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peeeo a oac ycooc ec oac, yp oopo apaea pxoa oopa cooecye oac c ao co ex ope. B pao oac epec aee apaepa v o oy pepe ccea poepec a ycooc.

Pc. 6.43 -paee o ooy apaepy Ta a v eeceoe co, o oyeo oac e oo opeo eeceo oc, eae oac ycooc, apep, opeo AB.

6.9.3 -paee o y apaepa Ha pae aco peyec c e a ycooc yx, a e ooo apaepa.

Xapaepcecoe ypaee o cyae poc y:

D(s) = N(s) + M(s) + L(s) = 0, (6.63) oca s = i, oya ypaee pa -pae D(i) = N(i) + M(i) + L(i) = 0. (6.64) Ec ooa (6.65) o ypaee pa oo pa a a:

N1 () + M1 () + L1 () = 0; (6.66) N2 () + M2 () + L2 () = 0.

oce ccea peaec ooceo apaepo :

= ; =, (6.67) e aaa pae ae aco o - o, aoo ee ae o apaepec ypae opeec e cpoc paa -pae.

p o oo ceye p cya.

1 p aao acoe opeee 0; 1 0; 2 0 o o y. Bo cyae ccea coeca, ypae (6.66) peca coo pe ococ - (pc. 6.44, a).

Pc. 6.44 cpa cyecoa pee cce ypae (6.66):

a - peee cyecye; oex pee e;

- peee eopeeeo 2 p eoopo ae = 0, a 1 0; 2 0. Toa ccea (6.66) ecoeca, oex pee e. pe 1 2 apae (pc. 6.44, ).

3 p eoopo ae ce opeee pa y, oa caoc eopeee. pe 1 2 cac py c pyo, o cyae oya e oy, a, a aaey, ocoy py (pc. 6.44, ), ypaee oopo:

N1() + M1() + L1() = 0. (6.68) Ocoa pa e oocc po -pae, a a ce ee oa cooecye oo o e aee aco, apaee e o e ycao eooo.

B ocoo ocoe pe oa p = 0 =, o o cyae, oa an = 0 o a0 = 0, cooeceo. Ec a0 an e ac o , o ocoe pe ocycy.

oce ocpoe pa -pae ocox px eoxoo x apxoa, oyc cey pao: p opaca o - o paa pae pxyec cea, ec > 0, cpaa, ec < 0.

Ta a c e y, o pa -pae ooex opaex aco coaa, ooy py -pae oxo a, oa cea pxyec oo pxoo.

pxoa ocox , a pao, oapa pxyec a, o ecax cope c -pae apxoae eapxoae copo po po apae py pyy (pc. 6.45 a, ).

B ex cyax, oa ocoa pa ee eco p eoopo oeo ae aco = 0 p o poxo epe y ee a, ocoa pa pxyec coaco pay, o oo pxoo (pc. 6.45, ). Ec e e ee a, o ocoa pa e pxyec paccope pacaec (pc. 6.45, ).

oce aece pxo opee oac, peeyy a oac ycooc, .e. oac, yp oopo apaea pxoa.

epeceee pa -pae apxoao o eapxoay cooecye epexoy yx oeco-cope-x ope eo oyococ ope pay, aoopo. epeceee ocoo po c oo pxoo cooecye epexoy ooo op.

Pc. 6.45 pao pxo ocoo po p -pae o y apaepa:

a, - oapa pxoa; - oa pxoa; - e pxyec 6.10 CTOBOCT CCTEM C AABAHEM CCTEM C PPAOHAHM BEHM Bce peae cce aoaecoo peypoa c ccea c aaae. Heoxo ocao ycoe ycooc ex cce c oco aaae ec pacooee cex ope xapaepcecoo ypae eo oyococ.

Heocpeceoe axoee ope xapaepcecoo ypae apyeo, c c eo paeeoc, ooy pe pep ycooc. Oao oo ope pe oo pep ycooc Haca.

Ec Wp.c(i) - ayo-aoa xapaepca paoyo cce e aaa, a Wp.c. (i) - ayo-aoa xapaepca paoyo cce c aaae, o oo aca:

Wp.c.(i) = Wp.c(i)e-i;

M() = M();

() = () -.

pa AX paoyx cce e aaa c aaae pecae a pc. 6.46. a o paa, AX paoyo cce c aaae apyaec, a a aa p ee aco o 0 o + eec o 0 o -.

Ec e pe aaa, o oo a, a aaeoe, pecoe aee, p oopo ccea ye axoc a pae ycooc.

Pc. 6.46 AX paoyo cce c aaae oo pecoo cya cpaea ac Wp.c. (ip) = = 1. (6.68) coooe (6.68) oo aca ae aoacoo xapaepc, p oopx epeceaec opaea ecea oc, .e.

(ip) = (p) pp = (2j + 1), (6.69) e j = 0, 1, 2,..., oya (6.70) Maoe pecoe pe aaa ec pa opeeec p j = 0:

(6.71) Eo oo opee paec cocoo, oo pooc opyoc eoo payca a ococ AX, ee epeceee c AX paoyo cce e aaa opeee (p), a c aaae ooe opee p cooeceo p.

6.11 TPEHPOBOHE AAH 1 Bca ccea aoaecoo ypae oa paoa ycoo. o ycooc oaec cocooc cce opaac epoaaoe cocoe oce c oye, .e. y(t) 0 p t. Heoxo ocao ycoe ycooc ec opaeoc eceo ac cex ope xapaepcecoo ypae.

A aa ccea aaec epao B ye ccea aoaecoo ypae ycoo, ec op xapaepcecoo ypae:

S1 = -2; S2,3 = -3 + 4i; S4 = 5 C ye ccea aoaecoo ypae ycoo, ec op xapaepcecoo ypae pacooe cea o o oc 2 oea a opoc o ycooc cce aoaecoo ypae coyc pep ycooc, ooe cy o ycooc, e axo eo ope. ep ec eoxooe ycoe, coaco oopoy ce oe xapaepcecoo ypae o ooe. Ceye pyo pepe c aepaece pep ycooc, pee ceo, o pep Payca pep ypa.

A ax cce aoaecoo ypae eoxooe ycoe ycooc ec ocao B Ec xapaepcecoe ypaee cce 3S3 + 4S2 + 2S + 1 = 0, o cooec c pepe ypa a ccea a) ycoa;

) eycoa;

) axoc a pae ycooc.

C a cxo a eoxoo pacoaa, o cceoa ycooc oo o pe pep Payca 3 cceoa ycooc poo pec acoe pep ycooc. B cooec c pepe Mxaoa cpoc oopa Mxaoa, oop ycox cce oe aac a eceo ooeo oyoc, oxo oceoaeo, yxo ecoeoc, e e opaac y, n apao oopao ococ, e n - opo xapaepcecoo ypae.

Bop aco pepe ec pep Haca, oo cy o ycooc ayo cce o AX paoyo cce, pe paoya ccea oe ycoo, eycoo epao, o aya ccea p oe opeeex yco oe o cex cyax ycoo A Copypye pep Haca cya, oa paoya ccea e ycoa.

B ye ycoa ccea aoaecoo ypae cooec c pepe Mxaoa, ec ecea y Mxaoa U() = 2 - 32;

a y Mxaoa V() = + 33 C yc paoya ccea ycoa ee AX:

ye aya ccea ycoo 6.12 TECT 1 aa ecx cce ye ycoo 2 aa ccea aaec ycoo, ec oce c oye A Ccea e opaaec cxooe cocoe.

B pae ooe ycaoeec cocoe, ooe o epoaaoo.

C Ccea opaaec cxooe cocoe.

3 aa cce, ocaex ypaee, ye eycoo A y''(t) + 2 y'(t) +3 y(t) = 0.

B y'''(t) + y''(t) +4 y'(t) + 3 y(t) = 0.

C y''(t) - y'(t) + y(t) = 0.

4 Oe ee xapaepcecoe ypaee a3s3 + a2s2 + a1s + a0 = 0. ao opeeee ec opeeee ypa:

A ;

B ;

C.

5 Coaco aepaecoy pep ypa ccea ycoa, ec A Bce aoae op aoo opeee ypa ooe.

B a opeee ypa ooee, a aoae op opae.

C aoae op aoo opeee ypa eoo opa ooe, eeoo opae.

6 aa cce coaco pep Mxaoa ye ycoo, ec oopa Mxaoa ee 7 aa cce coaco pep Mxaoa ye axoc a pae ycooc:

8 a o op xapaepcecoo ypae ycoo cce A C opaeo eceo ac.

B C ooeo eceo ac.

C oeco-copee c opae ooe ece ac.

9 aa cce ye ycoo, ec ecea a y Mxaoa e 10 yc paoya ccea ycoa, o aa ayx cce ye ycoa, ec AX paoyo cce ee :

11 yc paoya ccea epaa, o aa aya ccea ye ycoa, ec AX paoyo cce ee :

12 yc paoya ccea e ycoa, o aa aya ccea ye ycoa, ec AX paoyo cce ee :

7 OECEEHE CTOBOCT 7.1 CTOBE HECTOBE BEH COEHEH Bce e cce aoaecoo peypoa opaec a ycoe eycoe. Ta, eeape e, a ye oeaoc, c yco, cee cocae eppyee eo, ooceec pye epax ee.

Heycoe e e oc pao oyococ aoee pacpocpae pepo ax ee ec aepooe eo.

Ha ycooc cce oaa e apaep peypyeoo oea. oo, o ccea a cao, eoxoo oece peye aac ycooc, pe, ec apaep opeee peo oy ec poecce cyaa cce, o aac ycooc ceye aa o, e p oo ycaoex eex apaepax. ocee ycooc ooo ocyec ae opo cooecyx eeo cce peypoa. B acoc, ceye pa ae acpo peyopo, o ccea a ycoo.

ae ceo opee acpo peyopo, p oopx op xapaepcecoo ypae ayo cce axoc a o oc (ACP axoc a pae ycooc) oo, o ae o ec eoa coa ycoy ACP c aa coca.

7.2 CHTE CTOBX CCTEM Ce ycox cce aoaecoo peypoa coc, a yoyo e, opy acpoe peyopo a opao, o aya ccea aoaecoo peypoa a ycoo.

Coaco pep Haca paa ycooc opeeec ypaee Wo(i)Wpe(S0, S1, S2, i) = -1, (7.1) eoepec opaa a poxoe AX paoyo cce epe oy (-1, i0). ec Wpe(S0, S1, S2, i) - AX -peyopa; S0, S1, S2 - acpo peyopa. a eco -aoa peypoa oo oy pae ao peypoa. Paccop ce ycoo oooypo cce peypoa c pa a peyopo.

7.2.1 ocpoee pa ycooc cce c -peyopo paa ycooc, opeeea o ypae (7.1), cce c -peyopo aec a Wo(i)Wpe(S0, S1, i) = -1. (7.2) oceee ypaee oo aca e cce ypae, coy ayo-acoe aoacoe xapaepc:

(7.2, a) eecee e acoe xapaepc:

(7.2, ) B ococ apaepo acpoe S0, S1 -peyopa cpoc paa ycooc (pc. 7.1) o ypae (7.2), oopx o aao acoe opeec acpo S0 S1. oyea pa ec pae ycooc, e o po pacoaaec oac ycoo pao, a e - oac eycoo pao cce peypoa.

To 1 2 a po cooecy pae ycooc - -peyopo.

Pc. 7.1 paa ycooc cce c -peyopo 7.2.2 pa ycooc cce c -peyopo Ec ccee aoaecoo peypoa coyec -peyop c epeaoo ye Wpe (s) = -S1, o ccea ypae (7.2) pae :

(7.3) opoo ypae cce (7.3) opeeec paoa acoa p (pc. 7.2), cooecya pae ycooc, o oopo epoo ypae opeeec peeoe aee acpo S1:

(7.4) Pc. 7.2 Opeeee aco pa ycooc cce c -peyopo peeoe aee acpo -peyopa S1 oo opee paec eoo, coy coooee Wo(i) S1 = 1. Ec p, o S1 = 1, o opeo d a opaeo eeceo oyoc ooc opeeec AX oea cooecye ee eceo ac p paece o y. B o cyae AX paoyo cce coaae c AX oea.

Pc. 7.3 paecoe opeeee peeoo ae acpo -peyopa eee acpo S1 po oy, o AX paoyo cce aae yeac oceae a eeceo opaeo oyoc opeo r = dS1.

aeee yeee S1 po oy, o p ao-o ae S1 AX paoyo cce poe epe oy (-1, i0), .e. ccea e a pay ycooc r = 1. o aee S1 ye c pee opeec coooe dS1pe = 1, ceoaeo, S1pe=, .e. opeee acpo ocaoo ocpo AX oea ep opeo d.

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