + и— = "и------
ПШ 41/ °4i/
hridqh Imfqinqq drpdbq
6 9 ho Odqqdrjqdo qmpijmtnqmhi i|fmi|bdqq} q dnbuhi
3 -pM '0 Ogiufhom gmpdB i|inqmhd бЦдюМтиЬЬъ
°-"Ед- omhmodbqn hulqqmqmZq ,(6g qq) OpiuiJB
------- tVvvvvwv» Цслдгтфб (qmfaiudmhdq ЦЗЦ1т %э=7) qrtf
- -еИигфпртц “л md|i qgudinqqlj uirnbm pdm?
*Om dgqhdmuii|tj ihn^^ tjqmnlnpa^ •[
OqiuW
-lUQmqnJmh pmBqqiu ЦрпфЬдтЪ BiJgiuWiub
-mdm q dmpmq ddqppiurdmd Odqqdqqdo qmpqmlnqmbn дтПтсппЦМл
-mkx< hulqdubmqpdq qruj quqmdti ‘Oqpmqmd pmq?q ) Iqinmuinmq gtJhud’
Oqudfnpqc hudqqpiuipm? qmpq Oqpmgmd (srzt) qmqminndhi|inmlqa Iqt
-iuinn nqtnmqmgmd ) ijlqdmq mtnm ‘(q-A qmq 'dmdmqinqq) OqwfdiutxrnJni
i|dqqhi|qnmp (j i|qdl dginfmq ?Q6iu6mdl qdq piudqpduifi gmpdB ddqghiji)
-nmp g mdh ddqqqudinqqh pdmZqm piuqqBnj dqunlQb fyuiJtnpQC
} Iqbiuinn Mqiulddm (gl Zt) рт^втшп inqq Udhiqb Wm 6qqq dqqgiu pdut)
dgqp piutxJmqmpmq duuimdudml qqdm|iZmq 'Отптф lulqqqi pmhn|mh
dpmhbqmb qmhmuinilhqinmlqo B^qiufehubrndm ) inqdmpZp qelq 'piudhiqb
Цп^Цшй t tlbQLnpnhp Qndu^Lnnbfluh ujtfipfi bpQujpni.pjni[iCkpfadG
ЛА = 2Д,$т:0/2: (42.22)
LUwinfaGp. np ujqiuin ЦЬЦшрпЬЬ Црш дрЦЬфи у -рЦшОипЬ шфр(1 Ьр
QiupnipjniGo ObduiGnid (: Ош ЬшиЦш6ш(р t. ршОр пр gpOiuG dujikuGwli
рЦшЬшр ttbUinpnQpG hajqnpqnuJ t прпгиЛф IGbpqbuu L pdu|nqu: Оф
рЦшОшр tGbpqpuj/i L Ь^щпцир йЦшргпйр hiuOiuajuJinuJuflJUjGnit) ( йрщ
ЬшЛш(итр)шй ОЦшдйшОр (ЦшО шфрр ЬрЦшртр]ш& ш/фО): ЗрЦшй у -
рЦшОспр шфрГ> Ьр1|шртр]ш0 ipnipnfunipjwG шЬйрршЦшй ^шфтДОЬрр
(1920р.) hwuinuiinbi Ьй (42.22) ршОшЛЬр
3. йшйшйшЦшЦрд ОрртЦшфО }>pqpl|iuG ipnpdGtuljujGnpbG РрйОшЦп-
pb) t OujuGhllb ршршрр tGbpqpiujfi £,, - тс2 pCJuGuidbp Ош ЦшипшрЦЦ t
шшрршЦиЖ i5iuuGhl|Gbpb ujGGfihhiuugtuufi bpLnijpb nuiniOGuuppnip^judp
Uju bpLnijpp фпрдОшЦшОпрЬО титйЬширрЦтй t иЦишд 1932 рЦрд, bpp
Рш^спйшрЬрЦЬд ([bljinpnGh ЬшЦшйшиЬЬЦо ujnqhinpnGo tibl|inpnGh qiuQ-
цЦшдпЦ ppiuUwG (ЬдршЦпрЦшд OiuuGplfo: t|bl|uipnGh L iqnqpinpnG|i
luGGbhpiiughujjti ЬЬтЬиЮрпЦ шЦриллЦтй t 2/n? kGbpqhiu t|bl|inpw-
йшдйришЦшС биюшдшиэйшй слЬирпЦ: Ujp tGbpqpiujp гшфпиЮЬрпЦ t|
Рш1ЛЛШ1пЦЬ| t £o * m<r ршОшйЬр. ЬршЦшОшдЦЬ[ t GiuL РшЦшршр!
uipngbup. bpp ((ЬЦтршйшдОришЦшО nuj^inp рЦшЬтр bGniO t ([ЬЦтрпб-
iqnqpcnpnG qnqq UuiUujjG ррш Ьшйшр рЦшЬслр iqbinp t оЛлЦшд ih&ti
-nig йЬд tGbpqhiujnq:
§43. ФЛФптичт аиъочиопч иигиъь сотенкис:
U|u щшршдршфтй оцтшдпрдЦпр «фпфп|ъЦпр дшйдЦшд» ИшиЦш-
gnipjntGp pjqbinp ( ?фпрЬ[ шршцтркиЦИд чшЦдЦшдЬ r?biiuintiQiuiAii-
L|luG 1|Ш|иЦшдтр)шЦ hfain Фпфп|ишЦшО дшбцЦшдпЦ OuupOGp ^uupdniil
шиЬ(пЦ РшиЦшОтй bG гшрдтйЬЬр, npnGg рйршдргий ^шрдЦпр йшрй(ти)
inbqfi t niGbGntd Gjnipp шЬоЬгфшт шрикиЬпир Цшй Gbphnup: OpfiGwU
фпрпдЬЬро 2ППП ujQuiniJbpbGujjh гшрФчйр. дЬрйшдЬдшй рршДО qn-
(пр2тй uuGdpbh ЦшрЬФ шЬЦгийо, npb рЬршдртй Цшр(Х0 ИшралшйпиЗ (
2Ph GnpuiGnp йп|Ы|ПцЬЬрпЦ, оЦЦЬшЬпитй hujunq ишодшрЬЦпр|1 2^
дтйр. рЬршдртй рЬг?ЬшршфЦпр Цшй рЬрЬшЦпрЦпг| Цшдлйр zwpdnuiQ.
пЬшЦифЦ hGpGiuphnGbpb L hpphoGbph гшрйгнйр L шц0: IBbL флфп|иЦпп
quiGq4iudn4 OiupO^GGbpp 2шр<Мш0 niumdGwutlpnipjniGGbpG niCibG jnipj
bpQni hwpjntp шшрЦш tqujiniJnipjniG, uujI|ujjG qpujGp qnp6Guul|iuG Jbd
l|upGnpnipjniG uinwgujG XX qiupp l|bubphg. ?Gnphpq hpppfHujpG jwpchkuO
pmnG qujpqwgihuG:
1. Фпфп/ифпд quiliqi/ujdni[ ifiupiftifi puipchhnli himjuiutnpntdp rlpgntp
ЬшгЦшрЦЬ iwpnpwinnp hwikuQujpqnid дшйшйшЦр t iqiuhpG niGbGp bptpi
ikuuOhUGbp m(tj L dm qwGqqwdGbpnq, npnGp ^wpchjnti) bG hwiliuiqujinw-
ufuwGiupwp v l> vi wpwqnipjniGGbpnq lujGiqbu. np z+rfz iqujhpG рш|иЦЬ[пЦ
ilfiwGmd bG, шгли2шдЬЬ[пЦ m+dm qujGqi|iudni| v+dv ujpujqnipjujdp piupd-
i|nq OiuuGpb hG^tqbu GQujinnid Ьр, шшрршЦшО dt diuikuGujQniO pGpujgnq
tuju bpbnijpQ JwuGpqGbpp ptugiupduAj гц шпшйдшЦшй pwfuntd t (bpb
dm>0) Iftud dwubfiltfi МрйшЦшй Lnpnhnit} (bpb dm<0). ЬрцрЦшЦшй inb-
uiuGQjniGpg иш t ipmpnfuu/LiujO дшСкр/шдпф йшрййр ^ojpdmM cutibG dp
!лирршОшй dt Лийшйи/Цтй -
ПрлгЬйр drdiuikuGujljnid hwdtu|uilph Ntqnqup шЛр: ₽wGp np
p(^) = m(r)v + vfdm, p(t + dt) = (m + dm)(y + dv),
unqiu
<ip= p(t + dt)-p(t) = mdv^fv-vjdm, (43.1)
nptnbq wGtnbuQbg dmdv bpQpnpq lnupqp ujGQbpp фпррр:
<шйшдш)0 (20.13) ЬшЦшишрйшй, bOiqnqufi (43 1) mdp huuQujixup t dt
(huiJujGiuqnuJ Ршйш|ийрр i|piu luqqnri hwdtuqnp mdftрйщпциМ
mdv + (v - v, )dm = Fdt,
npinbqhg
mdv/dt+fy-vjdm/dt = F: (43.2)
Ujuinbq
• (433)
i(Gl(innpQ GwuGfiqpG lipiugnq Цшй GptuGpg iuG$ujinQnq qiuGqqiudp wpiu-
qnipjniGG t GuiuGhUb bfain ЦилдЦшд hiu^Qiupljp ЬшйшЦшрдтО L Цп^Цтй t
tifttul^nq дшйдс/шдр ЬшрсирЬршЦшЬ ujpujqrupjniG: <шг4Ь июйЬрЦ
(43.3) G^wGujlinLdp, (43.2) ИшЦшишртйр (jGbpQwjmgGGGp ИЬипЬцц infau-
8N
m dv/dt = F + u dm/dl (43.4)
Uuj ipnipn|ui|nq qwQqywdnil йшрйЬр гшрсЮшй hpOGuiljiuG qp^bpbG-
дЬц hwqujuiupnidG L npG итшдЦЬ( t LTb^bpuQnt qnqiJhg 1897p L Цртй (
Gpm iuGnib(i (u|iupqi|nLi3t, hujOiuGOuiG ЬшЦшишртО uinwgwd t bqb| jb|u
qpinGwl|iuG РтЦгишй qbnLu 1812р.): Uju hwQuiuwpnulo LjntinnGh 2-pq
opbGpG tupinuihiujinnq hiuL|iuuiupniiJhg miuppbpQnid t GpuiOnQ. np iuju-
mbq OtupOGh qwGqQiudo ЛийшОшф oGpuigenid ihnipnfuQnq ObdnipimG fc
Ujp ipnQuifunipjiudp щш^шОшЦпоЦшй
Fr-udmldt (43.5)
ipmgmgpj шОршйо Цп^Цшй t оЬшЦтЩ Цшй hppfwiujttfj nut LjnipiuGijuG
qbinfi фОшфЦш]П
mdvjdl = F (43.6)
ЬшЦшишртфд Ubabpulini ЬшЦшишрйшй ОгЦшд iniuppbpnipjniGo шр.
cnuuhujjtnnid t пшшйЬф l|uipLnp tlfi фштл: tpb итшдЦиид t $hqhl)ujl|wG
Пшфиишртй GpuuGnul iknGnq pGj-np щшршйЬ1лрр huiuimuinniG шрдЬрр
qbiqpniO, uju|uj pGqhujGnip qbiqpnii) ЦшрЬф oqinqbj iuju Иш^шишра-
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(uuqdwjpG pwqwqppjdbpQ.
/«+Л> + /»“2£т'Л (46.12)
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(46 12)-t>g Цилшйшйр
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Z\ \Z
; dm
-----------------------------
A x € dx IX
LU 7.11
2. t'bbgfnujfc dntfbbuibkpfi huiptfdtub opfibuiljbkp:
Ziuilaiukn dnq/i /ibkpgfiuqfi dndbbugpXjvd^i npn^bGp dnqfi fiObpgfilujh
i5ni5b&uno Gpui А diujpnQ uiGgOnq
niqqiuhujjiug Z uuowGgpf? 0Цш(Л-
tiiudp (0l| 7.11): DiqqbGp X wQiubgpc
dnqfi bpl|UJjGpnq Z шпшйдррд x hb-
niui|npnipjuuG i[pw dm qiuGqi|uj<5nQ
iniupnt1 bObpgfiwjti dnObGirp LupGfi
dl=x:dm <Ш2ЦГ> шоОЬрЦ, np dm =
(m/ljdx, npinbq m -p finqp qwOqQwM
11 -o' bpljUJpnipjniGp. Z OJi?mGgph ОЦцдлйшйр finqh bGbpgfiuJh dndbGuih
htudiup L|uiniuGiuGp'
I'bbpgfuujh l)bGinpnGnQ ujGgGnq Z iwuuGgph ЬЦсишОшОр dnqp hGbp-
ghiujh lindbCinp ЦпрпгЬОр. oqinQbinQ Cmbjtibpti pbnpbdfig.
= /f + m(//2)1,
npinbqhg'
/r = m/J/l2: (46.K)
nLqquiblynib huiduiukn f»fipbq/i [ibhpglnujfi д^иш^пр dndbbmbhpp.
lafipbqh h&bpgtiujjfi ljbOinpnbnt| wligOnq Y qifuwL(np шпшЬдрЬ ОЦиллйшйр
tiObpgbiujh JndbGino hw2i|b|ni hiudiup inpnhbGp phptqG tujq iuniuGgp0L
qmqiuhbp dx iwjGnipjujG dm дшйцЦшд niGbgnq ^bpmbpp: PwGh np тцдц
Zbpmh pninp iniuppfcpQ dh^GnijG x hbmjuQnpnipjujG Црш bG Y шгзшйдрЬд
(0Ц.7.12Х шицш Gpw hObpghuijh JnObGinfi hiudiup l^wpnq bGp qpb(
di., - x ‘dm = obx2dx: (46.17)
Ujuinbq hui2Qri ujoGQbg dm - crbdx ршОш-
6liQ, npinbq m/ab-L phPtqfi qiuGqQiufl|i
ОшЦЬрЬтрифЬ luinnipjniGG t bGuibqpbinQ
(46.I7)-q -al2,o/2 uwhihuGGbpnid, Ipinw-
GujGp
/j»me2/12: (46.18)
ЪйшЬ 6Lni|
it-mb2/12: (46.19)
ЪЦшшЬОр. np pfipbqh X L Y oJOwGgpGbpp ОЦшшОшОр hGbpgpiujh
qifuiui|np dnObGinGbpQ wpinwhiuj-
UMjnii) bG buiduiubn dnqfi pGbp-
gpiujh mfuiui|np dndbGinh (46 16)
pwGwdLnQ: OhpbqpG niqqwhw-
jujg. Opiu hGbpghiujt) L|bGinpnOni|
wGgGnq qtfULuqnp Z iwwGgph
[КщдлОшйр pGbpghwjh dndbGirp
(дллшОшСр (46.14) ршОшдЦ)
oqGntpjujdp
U|.7 13
/j = m(a2 +b2)/]2 : (46.20)
2ш11шикп qiuili/i />ЬЬрд/1Ш]/1 q[/uun(np dnifbbmbLpp Ъш(И npn^bGp
QwGb hGbpghujjti OndbOino A ИрйрпЦ luGgGnq X wrjujOgpp ОЦцдлОшйр
(0(4.7.13): UuinQh inpnhbGp q[iuGp dz huiuinnipjniO L dm -= pnR’dz (p =
qwGqQujdh 6шЦш(ш|)0 ftjinnipjmGG t) qiuGqQujd ntGbgnq pwntulj
iXjw4uji?wl|Gbn|T CuibjGbph pbnpbOh
dl4 = dl, + z2dm =(R2 /4 + 22)dm:
bGinbqpb(ni( иихидЦшд wpinwhwjirnipjnibQ OJ uwhdujGGbpnuI,
huiniuGiuOp
1Л = mR2/4 + ml213: (4621)
Lnpfig одшЦЫпЦ CuibjGbph pbnpbdhg, ЦшОЬйшОр q(ujGh hbbngtMi
qtfuujLlnp OndbGinObpQ
/, = /, = mR2/4 + ml2/12,
I,.^42-. (4622)
Дт/шикп qhquijfibpuiqmbpfi h qbq/i /1Ькрд/ии]/1 qtfuiuijnp dnilbbinbL-
pp: Ob' qGnujjhG pojqiuQpfi L pb' qQrtfi hObpgtuujh qifutuQnp OndbGinGbpb
hwikup niGbGp
А = Д = А = /:
iljq qfauipnuJ (46.12) woGjnippi&o iniu(fxj (
/)©, (4623)
npmbq €Ui btibpgbcujh QbGinpnGp ОЦцллОшйр |iGbpg|iwjti OnObGinG t:
•Ul AX (HZ. ho) dqqmbiub qddqqdBqmam ,д.х Qmqp m?dp dqmdq
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6drpu[eliudinf]O ddquiqO v q о qq n|mhqm ‘Oqiufehubmdm
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-mrjmd (frz.fr)} piuqmqq Отптф qmfehulub ddBqmam qqfmeidmelqhn
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ьшр|Кф Qpiu hiuppmpjiuG linqdfig 7.18
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(ret-)
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<ГК-тй fuiufuuiQnid t ЬшршрЬршЦшйгчр]шй uQqpnibpp: rku щшр.
qnpn? bpLnid t оРшшпЦЦшд opbGujqGbpbg: ЬиЦшщЬи. niqqwdbqbg 6п4и-
Guiqh ptaih zbrplwG (53.10) ajGQjntG(i ^шфЩпЦ ЦшрЬф t npn^bi qGuigpb ш-
pwqiugnidp. hbinLuiptup, hmjinGiupbpt| qGmgpb zwpdrudQ: <t>2bGp. np
<h<-rnd прЩ фпрдпЦ hGwpiuQnp )t quj ЦидлшрЬ|:
§54. CUPdUUL гичиииГПкШ? гисчигчь чииивичиъ
ПЗ ЬЪЬГвЬШ, ZUUUMUTQbmtU
CLpuuqptGp S-Q K-b Gqiuindwdp Цшшшршй к ЦшйицшЦшО jwpdntil,
npg. QxuiiLnnpbG, щЬ^П dwpdGb l|iudajjwl|wG 2iupdnidG t Ъш(ипрр qjfunU
gmjg inpQbg, np iqtiGq diupdGh liiudwjiuQuiG гшрйтйр GbplKujiugGnid t
Gpui прЦ О bbinh «« lupwqnipjuidp hwOpGpujg L iujp ЦЬшпЦ wGgGnq шЦО-
pwppiujhG uJowGgpb 2ntR2 щинлшЦшО ^ujpdniOGbpb qniOiup: Uju iqwj-
ikuGGbnmd S-h hbin ЦшщЦшд qnnpqpGmcnujjhG ajoujGgfiGbpb Q.k oppbpc
uqininQnid bG wljGpiuppiujhG WRiuGgpp 2niP2 О uuGqjniGujjpG lupiuqnip-
juiilp: OqinQbinQ OnqnqnQ huiuinujinniG, iqininQnq ЦЬЦшпрЬ Quin diudw-
ОшЦЬ uj6iuGgjiu(h (513) piuGiubLbg, Ijiupnq bGp qpbi
/ = [Ш]. 7 = [ПД *=in*J: (Ml)
1. ZAZ-»Z/?2 uibgifuib шршдтррпЬЬкрр li uipuiquignuPikpfi dbu»/io
funipjnibhkpp: Lwfu umuuGiuGp K-hg S luGgikuG ujpiuqnipjniGGbpb OGw
ihnfunipjUjG piuGwOLq: Ujq ОицшшшЦпЦ лшгЦЬОр
v, =v0 + r (543
ршОшйЬтй r dbdnipjniGQ'
r = lx^Jy-^kzp-ix + )y-tkz= (J4]
-Л+[П(& + /у + *1)]-^+(Пг].
npinbq htuzQb woGQbgbG (522), (54.1) uifjGinipjntGGbpo, L Gbpdnidi|bg
v* = ix + Jy 4- kz (54>
QbdnipjniGQ, про OiuuGbUp wpujqntpjniGG t hw2i|iupl|b w)G ЬшйшЦшрдпи
npb Gliiuindujdp ij.k oppbpG ш(|фпфп|и bG ((54 3) -md uijq wGryxidnid ijk
G hwdwpfai bGp huiuimuinniG): UQGhuijin t, np piu uipuiqmpjniGG t <П< •
Gljiuindiudp, lujubGgG (54.4j-g dujuGhlih ЬшршрЬрш^шС/ шршдтр/ткЛ
Sbqiur)pb|ni| (54.3) -Q (54.2) -nid. ЦишшйшОр
*. e** + *o+(Or] = , (54.5)
npinbq
v. =*.+[Пг]. (54.6)
ikuuGpl|p тЬршфпрлиЦшй ujpujqnipjntfib f;
(lipbilQ, diuuGpqp ршдшрйшЬ шршцт^гийр йрш uibpujipnfiJUjQujb L
hwpwpbpujQujb шршдпщгиййЬрр qnukupti t: Uju oppGuQwQini₽jniG(i
luwhJinQntd t ujpujqujgniOGbpp hwikup, bpb <Л<-р ujininQnq t:
Цитшйшйр шршдшдйшй йЬилрп(ип1р]щй ршйшЛЬр:
UdiiiGgbGp (54.5) ршОшйкр йш|ц L wj dwubpQ puin duiikuGiul|p.
v„ = au = vA + va :
Ujuinbq
*.=4 +[nr]+[Qr] = ae4-(cr]-|-[nvj4-[Q[QrJ], (54.7)
M
S =^+^+Az4-ir+/y+Az = a)I+[QvJ, (54.7Э
npinfaq hw2Qh ajr?Gi|bgpG (54.1), (54.4), (54.6) piuGiudLbpo. риЦ
a^&^jy^kz (54.8)
ikuuGhQp hujptupbpLUlpuG шршцшдыйй f:
Sbnwnpbinq (54.7)-G nt (54.7>o wpwqajgniiJGbph fiGwQinfunipiujG ptu-
kudlinid, LjuiniuGiuGp.
aa = 0, +[£ d - ^4 +e* + 2[QvJ, (54.9)
npc L|Gbpl^ujjmgGbGp hbinLjwt ЦЬрщ.
(54.10)
Tinbq
•<«=2(0»*]. (54.11)
fl. =«<>+[« : (54.12)
UpiuqiugnuJGbph йЬшфп|ип1₽)шО (54.10) opbGpnid a,-{] OwuGhtih mb-
Чшфп/ишОшй ujpwqmgnitiQ t. pcuGp np <Cl<-nid шО;шрд йиииОрЦр <Ь<-ф
^штйшйр qniGbGuj hbGg (54.12) ajpujqujgnitj[i: Jjniuo aK qnidujpbipG
Wlnid t LtnppniptJiujG шршдшдпиУ p щштрЦ фршЬиршдр qpinGuuqujG
Зиял/ц/р ^nppnipup{ 1792-1843). npQ ujQWjpGG t GbpOnuftq ujju Jtdnipjni-
(0 йЬ|иш0р1|Щ)пи5: UjG ц|Ш)йшОшЦпрЦшд t pGjiqbu йшийрЦр hwpajptpiu-
И гшрОтйлЦ, ujjGiqbu Ц <Л<-р iquinijinnq: (54.10) lupqjni&pQ hwjinGp (
dpmpmmhq qdBqmam qmpmmhi gq pmhnfmh DqiufdiulAnu iu qqiufdiupqp
dpiu nhunjmqudinqqh ‘i|piu BmdqOpmq u|fmL|BUqQt| qiufdiudqddmm q
:q¥mq
giulmbo quqdrrigaqq Uudminmh dqqqiuldiupdmh dpmmukfhn qfiubmdpdmd
‘Qbdmp Uufimmhi piulqniudmh nqiqdmmmh pdmtimSdZ Omdufnnqmdm
ikiuqLiu 1 piuhhdmdqq OqmfdiuBqtibm dpiu Ufn :6qdBqmum qmpmmhn Oh
-qqnmp IqqBmuqq } piuinbp Odu piu nfiunfmqudinqqr] QfmL/Bdqqd } piufrtuh
UlM) ‘ Xu* = *Л
qdlqdmpiub tidudduc
piu ImqBqqbqmui L/fmi/BdqqQ dqqqmhqmh qffl dudiucntn itimtmdmnmfimq
<jm Q~>U> 1 Bqiufbdm Opmtiqm bduddq :piu<tmdbmdmhn tidun|mg dqq Iqh
-dmqqd Odqqpmtiqm iuhdq qddmum qnmp 3m qmpdmnmhmq (sift)
(9IW) :jp/4? = d
_ ip
(51K) '[ил]шг + \иш + [э7]ш+ vu-j = — ш
tndqp Imfquiqq dqqqBmf
fntyjqqt) piu->u> qmpmfmpmp Dpiudmnmpmq qmppdm? qmqmdqdmdmq
'Onaqtirjd <</» puHfrl'W) hulqgbud Втд :qiuuinninnmi| Iqdmpmq } auiqfn
Ddqddo 3qp gmpdmnmhmq (ti ts) du nqfngfn :gq dqgduuihqb rpuin
•ттлтм Odqddo dfm piu- s :dpmpinmho d->q> дГггф OP piuhnJuihuQi piuS
-BmdgO dhmgmpmp Odqddo f/> d->U> ^7 qiufdiulvuu/tj duqdmt] Цл
:gddqpiu
rim qmq qq piudqdmdqh Odqqipufdiuliuindtj pmhdminmh dmpmq qdqpiu
ilmqBdqgd piucfcmdbmdmhi Udunjmq :dqpiu ifmdCdqqd bubbrn mdh UhUO
-лтр piu->j> qmhmlmpmh qq piuqBmfmhdqq Odqqpmbqm dulud pmBmqp
qpiu gmfquiniufq Odu 'ЦртЪдт qUSmum Цптр 3m dpmfdiuumBma
(UK) : *viu — ‘ош - j = "ош
Opmtiqm qfmdp dqqqliud piunmp nfmp q 3qp qmpdmn
-mfimq dquimufrq Q-(6K) dqqdtimUqin dmpmq lulmqminn qfp rijwudmn
m/irntf qmppdm? qmljmdqdmdmq iftpjqnmp piu-^J? qmljmfmpm}) •£
:6qdqqpiu6mbmdm [л] ImdBqqbqmm Qmhduhmqmpfmhn hum
•flumtn i|im?mdmnmhmqqm q->(j> q ’-/-U- bQpmqudinqqt] fimdqdpmq
Bddqqdlqdmpiub Sqdq 1 QmBmhUmd OpiuBmbmdm qmhmnjuQimUqs
:qt/dmpiub QdqqpiuBmbmdm qmpmdqdmdmq 7 qmfnqhjQduh qmpmn/utp
mbqtn f dmnmfimq OpiuBmbmdm qmpdmBmd pqduqd QnQhjqdur) nqfndu
dujuGhUh qpwQwd qppppg: Uj(j, niqqQiud |pGt[nQ iqiuinihuG шпшОдррд
qnipu, w6nid t wjn uiniuGgppg OwuGpqp niGbgiub hbPiui|npnipjiuGD hiudb-
(kuinojQiuG opbGpnQ ЧиялйшО шпшОдрр Qpiu qmGQnq йилЛ^ЦЬЬпа &O-
спрпйш/иги/и map luqpbgniptujUQ ibCi ЬйршпОЦтй:
Hfignip m цшБцЦшдпЦ фшцлди jnpuniG qpQiud t (2= const luGLuniGui-
JpO tupiuqnipjuuiJp iqininQnq иЦшЦшошЦрО iqinindiuG wixuGgppg r hbntu-
QnprupjwG Црш (Gl|. 8.4): Эпритр Црш luqqnq GjniinntywG nidbpp diuGpm-
pjiuG mg U иЦшЦишшЦр nbujQgpiujh V nicfbpG bG (ppwGp htudiuL^pnid bG
ppwp b GLfujpnid jbG щидлЦЬрЦшд), pG^bu GiuL qbiqp tqininiJujG iwiuGgp
ntqqQiud qujqiupp atpdujG nictp: иЦшЦшгхиЦр hbin Цшо|Цш6 <D<-nnJ jnp-
ипф Qpiu wqqnu) t GiuL pGbpgpiujp QbGinpnGiu|unqu mdp, npp hwdwltf-
ошй t гфйшЬ nidpG. wiqiuhnQbinQ ^npunip qiupiupp uQiuQiwiuQn Gljwin-
йшйр.
F^^mQ2r = 0: (54 18)
Л
'’lujpq t, np <h<-niiJ pGbpgbujjh m-
dtpp ршдшЦццтй bG, риЦ ppuniG Цш-
inwpniiJ t 2Р2шЬшддш1рЬ гшрдпи): UjG-
iqbu np lujuinbq ^npunip Qpiu luqqnp i)p-
tuQ jhwihultfoQwd A> nidp luiqiuhnQnii) t
jnpump QbGmpnGujdpq шршдшдтйр
ЪЦ 8 4
Ftr =mv2/r = m£fr:
(54.19)
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apjwGwqdiujpG zujpdnulp-
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inpump ршпшрр hGajpujQnp t, piuGp qbtj t|bGinpnbuu|ijnqu mctp jp qbpiu-
qwGgnuJ ршршрр ujr?iui|b(u>qnijG nmg nidp: <binLwpiup, Д2 > pg/r qbiq-
pnul )npuniG Quiuhp uQwQwoijuIiP QpwjnQ: Ujq tqiuhpg иЦишд <П<-пп) jnp-
uniG qbGptupQQp GiuL Qnpfmttnjfi
FK - 2m[vO ] (5420)
n«ffi luqnbgnipjiuGp, npinbq v -G uQwQiunujQp Gluuindiudp jnpunip iupuj-
qnipjniGG t: flipbiJG. <h<-nid ppuniG 2шрЛ|шй t pp lupwqnipjiuGo hiuliiu-
ixul| niqqQuud uiuhpp 2Ф^шО mdp luqqbgntpjiudp, iujG qbiqpntd bpp <Л<-
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Ml
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•fnpmq qq piuqBm3mom q aqudu qq qdqpiu qmfnqiuddut] 6qqq ddqpiu
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liudqbqbmbdmp mdb duudm mhnbuhiup piu-8£ § bulmhamdmdqj-i
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: piubhdmdqq Dduqlnu UuhpdmZ hN 'Opiu n(iun|mqudinqqh qfmqp 1 piub
•bm mdb OduqUiu pdmZqm piuuiduhingmdin Uudmuimh pdmbmddZ ‘hmq
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aijqZg hiuuimq nq pmbqm hQTl
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m л aqqdq BqaBqrrwjm qhmumbmhn Uuhuimtn q OhUbqb mfbminqp Sqp qa
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bqirdu
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drjmrjmuinp dmpmq qmfdiupmpdml Quitmb quQBminiflifndb
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GhMb qtuLqQiudh Qpiu, QuiniuGiuGp'
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dhUqnmp nqhi?qq q gdqmqinqu qmqmSqpqm q-(6 l9) Odu dpmlehu?oam
(U !9) <dv- = - d> = jp(-t)S f
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piuh?uh q 6dpm|ibqmb iu dhdqnmp рпфбтр inZmU } njmhqm qqiufeliupqp
(0Г19)
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tLbPQbUV QrU4bSUSbnL СШ1ИЧ1Л
<4uintuf> pLnpbd: ЗршЦрслшдрпО qiU2inh [OjpQwdnipjujG (61.5), (61.6),
hGjiqbu GuiG iqninbGgfiwih (61.14), (61.15) pwGmdLbpQ ul|qpniOpnpbG рпц
b(j inuuihu npnzbi boiduj]UJl|UjD hwOiufuilph uuibqbujd qpiuqpLniugpnG qujj.
mp: Uwl|ijuj(i nprv qfaiqpbpnid hwpikup t oqinijbi (61.5) L (61 6)-hG hiudwp.
dtp Qujniufi рЬппЬй^д, прй ujjuinbp l|QGnru.GbGp шсшОд ujiqwgnijgp.
^uiduijujQuiCi ifKuQ liiuLtbpLinijpnQ qpujLl^ujgfinO rpujinf) [шр^шдщ.
ррий L/tilpnnpfi hnupQ htUL/шишр t uujp tkul/b-
pLnijpnQ щшрфшЦфид qcuDqLlLUdp L -4xG Jb-
dnipjujQ шрспшгцущрЬ
f gdZ = -4xGm ; (62.1)
Uiul|bnLnijph тшрршЦшй dl dujQbpbundg
dbQmnpp hnup шиЬ[гк1 ЬшиЦшйтй bO gdZ ui/ш-
pup ujpuiujripjujip (GQ9.7): Фш1| йшЦЬрЬлцрпЦ i|bl|innpfi hnupp ИшЦшишп
t pninp inujppbpnQ ЦЬЦшлрр hnupbph hwGpw-
Ixu24ujI|UiG qmdwppG:
OqinQbinQ Oojniufi pbnpbdfig. прпгЬйр M
qiuGqQuud L R 2Lur’^i[pq ntGbgnq hiuihuubn
qGqti qpwQfiinwghnG qu^uVi |iupi(uJdnLpjniGo:
Lujfu прпгЬОр пш21П[] qOrjpg qnipu inp-
pnijpniil Ujrj 0и|Ш1ПшЦп1[ йслпф шпшЬй&шд-
GbGp qGqhG hunkul|bGinpnG r>R 2Шпид||Т1Л1|
фшЦ i)wl|bpLntjp (GG.9.8) L hu^QbGp GpiuGrx(
qGrtfi qpiuQpiniDgpnG pu^inh iiupQwdnipjwD
фзЦслпрЬ hnupo <iui5w2wihnipjiuG ОЦиилш-
nniilGbphg biGbinQ’ l|iupb[h ( iqGqbi, np g -G wdbOmpbp пщрЦшд t qbuji
q(jpp l^bGinpnG L ЦшГиЦшд t JhuujG qGrtfi L|bGirpnGfig гфтшрЩпг’ Qbinfi r
hbnujQnpnipjniGbg.
g = ~rg(r):
(62.2)
Tiupq t GuiL, np qOqiujfiO i)wl|bpLnijpfi дшйЦшдшд inuipph hwdwp
dZ = rdZ: <binLujpuJp
gdZ = -g(r)dZ:
(62.3)
<UJ2i[b wnGbinQ, np (62.1) -nil) htiinbqpnido ЦцдлшрЦшй t r - conn
|5ш1|ЬрЬлцрпЦ. npp Црш g(r) - const, ЦшлшйшОс
j gdZ = -g(r)£dE = -4trr2g(r): (62.4)
₽wGp np рршшрЦЦпр OujqbpLnijpp GbpunuJ щшрфшЦЦшд t qGpp np?
qwGqQiudo. шщш (62.4) U (62.1) piuGujfiLbppg ЦшОЬОшОр. 4trr:g(r) =
ДяОЧ/пршЬррд
g(r)^~. (r>R): (62.5)
OipbdG, htuihuubo qGpp qpiuQiinujgpnG puling qGppg pmpti mppmj-
ртй ЬшйдОЦйтй (рр qbGinpnGmil тЬршЦпрЦшд GnijG ршйрЦшдпЦ Gjm-
ВшЦшй ЦЬтр piu?inp hbin: Ujp inppnijpmi) qinGQnq m ршЬрЦшдпЦ йшиОр-
4CqGqp Цпрйрд ЦбрЦр inpbqbpiul|iuG dqnqnipjUjG opbGpnQ трЦпр
F~ntg=GMnlr> (626)
ntdnQ: UjGiqbu np. ppnp, (62.6) opbGpg ipzm t pGjiqbu qbinuujpG, lujGiqbu Ц
qGpuujpG iSujpdhGbbph hiuiJujp: <iudiuGikuG дйлЦ qGppg qnipu тррпцртй
qpujilhiniughnG ршгтр ojninfaGgtHuig ЦшртшИш^пЦр GmjG qujGqqiudnq
UbinLu/iG QujpdGh итЬрдшд n|ninbGgpuu(p риЮшйЬпЦ.
<’('') = • g(r)dr = -GM Ir, (r>R): (62.7)
DpnzbGp qpujQfiinujghnG рш^тр iiupQuudmpjniGg qGpp Gbpunid: Ujp
ЬщидлшЦпЦ gGinpbGp qGppG hiui5ujl|bGLnpnG r < R гшошЦррпЦ qGpiufiG
Aul|bpUnijp (0Ц.9.8) U oqinQbGp Оштир pbnpfadpg: Lnppg g ЦЬЦсппрр hnu-
Cp hiuduip L|iatiujGujGp (62.4) iupqjniGp[i ПшБрЦшдр paj^hjduiG РшйшиЬ-
onipjmGpg iqujpq t, np r < R гшпшЦррпЦ qGpiujpG йшЦЬрЬпцрр Gbpuntd
щшрфшЦЦшй t
т(г)=Мг2^ (62.8)
qiu&qQujd: QbpjpGpu ИшгЦшпйшйр Оштир pbnpbdpg t|uimuGujG₽
g(r) = GMr/R3 =Gm(r)/r\ (r<R); (62.9)
□тшдЦЬд Цшркпр шрррШр. qZ/p/> г < R Qtcnntd qinGQnri йшийрЦр
4fmj ujqqntt]t dfKUjG г qCiqut/ftCi dtnQtjpLnijpnid ицирфш^шб
\dfr\ йшЦЬркпцррд pmpu qinGQnp qiuGqi(ijud[i йшийрЦр Црш jp
wqpnul Ujuinbqpg ОшийшЦпршщЬи hbinLnu) t, np qGppG huiiJiul|bGinpnG
г<Й2ШРшЦррпЦ funpnjmd qpu^hinuigpnG puling ршдшЦш)тй (:
dqpmqmd i/mQbdqij)
quipmuiiftirndb qbqb dqmqmmnlg ‘qpmtibqmb innfl Jiulqdbqinqq q piu-
(П79) fiulqdUmUqm фи- (j)u 0- j 0iH£Z9) hulqinfmqmindri :8qminmn|?m
(IГ39) *ПР~ = —— = M №- = VP
qqdminmt]li Odqpiu quqfi
•nundbmdb (ОГбШ dmpmq lulqngmd SdiuZ qbqb q lulqdqd BqqiuWiuSdqb
•gm dqmbmd hupmjibqmb шр pmmZmb qbqb tiupmfibqmb (^)ш Qmfidufi
-mpbmq qqtidm piuaBmdqO nfp :Uqiub UuBqqiu Uqfimam? у q pmtibqmb
W 3qq piudufimpbrnh Jiulqdqd Qmjibqmb BdqiufehuBdqfiqm diuBtft,
qmqbdqq) quqbmunjfimdb qbqb aqnmpmq ifqqZudu
tfqmuimnJZm qmt]
mdb qqdminmh ) duiqfn Odqpiu rjddmindm 01 6
dmpmq iulqfmd(mJ Odpiunjmpmq du dqmd
') Qiuleliupqp qmhmnmBmd qmqbdqrp quqfi
•mmqhmdt) :ndlqq6muqq Jdqbqm BqBqmfpqp
Odqqfiqqnmp Uupbmf] Odpiunjmpmq .qdqqnfm
mdlqlmdlmd Odpiunjmpmq Odqpiu quqBmui
-iftimdb qqadqi) rjqdminmhh Odu q rjaqmui
-mnJZm q(m qmqbdqq} guqBminqtimdo
(01Z9)
"np- = VP
mi/bdqq) quQ6mmqtimdb ) piutfut) qmqbdqfj] lmq6qqm
utri Qmpnpqn qdpnjmpmq Iv/ibmcnQhrndQ :6q(mq6mdiubq<tqut) qdprdmp
•mq ) pmhnjmh Odu bufmqbdqq) ImdBqqinuhn qmhmqiqn dqqBqdbmdiugd
OBi)mLnmnJZm qdqpiu bquimhdqnquh odadqq qdpnjmpmq qdqqhUonmp
P’u-9Z§ qum q Odqqmhqunhmlmb 'ilbdmqmpmq qqimqhmbqdm 'Odqqbmdul
up ‘Ohmbqdp 'Obqiubmdf]dq qq dqdpnjmpmq qnqh’iWn UubBmuiqfimdb qq
piuhZuf) ‘hudqpiu qmWiuUubp qmh
•mdqbqqLn qq piufiqmtn q Iqfiduhmp
•bmlg aqudu ‘Odqdpn(mpm> qmifb
^41 qtn/fimmt/pmi/b
:piu- 6 6
*10 qq pmbBmfmhdqq Odqqpiun|mh
(6Z9)q (5 79) qmldiupmtidml qinZmb
OuqBmuiqfimdb qbqb uqnmpm>
* R 5 R
HipbOG. hujiJujubo qGrtfi дршЦршшдрпО tGbpqpujG ИшЦшпшрд htuiJb-
йшшшЦшО t Gpuj гшрииЦргфО: ФпрршдОЬ[пЦ irQjuji W qiuGqqiudnq qGqp
jwoiuqhQQ. wjupGpG ОЬдшдОЬ|пЦ qiuGqqajdp ftjcnmpjniGQ, ЦшрЬф ( qGqp
дршЦртшдрпО tGbpqbiuG ршрйЬЬ( bp гзЬ[цлпрЦриспшЦш& A/? tGbpqbujjp
qwpqp: QGrtfi гшашЦцр iujq uipdbpc Цп^Цгий t дршфтшд^пйjwnujQpq
R'KGM/c2, (62.13)
про Цш|иЦшд t OhiujG qGqp qwGqQuudhg. Upbqwqp Ьшйшр (M©* 2.1O,ol|q)
wjG Mndbinph qiupqh t, huq bpqpmqGqh hwiJujp dbinph (M® = 6.io2,qq):
bpb ИшгФ uinGbGp, np Upbqujqh гшошфгц]' R© = 700 hwqwp qd fc, puq
ЬрЦрЬ&О Re = 6400 l|d, UJiqiu iquupq qqwr?Giu, np ujjrq OujpiIpGGbpp qpwqp-
jiwghnG tGbpqbujCibpQ GpiuGg оЬрятЬфишшЦшЬ tGbpqpujQbph ^GjpG
ikuuG bG qwqdnii); UiuqwjG qbphjpui (й^тЦифО ftjinnipjniG mGbgnry.
шдцЬи Цп^Цшд GbjinpnGujjtilj luurifapp Пшйшр, npnGp niGbG ирЬдшф
qiuliqqiudp l|wpq|i qojGqQiudGbp. pujjg R =10 Цй гшошфл, дршфшш-
jpnO tCbpqhiuG qwqOnid t hwGquinh tlifapq|uujh 10% - 30%: ЪйшО qbp|uhin
dujpOhGGbph znips qpiuqpinwgpnG qu^inbpG сидЬи jbG ОЦшршдрЦтй
(iFULnnCjjLuQ (61.3) L (61.12) ршОшйЬЬрпЦ: tjGzinbjGo (1915р.) qiur?ntgb[ t
tjbphqnp L tupujq фпфп|иЦпг] дршфтшдрпО nujzinbpp inbunipjniGQ, npp
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4ш|5ш^шфт₽]П1й|1д b[tib[ni|' Цшрпр bGp LqGqbi, np N, ЛГ/итпЦр шйрш-
gObGpdnqo В MbGinpnGpg ЮСгфро hojGqbgt|nuJ1 GM 10.9q-nuJ iquuinl|bp-
qiud nbiqppG: N2 nidp ajqqbgnipjwdp dnqp BC йшир C bajjpp фЬрЦр ЦЬр
Л = (7M1)
2 EoHzJ
(75.11) ^шфпЦ, риЦ иЬфшЦшЬ Q2
Ц2гф luqqbgnipjiudp GmjG С ЦЬто
lybqQp дшб
A = -^ 1Г (75.12)
4Eab'
ццфпЦ: UpqjniGpnid ВС йшир ЙЦйшЬ цшрр Цф&р (рЫчИ ЦЬр zbqnidQ).
Л-А?-Л,.- (75.13)
СшгЦр ujnGbinQ GwL huuQwuiupujluonipjiuG
2\ + ^ = 0 (75.U)
miujdiuGn. (75.1 IH75.13) woGgiipjntGGbpb oqGmpjtudp QuinwGwGp.
х' = У2=:17е+^А’ (n,5)
bpb ргцпр hbGujpajGGbpg qinGi|niiJ bG i)|ibGnijG hnphqnGiul|wG йш-
1|шрпш1ф Црш, шщшл^О, L (75.15)фд ЦишиЮшЬр
N^5-Q. (75.16)
10 о
ОтшдЦшд (75.15) cupruniGpfifl hbuibnuJ t. np дпгф ЦгоЬ ршгГитйд
bpbp hbGiupujGbbph Црш |ирисп прп;ш1ф t: OGq пртй HbGujpiuGGbpp Црш
ЙйгйшО nidbpp шрдЬрЬЬро Цш|иЦшд bG finqp (fupuui шишд, GiuL hbGui-
pujGGbpp, npnGp 1лфш( nbuipaii) ЬшйшрЦЬдрО ршдшрйшЦ ифйП) илтшй-
qwljiuG hiuinMnipjniGGbppg-
El£
:Opmbqm mufp L|3dmZ IqijBdqfi } inZqpmdu
-qm mhnm 'o=(O)d du -dhbdmhn qdq :Bdbdun|mg 1 ЬЗиф inmpqpmqgm dpmf
-ehupqp dd pmbrjm bduSmu diuRgmdmdiug :} 9- (q)jx Opmbgm rjmt]mr)pdd
dddmZ (Г9Д) piuatnqb ddqijpiuUq? d8uQi ddqhon :O~(O)J mhnm ‘piubbm
J? piu mdfi dtldonmp piuaddb Q~x gmfeliu{J?t]mdmnm|imq du dgm^
rdqglmfBgmpm Ц-xinnO qq piub|mgmZf] OdqqnJddinZ Uqindu
9 Z
(Г94) ‘"+(0)(.(г/ — *(0)nJ— + (o)<Jx + (o)./=’.У
Г t?
tiuddmZL/duVqQ ddqqqmydinnm Ц-х unnO lqqBm(mf]dqr) 1 dlQdmf]
inZdP gfm ‘ВЦфт? x gmpbqZ dhdqnmp BdBUdb qmidiuaZhnndrinnmbmii Orjiufd
•lupmfinjnnh dpiu j UuqpUmUmdqtn 5 gdndhn?gd qd ‘Bdgmdg njmhqn
:inqy ddqgpiuliqZ ивиф ф|1|дптр 6dadi|ti gmfeiiiiaZtimdmnmfi
-mu piugqrpu 3gq pdub aqqp piudqgddUi]n| duqdmt] 3dmZ dr Uig6mfmh|dqq
giufeliuduqdmh gmtimrjpdub gfmtimn fiudqqmdBtlOiutt Udmd } piufiinfmii
-mindm ВЦфт? qmpUqZ dhd9nmP Bdaddti qmfeliuuZqmdmnmtimi| Dipufd
-iupm|nn|mf| dpiu Uugpdmdmdq|n piu3hnqU diugmi|tjr)Q :piu pmJiUViu rjadifd
gmfdiuaZqmdmnmtimq dbnqb piugmSmam } piuahnqti qmpbqZ dhdqnmp Bija
-dub bfm du dqma 'DSdiu? dadifti gnidiuaZhmdmnmbmii ijiufmfi rjfmdp 5 duh
mdmrjii OpiupdmZ gm^mbugminmui dhdqnmp du ‘agdBPb^ BfiuB piu<mdb
-mdrnhn qfiuq :piuelfiuddui ртЬИппфтдтрчтп budquiqt] gmpSdZ OpiupdmZ
dd } piughdh dmdmdqddmhn 0hd9nmp qagdnfn :dhui)d ddqopiugminmin
dgiu gfm piuduu rjdfmlmUBgqunuhn du ‘agmnqin piu-O£§ ‘OpiupdmZ dhdO
-лтр piuinZmbmpiu gifmlmdBgqinuhi qdamindm bulqddnmgpiunuj
janjiqu^nsns
[ХПЬПЛЪ
.Bijbqindu
К
: —UIS3IE =
X •
aqmqminnf] t|-x mnO fiulqdbqinqd odu
nqhinfm aqqqBmfmhdqq 0-<Г94) ‘Bdqiufehunjuipmqp
(iPVVl _
t\*p) P I XZP
bulqbintw о
Ш
(S 94) ' im у
piuhmqmZq aqqdminmh
(K94) :°л = (о)л !°r = (o)r
qi|qmtn q = / du fiulqdlimelqq ‘Opiupiul diuqmqbqO iHt'94) aqmqminn
:qlm q Oqdpdmp pm|in|mq Bilhmqmhinb ‘Odqqhmqmy
-uy qmhmhdbdt q qmhmhQinmpqeimp qq dqqhmqddo ddu -duinmkjbno rjif
-mpb 1 piub?uh Obdmhmpmq Uudminmh dqqpiuqminmin ОЭиф qmpq./па/
•mnmpmq Qdqqpwjminmui t]mq?mtidqr) j piufiJul] Qdu ‘^lupiudmnmbmu
(Г94) 4- * ХШ
} piufidbmdnrt)q Opiupdm? ijinqh
qmhmeliirfq tiupmfibqmb ш dpmfeliuBqbbm t|piu qmhmbpmomi|bm|ia
piu Qm^mbpmijmtJbmhd } piufiiuh qlf) :piudqqdi|tiqnj
qmbmpbmd ЦГт^ЦЬОф ni|lmb } in(mi| i| q inqq qmfehuuifmumindm dpiu
qmfeliugmqmbpmtjm } piuqqqOpmq nqhnmqamindm qpiu (F9t) pmfiBminn
Ohmpifti qmidiuuZh'ndmnmhmd 1 piudbmdiuqd q } qiuinminnmq pmtinjmt]
Bddqdinqpmdmfn qmf|mhdbd<t ЦЬОтОтртц OBdhmpdub । Uqinnfn
(Г94) =
qmunM]
-mq OqmpUqZ 1 pmhbUiu qpiu Uuqpdmbmdqh du dqma 'o > y- = (QJ.J P^
-hiqti qmpUqZ d8uip 3dqfiqm BQaddU qm(eiiuaZhr™Jninrri|imq qiufmh
JQ'UVU'VnsnS hnoanum -94§
Н€
} рпфГптГ]
jiqq qmWiunJmpmq qdlmqmSd? л ipufdnjnjmymq qQfmqb ) piub?ut] Odu
(01 9L) '1!\ ~л
Ц|)Ц1Ь ОЬЦй ijdqripiuqminmin piuhmqmpmp dufimQf)
Xqiufdiuhinmq^mAyxi/Tt/uWyZx/ ddqqpiuominmtn) GQeffiuqfmlfjmp
ymnmui ) njmfyjm qqiufdiudqddm/n ijmprjmuimcn fjm^mddqq .ipufdtud
qddmtn qmpqmuimm q piub?ut) q } rjhmrjmpmp gmprjminmin t>ddl hqp tyi
Ml)
: 1/tn^J/Z = °ro s 1 ‘“*2 =
1 mjlrrxn nrjd&Jqb dpmpumbZmq Q-(99Z.)
:U + ')X = (')*
•rjaqqnfm ‘dboh
dqq OpiupdmZ Brjm hmqmp
mp i OhmZudu mhim Л тЦб
t]ml]dqddmhi Omuq
ф du dqma (Л) hmp qmt)
mqdbtin - qdqmhi o-; 03qp
-dm i|du 'Ииф ijmpfjmuimn
ty- A+flm
TtfmqmdiJ? ‘(biuini|lhi
•fltn) efiuqfml Qmprjmuimin
tin
1 piub?uh Oqiufdiuqqp и :piu- t n t|0 1 qm^dq^mmhi rjqdutidtnTdb Odu
^KiQmcnmin t)mi]ZmtJdqr) } piuNuh OpiupdmZ Uufidin hudrjqdo (9 9Z.)
(Г9£) ;°х0®/°л=^ ^я>/°Л4°х^=К
dqmriqrpuh dmpmq ddqqipuinminnmq qmpdbqcnqd Bdbqtndu
'<b soo °(X>k = °a *d uis к = °x
drymrjminnb
(£94) -(d +Ao)soo°rt>y = r = (j)a
Oagqdo отргЦиЦтиф
'jmfehubmdm dhdqnmp bulqqum Щч^тц eddqqijmpfmtn (t'94) rjmtimqdbhn
hulqhuibo qq dqt)f)iuinminnmq qmpdbquiqd Zuduqm ly * ч q- и Uqindu
(994) • (Л uis у = (/)x
Oarjqdo rjmppdmZ dhdonmp } piuqmqq 6i|di)iufUdm рггфбгтлп
a>0 = 2flv (76.11)
wo(Qru.pjiudp: QbpspGpg PbinLnid t. np ci>u-(i 2л QwjpLuiuGnid inwinwGnuJ-
(ibpp ppQG t:
ЪЬрпшгОшЦ iniuiniuGniiSGbp l|winiupnq OwpilGp 1ПГ»Ц i)btuiuGtil|wl|uiG
tObpqhiuG duiiiwGwlih l|mikujwl|iuG щшРрй huiQuiuuip t рЦиицршпшйцш-
цшй тф ш2|иш1Лш0рпЦ ицш^шйшЦпрЦшд кх1/? ьцтлЬОдриц L йшийрЦр
фйЬелрЬ tGbpqpujGbph qniihuppO.
_ mi mailx1 I , _a ...
E = — +------2— = — ma)'nA2 - const, (76.12)
2 2 2 0
npinbn oqinqbgpGp (76.5). (76.6) L (76.7) ujoGinipjniOGbppg: UincugQiudo
ttibpqfiujjh u|whu|iuGiJujG opbGpG t оидрцхдлпрр hiuiliup, pujGp np Gbp-
фи20шЦ inwinwGnu5Gbp[i итшдЦтй bG гффьцилпрЦ nidbpp ршдшЦии-
jmpjwL qbuipnid:
ItoujQbiwqnijG pbnikuG ЦЬйтЦпи) оидрцхклпрр ItfiGbinbli IGbpqpujG
qpn t, |iul| iphM Jb|uiuGhl|wl|iuG IGbpqhiuG РшЦшишр t mninbGghwi tGbp-
qpwjtiG: <ш4шишрш1|2ЬП1р|шО qpppnQ шйдйЬ|ри оидЬцитпро pGmpujqp-
Qmd t ipM tGbpqpUJjbG ЬшЦшишр qpGbinhlj IGbpqpujjnq:
{wdwqwpqh l|iujniG ЬшЦшишршЦг^РМ^ ^PP^Q ul|qpGml|iuG 2^1-
ikudp шпшршдшй тштшЬтйЬЬро Цп^Цпи) bG иЬфсиЦшй (лштшОтй-
(/tip: иЬфшЦшЬ inwinwGniiJGbph huj6ujftjnipjntG(i 1|ш1иЦш6 t hwdu>-
Ijwpqh l|UJjniG Ьил|шишрш1|2ПП1р)шЬ ЦЬбшЦр pGnipwqpnq $pqpl|Ujl|UjG
libbnipjniGGbppg:
иЬрпшгОшЦ uuuintuGntJGbpQ htupdeup t GbpQwjwgGb| ЦпйщЬри
тЬирпЦ. oqinQb[ni| tjibpfi ршйшйЦк}
e,a = cos a + /sin a, (i2 = ~1): (76.13)
PlipbilG (76.6) Gbpqiu2GuJl| тидлшОтйр ЦшрЬф t Gbpl|UUjwgGb| np-
u|bu (76.13) ЦпйицЬри dbdmpjujG рршЦшй йши.
*(/)=Яе{л/-‘л>). (76.14)
npinfaq <pi uliqpOiul|wG фпцр (76.6) pidduiG uliqpGiul|iuG фпцрд iniup-
pbpQmd t ж/2-лф UnQnpmpujp hw24wpl|Gbp ЦиппшрЬфи hupdiup t (ru-
dnidp Gbpl|iujujgGbi
х(/)«Л/*м> (76.15)
91Е
piupdnSmp i|f)iu
q piuinqh 3/i =wr piuqumli } udb qfn piu-CI ihl 1 pmhBmfmhdqq OBnqin
Jfmi|6hqiu(t Ufm piudhiqti diuqmijUqo :dqddmtn c|gUlh Bdludmdmh) Op
•iuUqZ qfmq6hoiu<t (x),q -eqdqpdm ddinqpmdmln з piu- (zu) pmhnjmn
qddbqnj qmppdm? ЦЗДлтр piuin?mb qddmin
•dm hulmdBqqinuhn (rz.4) 1 piuhBqbqmq Oqiufdiuddnmqpiuniu qmppdm?
Jduinmldftio qdfmpb ?u du 'dqq piuinmhn. duinmldBno qmg?mUdqq ?u
pmh qdfmpb ?u } piuh?ut] Obdmhmpmii Uudminmt] dqqpiuqmuimin qdfmpb
?□ qdfmpb ?u qq piuh?uh Odqqpiuqminmin Uuhdbmdmhq fiudqqpiudmn
-mfimq Uuhmqiudmhi dqqpmbqm i|bdmh
dgdmd L|lqhm q qdfmmuhmamd qmp Z'H'hh
•bqZ Bdaddb qmfdiua?hmdmnmhm> x ,.,v о lttx
(ru) * \ j /"pV
(ILL) ’(*)/> “"j \
Uqindu \
(ru) '4>lnp-**u
.nqhinfm aqqq6mfmt|dqqt] Opiudmnmfimu qmp
•pdm? qt]dqnmp piuainqli Ufp :0pmbqm dbdmi] .x qmq Iqqam dfiZmq } in?qp
-mduqm piuddm? (rgj mhim •duhmidqb Bfmd q d3uip OpiuUq? dhdqnmp
flqaddb qmfeliuu?qmdmnm}imq qdq t]mt}?mUdqi] iu 1} nqhiqfm ‘hmqZmbdqq
iqln?qd Iqqdl qq Uudmh Odqqpiuqminmin qmhmdiqn dbdmqmpm>
JQ'VPUn.nsnS n.qenot> CU
:dpmfehuddnmqpiuniu ddqqpiuqminmin hniq
•Zmtidqq Iqhhmifimqmpqmn ndlmui } Ifiud Oinnmip nfn :(pqduq«l dqfdiu<t)
Wnqin qmpdtimdqh ddqqpiuqminmin hmq?mtidqq UuBqqiu dqqdfiuqfml
1 ilqliuip qmhmqdbqn •dqqqiufdiun|mpmu dqddmin IqqBmfmhdqq 1 dlqdmh
Uqqpiuqminmm Udmd dulud UuhidUqmu bqp du *} pm|i6iu6mhin
indlqpiul dqqpiudmnmhmu dqd
drmn Uudqdmdqb Oqmppdm? qmhmUuqminmin 'qmpdUmdqh Bqmdq 1 dmp
dmi| OlqqBmfmhdqq huflnqin (srgzJ Odqqpiuqminmin hmqZmbdqn.
;0nmp qmhmdd qmppiul IqqBmq
pijmam 5qp qmfdiuinfmi|mindm qmhmqSqfi qfmdp q hudnqin nflqlhipuh
£l£
nqhinfm qpiudmnmhmq
Ufm arjqfjBmfmhdqq dpmpinmho qqqSmum Iqnqinqm 1 qiqdmh *Уотр1тЬ1
°K» ’* hqqduqZ ‘OdqqpmUqm iuhdq rjq3dqh piupbmhmqi qnmp 3m qdu
‘(f'x + i°m uis 'xVz + /°(P tuis fV) °тз - + '*
.Opiudmnmh
-my Imfqmqy aqmqnmnnh dmpmq q- 'x *piu-($'u) O-U 'LL) bulqdtimUqs
:Bq3qqdo qmfdiuh
-mqZmUdqrj OpiuUqZ qmppdmZ 5 piuqBmfmhdqq 4 ‘°r»l|xi Uqindu ‘huanqtn
(LLL) (/J'x + Aouis V = (/)x
aqqgBmfrnhdqqh Oaqqdo gmppdmZ
qhdhnmp q piuduinurq qmppdmZ (974.) nqhidu aqqini|Uh Onmp 3m piiHfU.)
mtnm *о#з qdq OpiupdmZ pmhduinunK } piuqBmfmhdqr) Odu ‘huaqqdo
(9ZX) /°rou!sVx(j)°x
qmfdiuhmqZmUdqrj} piufidin piuahiqdo ~3 OpiupdmZ qduinmiqBno
<SLL) ::xtW=x?«’ + J
fiudnqin Imfqui
-qy ‘Opiudmnmfimy (1 u) aqqgBmfrnhdqf] *6q-(rzz) '(£’94) hulqhinbo
:Bqqiu(diunqin qdqrjpiuduinunJ Iqbinbo q piudum
-un| kjdmpmy } qiqdmh OpmUqm qdfmpb ?u 3qp qmpdmnm|imy qmppdmZ
qhqqnmp (dmpmy m“/7»3 .qdqqmqbdqq} dduqi) piudfiudqm «x| »|*| q pqp
qm?mqmhmhmd I)- (aFr ddq ‘piudhiqU qdqqdqpdm d3uqi q-э qfmhmn Ьиб
-U3qp qdqqmqBhqiut qiuinmy Udmd ) piu}iuifmymindm piudhiqU qdqrjdqp
-dm qmhmfmpmh q- 3 Odr/qdo (i)x rjmppdm? с/йисптк/бпо gi/mpb ?u
Bqaqpdm qimqtxJqq} hqdl qqqqnmp q Bye
-nqui yimqflqqinutn (xjp } pm|in|mh Oqiufdiudqddmui Uffl QQ dqddmin Odqt]
-piuUqZ (piuatnqb Mn = 3 ‘hmqqdo) (yxq (|FX dqpUuh dqddmin BqadqU rynl
-diuaZhmdmnmhmy dhdhnmp Uudminmh dqqpiuqminmin qqfmpb ?u piu9
-tnqb diuijmybqO du ’aqqinmhq piudu Uqq > 3 > 0 dqqpiuqmm
-min qdqdnfm ‘piupdmZ indqd<t qdminmhh Ohdhnmp hufmqbdqq} 3 Ou
‘Iqbqtn 3qq Uudmh “eddyoaqiufUdm pmhBminn piu-oc§ Imfdqdmdqh qmpp
-dmZ qhdqnmp piuinZmUmpiu qqimlmqBqqinuhi qqamindm fiulqhinbo
:piuinqh £/(0)x: = (t|*
(VLL)
* ?LZfn =
qdi|bmehuqd qmf]m}
ktfimam qmrehuqfmpb ?u ‘nrndQd -mt, йутрбтбтат ddqqbdQupdmq Qb
dmt) pdmd piudqrjpiurjmLnmin ] piuqBqbqmq dqiuMiufjfmqb ?u du nqhiql]q
OqmpBmdmam ddqqhdqupdmq qmWiunJmymqpm-(l гдд)} piudqd
OpiuambZmu ddqqpmbqm qbdmh, /*(r pnHfZZ) du *} piufibdm^
bdq^pdmq bdudhdq } piu|i?uh| Qdu ‘Opmbqm but)
mqiudmtn fimzsoD } piuJiBmfmhdqq OpiupdmZ bfn :0piu6mlq|im qmppdmZ
dpmfdiuri|mymq »rof 1 piuqmfmt] OqiufeJiutiuimqmqpqmam duqdmt] Iqh
•mum Qdqqdo (| \ll) qmpqmmrrun ijqfmpb ?□ gamjztnmfri qmfdiuifimZmp
mqqm qmpbqZ rjhubmlqtimam ifhdonmp fuidqqrputoiubbiu qmtimnmB
•md q qmhmdb ddBqmam x qdlqdmpiub rpuinminnmy цг°уз bquinfn
(HU)
x
Odqqdo qmppdmZ
Imfqmqq } piuhBmum dmpmq ddqqpiuqminmin qdfmpb ?u qpqdiu
(01 u)
:j/:V3 = ‘о !9/г>з = *<?
dqmq
ffwinh ‘Odqqpmbqm inmbm q Odqq6dhmPdub Q- fimz503 piudqnmp njmp
1 8m 3qp qmfeliuZqcim pmfiBminn fiulqqBqdmnmfimq q piu-(g дд) 0-(6’LL)
hulqdbmbqs qq dqqqiuinminnrmi Odqqqiufdiupqp bqindu ‘fiuanqm
<6U)
(ru)
i°(9Z SOO + 'd = (/) *x
Opiupiul ndqdSdqfi hN
soo -1) - = 'x°ro + 'r
-minnh dmpmq ijmTehudQddmtn Qdqqpiuqmuimtn L/tynrjmyuy QmpmpObdt
'zqu+ ’f = 7
Bdpqduqd UdqqfqinQ Jiulq^inbo
:dpm(eliudqddmhi
qgw/^^Z = 7
(K8Z.)
piuijminmin pmrj?mbdqr] ] piut}6mfmt]dqq Opiupdm? pmfrduin
unj? Ортртуиу rjm^mhL/biJi ’qpqdnj
(£’8£) • 7= ’«>
Uqtndu
(rsz.) ‘0 »<**<»+«>
fiua
-nqin (f9£) aqqq6mlmf]dqqt| 0-(Г8£) ‘bupmU
-qm qdfmpb tiulqbhmd^mqmpqmn q dddm?
dduXqgj r)mUBt|rpu<t <huts Jiulqpmdqb
:iDhuintn hmumhmq OqmfdiuUUiu d?m
qmfriqm <b qmpUq? } piuqBmdmam quiqqpup
dpiu qnidiudqmp du ‘ndlmin } BfiuB Ogm?g
mufjdn ВЦспрЬ] qnnpnjmh } qqiufeliuduhmc
-qy ifoudinrjqh Э ijlmdBdqod q- q ‘dpmpinmho
Qa6<]m<jm buijBqm fruinqt] Y 1 Oinrjqpup dJmd6dqr)d i|t]nw)myu5? q- r/ Uqindu
(Г81)
;n
•dSuis^w- = ^-^7
□dnqin Imfqinqu dO’u dmpmy qqmrjrriyu? fjmhmtidbUt
Opiudmnmbmii ddqqmoqpup dompuimhq цаВдтот rjmqmrjubilduq ВтГту
-пйЛли gqmfdiueidmq ddmt]Q ‘UurjBrjm buinqh r :(n | hQ) buq’ufhqnn 6 nmp
-liq? ddBqmam эу dhrnnm^uy Bdflddti qmleliuaZhnndmnmfimd Iqdbmdiuijd
1 dlqdmf] nddnntn pmBmhnmB qqmgmpmp Mdi|d dhmqmpuy :(k) cnqh
-njmh dhnvjmpuy 1 piufrtut] Dinqt] qmpinmq ЦЬЦртЫли UuqBqm fiuqudtn
-qqh i|mU6dqqd qqmqmyu^ inqq dSBqmam qmlynqubUUu> h"*)
-myup qmhmtidbqt 1 piufrtuh Oqdpdmp Uqijhi pmhnjmh ВЦаВОлпат qmhmt)
-ubdduq UuqBqm? buqudinqqh dfmdBdqqq :dqnpiuqmtnmui qiftnuffj •/
аччнтпуиу
'Т.ПЬПЬЦЗПЛЭД'ПЛ Kl ЧПНПЬОбЦЧ; ‘84§
OZE
'qvtpi+q^j
.agmgminnh] ‘piu-(8'84)
qfmhulqdUmbqs 4*/’l*,4 Ц-(4 84) qlmpmpmq Odu *q-) = ,q Bfmo
(184) WPM'J
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йшЦшширпиЮ (iGinbqpbinig oqint[b[nq (76.5') 6UuQin|iinipjniGbg.
Ф2 = 2a>o(eosp-cos0c), (78.10)
npinbq hiU2i|b bG шоОЦшб hbinL}W[ uQqpGuil|iuG iqiujtkuGGbpo'
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hGuibqpbinQ (78.1 Q)-q l|uinwGwG₽
= f-^_±— -' f,
Jo ^cos^-cos^ y/2 %
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QbppfiG hGinbqpiutfi GpGpniGh hbinbjiui inbupg.
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0
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x(/)-f'’(4«“ + V*): (79.6)
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A! L A3 -o ul|qpGwl|UjG imjujdiuGGbplig npnzQnq huJuinujinniGGbp bG:
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bpp (79.5) ObdntpjniGo ppwUuiG t: Uju pbiqpnuJ (79.6) (Шдтйр Quipiniu-
hcujini||i (hpwGujG inbupnQ)
x(r) = A^e'r‘ создам + <z>) (79.8)
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npp hwuiniuinniG a) hiu6aj|unipjuji5p. puijg dujdiuGujl|p oGpujgpnid GQiuqnq
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162.2 ий'4
5.997-1027 q
6.378-10* ий
5.517 q/ий3
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11.2 Цй'4
1.99- IO”q
6.96- 10’° ий
1.41 фий3
617.7-Цй/4
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