182

IHJY>HD <UIHEG?GBY J:;HLU

1. Ihke_ \dexq_gby gZkhkZ, ih^Zxs_]h \h^m \ gZihjguc [Zd, hldjulb_f

j_]mebjmxs_c aZ^\b`db gZ iblZxs_f ljm[hijh\h^_ mklZgZ\eb\Z_lky

g_h[oh^bfuc jZkoh^ \h^u \ ]b^jZ\ebq_kdhf ehld_.

2. K bkihevah\Zgb_f baf_jbl_evgh]h \h^hkeb\Z, mklZgh\e_ggh]h \ f_jghf

ehld_, baf_jy_lky jZkoh^ \h^u (ih^jh[g__ kf. jZ[hlm 4) b ^Zggu_ ih baf_j_gbx

jZkoh^Z aZghkylky \ lZ[ebpm 18.1.

LZ[ebpZ 18.1

Hlf_ldZ

\_jrbgu

lj_m]hevgh]h

baf_jbl_evgh]h

\h^hkeb\Z, �1, kf

Hlf_ldZ

k\h[h^ghc

ih\_joghklb

\h^u i_j_^

\h^hkeb\hf, �2 ,

kf

GZihj gZ

\h^hkeb\_,

�2 - �1, kf

Baf_j_gguc

jZkoh^ \h^u,

Q, e/k

3. K ihfhsvx aZl\hjZ - `Zexab, mklZgh\e_ggh]h \ dhgp_ ehldZ \ gb`g_f

[v_n_, mklZgZ\eb\Z_lky ]em[bgZ ihlhdZ h[, g_h[oh^bfZy ^ey h[jZah\Zgby

hlh]gZggh]h kh\_jr_ggh]h ]b^jZ\ebq_kdh]h iju`dZ.

4. Ijb mklZgh\b\r_fky ^\b`_gbb \h^u gZ [ukljhlhd_ b]hevqZluf

mjh\g_f_jhf nbdkbjmxlky hlf_ldb ^gZ fh^_eb b k\h[h^ghc ih\_joghklb gZ

\oh^_, \ k_q_gbyo 1-1, 2-2, 3-3 b gZ \uoh^_ k \h^hkdZlZ. H^gh\j_f_ggh

baf_jyxlky jZkklhygby hl \oh^gh]h k_q_gby gZ \h^hkdZl_ ^h k_q_gbc 1-1, 2-2, 3-3

b \uoh^gh]h k_q_gby. JZkklhygb_ L hl \oh^gh]h ^h \uoh^gh]h k_q_gby _klv ^ebgZ

\h^hkdZlZ.

183

Ih jZaghklb hlf_lhd hij_^_eyxlky ]em[bgu h \ khhl\_lkl\mxsbo k_q_gbyo

b mdehg ^gZ [ukljhlhdZ i . J_amevlZlu baf_j_gbc b ih^kq_lh\ aZghkylky \

lZ[ebpm 18.3.

LZ[ebpZ 18.3

F_klh

baf_j_gby

JZkklhygb_ hl

\oh^gh]h

k_q_gby

\h^hkdZlZ

Hlf_ldZ

k\h[h^ghc

ih\_joghklb,

�1

Hlf_ldZ ^gZ

\h^hkdZlZ, �

=em[bgZ

h =�1 - �

JZaf_jghklv kf kf kf kf

GZ \oh^_

\h^hkdZlZ

< k_q_gbb 1-1

< k_q_gbb 2-2

< k_q_gbb 3-3

GZ \uoh^_ k

\h^hkdZlZ

>ebgZ \h^hkdZlZ L = kf

H;J:;HLD: HIULGUO >:GGUO

1. <uqbkeyxl mdehg ^gZ \h^hkdZlZ i = sinE , l._.

L

i \uo\o ��� (18.1)

184

2. <uqbkeyxl djblbq_kdbc mdehg ^gZ ih nhjfme_

bC

gi

d

dd 2D

F (18.2)

]^_ b– rbjbgZ fh^_eb (ehldZ) [ukljhlhdZ; $ - kfhq_gguc i_jbf_lj ijb

]em[bg_ ihlhdZ, jZ\ghc djblbq_kdhc ]em[bg_ hd, dhlhjZy \uqbkey_lky ih nhjfme_,

32q

ghd

D (18.3)

dhb 2� F (18.4)

D # 1- dhwnnbpb_gl DhjbhebkZ (dhjj_dlb\ dbg_lbq_kdhc wg_j]bb); g – mkdhj_gb_

kbeu ly`_klb; Kd – dhwnnbpb_gl R_ab, \uqbkey_fuc ijb djblbq_kdhc ]em[bg_

ih nhjfme_

611

Rn

Kd , (18.5)

n – dhwnnbpb_gl r_jhoh\Zlhklb \h^hkdZlZ, agZq_gb_ dhlhjh]h mklZgZ\eb\Zxl ih

kijZ\hqguf ^Zgguf [30,35]; R – ]b^jZ\ebq_kdbc jZ^bmk, hij_^_ey_fuc ih

nhjfme_ ijb djblbq_kdhc ]em[bg_,

d

ddR

FZ

, (18.6)

&d – iehsZ^v `b\h]h k_q_gby, ijb djblbq_kdhc ]em[bg_

185

bhdd Z , (18.7)

q - m^_evguc jZkoh^, jZ\guc Q/b .

J_amevlZlu \uqbke_gbc aZghkyl \ lZ[ebpm 18.4.

LZ[ebpZ 18.4

OZjZdl_jbklbdZ

M^_evguc

jZkoh^

, q

Djblbq_kdZy

]em[bgZ

k_q_gby,

hd

IehsZ^v

`b\h]h

k_q_gby,

&d

Kfhq_gguc

i_jbf_lj

, $ d

=b^jZ\ebq_kdbc

jZ^bmk,

Rd

Dhwnnbpb_gl

R_ab

, Kd

Djblbq_kdbc

mdehg

,

i d

JZaf_jghklv

f2/k f f

2 f f f

0,5/k

AgZq_gby

3. Hij_^_eyxl agZq_gby ghjfZevghc ]em[bgu h0 ]jZnbq_kdbf kihkh[hf,

bkihevamy mjZ\g_gb_ b

RiCQ Z , (18.8)

aZf_j_ggu_ agZq_gby jZkoh^Z \h^u Qi rbjbgu [ukljhlhdZ b b mdehgZ [ukljhlhdZ

i. >ey wlh]h aZ^Zxlky ijhba\hevgufb agZq_gbyfb ]em[bgu h0 , ih dhlhjhc

\uqbkeyxl iZjZf_lju, \oh^ysb_ \ nhjfmem (18.8), b jZkoh^ \h^u Q, ^h[b\Zykv

jZ\_gkl\Z \uqbke_ggh]h jZkoh^Z baf_j_gghfm jZkoh^m. J_amevlZlu \uqbke_gbc

aZghkyl \ lZ[ebpm 18.5.

186

LZ[ebpZ 18.5

=em[bgZ,

h, f

IehsZ^v

k_q_gby,

&, f2

Kfhq_gguc

i_jbf_lj,

$, f

=b^jZ\ebq_

kdbc

jZ^bmk, R, f

Dhwnnbpb_

gl R_ab,

K, f0,5

/k

<uqbke_g

guc

jZkoh^, Q,

f3/k

Ih ^Zgguf lZ[ebpu 18.5 kljhblky ]jZnbd k\yab Q = f(h) gZ fbeebf_ljh\hc

[mfZ]_, jbk. 18.3.

Jbk. 18.3

Ih baf_j_gghfm jZkoh^m Qbaf kgbfZxl k ]jZnbdZ bkdhfmx ghjfZevgmx

]em[bgm gZ \h^hkdZl_ h0.

4. KjZ\gb\Zxl hiulgh_ b \uqbke_ggh_ agZq_gby mdehgh\ ^gZ fh^_eb

[ukljhlhdZ i c djblbq_kdbf mdehghf Id; ]em[bgu gZ \oh^_ [ukljhlhdZ h\o k

djblbq_kdhc ]em[bghc hd, lZd dZd gZ \oh^ghc qZklb [ukljhlhdZ kihdhcguc ihlhd

i_j_oh^bl \ [mjguc b wlh y\e_gb_ khijh\h`^Z_lky i_j_oh^hf q_j_a djblbq_kdmx

187

]em[bgm; ]em[bgu gZ \uoh^_ [ukljhlhdZ h\uo k ghjfZevghc ]em[bghc h0 , lZd dZd \

ij_^_e_ g_jZ\ghf_jgh_ ^\b`_gb_ \h^u \ujh`^Z_lky \ jZ\ghf_jgh_, dhlhjhfm

k\hckl\_ggZ ghjfZevgZy ]em[bgZ. J_amevlZlu \ghkyl \ lZ[ebpm 18.6.

LZ[ebpZ 18.6

Ghf_j

hiulZ

Mdehg

^gZ

[ukljhlh

dZ, i

Djblbq_k

dbc

mdehg, id

=em[bgZ

\h^u gZ

\oh^_,

h\o

Djblbq_kdZ

y ]em[bgZ,

hd

=em[bgZ

\h^u gZ

\uoh^_,

h\uo

GhjfZev

gZy

]em[bgZ,

h0

JZaf_jg

hklv

5. Hij_^_eyxl ]em[bgu hl l_hj_lbq_kdhc djb\hc k\h[h^ghc ih\_joghklb \

k_q_gbyo 1-1, 2-2, 3-3 b \uoh^ghf ih \ujZ`_gbx, ihemqZ_fhfm gZ hkgh\_

mjZ\g_gby ;_jgmeeb

� �0

l2 HZg

qh

� M

, (18.9)

]^_ Z – jZaghklv f_`^m hlf_ldZfb ^gZ gZ ]j_[g_ \h^hkeb\Z b \

jZkkfZljb\Z_fhf k_q_gbb gZ m^Ze_gbb l hl \oh^gh]h k_q_gby, Z = �\o - �^g;

G0 - iheguc gZihj g

VGG

2

20

0

D� ; G - ]_hf_ljbq_kdbc gZihj gZ \h^hkeb\_, G =

�\h^ - �\o; V0 – kj_^gyy kdhjhklv \ k_q_gbb ihlhdZ gZ ih^oh^_ d [ukljhlhdm

HJ

qV

� 0 , (18.10)

M - dhwnnbpb_gl kdhjhklb, agZq_gb_ dhlhjh]h fh`gh hij_^_eylv ih mjZ\g_gbx

188

M = 1,02 – (0,038 – 0,05i)dh

Z. (18.11)

Jbk. 18.4

J_amevlZlu jZkq_lZ \ghkyl \ lZ[ebpu 18.7 b 18.8.

LZ[ebpZ 18.7

Hlf_ldb

�\h^ �\o �

G= �\h^

- �\o J = �\o - � q V0 G0

LZ[ebpZ 18.8

K_q_gby IZjZf_lju

1-1 2-2 3-3 \uo

Z, kf

M

hl, kf

6. Ih hiulguf ^Zgguf \ fZkrlZ[_ \uq_jqb\Zxl gZ fbeebf_ljh\hc [mfZ]_

ko_fm [ukljhlhdZ k ebgbyfb djblbq_kdhc (D-D) b ghjfZevghc (N-N) ]em[bg b ih

189

hiulguf b l_hj_lbq_kdbf ]em[bgZf \ k_q_gbyo kljhyl h[_ djb\u_ k\h[h^ghc

ih\_joghklb \h^u gZ \h^hkdZl_ (hiulgmx b l_hj_lbq_kdmx). Hij_^_eyxl lbi

djb\hc.

7. < p_eyo khihklZ\e_gby djb\uo \uqbkeyxl hldehg_gby \ % hj^bgZl 'h

l_hj_lbq_kdhc djb\hc k\h[h^ghc ih\_joghklb \h^u hl hj^bgZl hiulghc djb\hc b

j_amevlZlu \ghkyl \ lZ[ebpm 18.10

1001100l% ¸

¹

ᬩ

§ � �

'h

h

h

hhh l (18.12)

LZ[ebpZ 18.10

K_q_gby IZjZf_lju

1-1 2-2 3-3 \uo

hl, kf

h, kf

'h%

J:;HL: 19

BAMQ?GB? ><B@?GBY <H>U < IJ?>?E:O ><MOKLMI?GQ:LH=H

I?J?I:>: DHEH>?AGH=H LBI: B IJH<?JD: MKEH<BC

KHHL<?LKL<BY FH>?EB KHHJM@?GBY IJHIMKD:?FHFM J:KOH>M

<H>GH=H IHLHD:

P_ev jZ[hlu: 1. GZ[ex^_gb_ ^\b`_gby ihlhdZ gZ fh^_eb i_j_iZ^Z ijb

jZaebqguo k[jhkguo jZkoh^Zo, dh]^Z ^ebgZ klmi_g_c ^hklZlhqgZ, b \ kemqZ_,

dh]^Z ^ebgZ bo g_^hklZlhqgZ.

2. Ih^[hj hkgh\guo jZaf_jh\ fh^_eb i_j_iZ^Z, \ gZb[hevr_c f_j_

khhl\_lkl\mxsbo hiulghfm jZkoh^m \ mkeh\byo ghjfZevghc jZ[hlu i_j_iZ^Z.

190

3. <uiheg_gb_ baf_j_gbc, g_h[oh^bfuo ^ey ihkljh_gby ijh^hevgh]h

ijhnbey k\h[h^ghc ih\_joghklb ihlhdZ \ ij_^_eZo i_j_iZ^Z ijb hiulghf

jZkoh^_.

4. Ijh\_jdZ gZ hkgh\_ ]b^jZ\ebq_kdh]h jZkq_lZ hkgh\guo jZaf_jh\ fh^_eb

i_j_iZ^Z ijb hiulghf jZkoh^_ \h^u.

H;SB? K<?>?GBY

I_j_iZ^u mkljZb\Zxlky gZ dZgZeZo, ijhe_]Zxsbo gZ f_klghklb k [hevrbf

mdehghf. ;eZ]h^Zjy mkljhckl\m i_j_iZ^Z fh`gh mf_gvrblv \_ebqbgm mdehgZ ^gZ

dZgZeZ b l_f kZfuf kgbablv \ g_f kdhjhklv ^\b`_gby \h^u. Bgh]^Z i_j_iZ^u

\oh^yl \ dhfie_dk ]b^jhl_ogbq_kdbo khhjm`_gbc jZaebqgh]h gZagZq_gby. Ijb

khhjm`_gbb Z\lhfh[bevguo ^hjh] i_j_iZ^u ijbf_gyxlky \ dx\_lZo gZ

dhkh]hjZo, gZ \uoh^_ ihlhdZ ba-ih^ fhklh\ b ljm[, ijb k[jhk_ \h^u ba

\h^hhl\h^guo dZgZeh\ \ ihgb`_ggu_ f_klZ b l.i. < aZ\bkbfhklb hl \ukhlu

iZ^_gby f_klghklb i_j_iZ^u fh]ml [ulv h^ghklmi_gqZlufb b

fgh]hklmi_gqZlufb, dheh^_agh]h b [_kdheh^_agh]h lbiZ. < f_klghklv emqr_

\ibku\Zxlky i_j_iZ^u dheh^_agh]h lbiZ.

>\moklmi_gqZluc i_j_iZ^ dheh^_agh]h lbiZ ij_^klZ\e_g gZ jbk. 19.1.

?]h hkgh\gufb we_f_glZfb y\eyxlky: Z) \oh^gZy qZklv, ij_^klZ\eyxsZy

kh[hc h[uqgh \h^hkeb\ k rbjhdbf ihjh]hf beb \h^hkeb\ ijZdlbq_kdh]h

ijhnbey; [) kl_gdZ iZ^_gby j, dhlhjZy fh`_l [ulv \_jlbdZevghc, gZdehgghc b

djb\hebg_cghc; _z \ukhlZ gZagZqZ_lky jZ\ghc 0,3-1,0 f, Z bgh]^Z b ^h 3 f b

dhgdj_lgh aZ\bkbl hl f_klguo mkeh\bc, l._. hl \hafh`ghklb \ibkZlv khhjm`_gb_ \

f_klghklv; \) \h^h[hcgZy qZklv (\h^h[hc) ijh_dlbjm_lky ]hjbahglZevghc, gh

fh`_l [ulv b k ijyfuf mdehghf; \ dhgp_ \h^h[hy mkljZb\Z_lky \h^h[hcgZy

kl_gdZ jkl, dhlhjZy ij_^klZ\ey_l kh[hc qZs_ \k_]h \h^hkeb\ ijZdlbq_kdh]h

ijhnbey; ]) \uoh^gZy qZklv ij_^klZ\e_gZ \h^h[hcguf dheh^p_f k mklmihf (beb

\h^h[hcghc kl_gdhc).

191

Jbk. 19.1

192

Ijb ijh_dlbjh\Zgbb fgh]hklmi_gqZluo i_j_iZ^h\ klj_fylky aZ^Z\Zlv

h^bgZdh\mx \ukhlm klmi_g_c k h^bgZdh\ufb \h^hkeb\Zfb gZ ijhf_`mlhqguo

klmi_gyo, qlh[u mkeh\by ^\b`_gby \h^u gZ gbo [ueb koh^gufb.

Khijy`_gb_ mjh\g_c gZ i_j_iZ^_ hkms_kl\ey_lky \ j_amevlZl_ ^\b`_gby

ihlhdZ ih klmi_gyf, ihklmie_gb_ \h^u gZ dZ`^uc \h^h[hc ZgZeh]bqgh bkl_q_gbx

q_j_a khhl\_lkl\mxsbc \h^hkeb\. GZ^h hlf_lblv, qlh i_j_iZ^u dheh^_agh]h lbiZ

\k_]^Z ijh_dlbjm_lky k lZdbf jZkq_lhf, qlh[u \h^hkeb\gu_ maeu bo

(h[jZah\Zggu_ \h^h[hcgufb kl_gdZfb beb, \ kemqZ_ i_j\hc klmi_gb, ^hgguf

keb\hf) jZ[hlZeb dZd g_ih^lhie_ggu_ \h^hkeb\u, Z ih^ i_j_eb\Zxsb_ky kljmb

^he`_g h[_ki_qb\Zlvky k\h[h^guc ih^\h^ \ha^moZ. B ihkdhevdm h^gbf ba

hkgh\guo ij_^gZagZq_gbc \h^h[h_\ i_j_iZ^Z y\ey_lky ]Zr_gb_ ba[ulhqghc

dbg_lbq_kdhc wg_j]bb, gZdhie_gghc ijb bkl_q_gbb q_j_a \h^hkeb\u \ k`Zlhf

k_q_gbb kljmb, lh \ ij_^_eZo \h^h[h_\ ij_^mkfZljb\Z_lky kha^Zgb_ mkeh\bc ^ey

\hagbdgh\_gby aZlhie_ggh]h ]b^jZ\ebq_kdh]h iju`dZ. < agZqbl_evghc f_j_ wlhc

p_eb kihkh[kl\m_l mkljhckl\h \h^h[hcghc kl_gdb beb mklmiZ \ dhgp_ \h^h[hy,

ijb wlhf `_ khdjZsZ_lky ^ebgZ \h^h[hcghc qZklb.

Ba \ur_ kdZaZggh]h klZgh\blky ykguf, qlh m fgh]hklmi_gqZluo i_j_iZ^h\

dheh^_agh]h lbiZ ]b^jZ\ebq_kdhfm jZkq_lm gZ^h ih^\_j]Zlv lhevdh ljb klmi_gb –

i_j\mx, \lhjmx b ihke_^gxx, lZd dZd mkeh\by ijhl_dZgby \h^u \ ij_^_eZo wlbo

klmi_g_c jZaebqgu_. Mkeh\by ijhl_dZgby gZ ijhf_`mlhqguo klmi_gyo lZdb_ `_,

dZd b gZ \lhjhc klmi_gb. Ihwlhfm ijhf_`mlhqgu_ klmi_gb g_ jZkkqblu\Zxl, Z

jZaf_ju bo ijbgbfZxl lZdbfb, dZd b jZaf_ju \lhjhc klmi_gb.

GZ \h^h[hyo i_j_iZ^h\ dheh^_agh]h lbiZ ij_^mkfZljb\Z_lky h[jZah\Zgb_

ih^i_jluo ]b^jZ\ebq_kdbo iju`dh\, gZqZeh dhlhjuo kh\iZ^Z_l kh k`Zluf

k_q_gb_f, beb k g_agZqbl_evguf aZlhie_gb_f k_q_gby. Kl_i_gv aZlhie_gby

ijbgylh oZjZdl_jbah\Zlv dhwnnbpb_glhf aZiZkZ (beb dhwnnbpb_glhf

aZlhie_gby) 13, ij_^klZ\eyxsbf kh[hc hlghr_gb_ aZlZieb\Zxs_c ]em[bgu haZl

193

dh \lhjhc khijy`_gghc ]em[bg_ iju`dZ h˝, l._. 13 = haZl/ h˝ AgZq_gb_ 13

ijbgbfZxl 13 = 1…1,1.

>ebgm \h^h[hy m\yau\Zxl k ^ebghc ih^i_jlh]h iju`dZ, Z g_ k gZebqb_f

\h^h\hjhlguo h[eZkl_c b bo jZaf_jZfb – dZd \ ijhreu_ ]h^u. Wlh hagZqZ_l, qlh

\h^h[hc gZ^h mkljZb\Zlv lhevdh lZf, ]^_ gZ[ex^Z_lky [mjgh_ ^\b`_gb_ ihlhdZ.

Dhg_p wlh]h ihlhdZ kh\iZ^Z_l k k_q_gb_f, \ dhlhjhf ljZgablgZy kljmy ^hklb]Z_l

fbgbfmfZ wg_j]bb, l._. k f_klhf, ]^_ gZqbgZ_lky kihdhcgh_ ^\b`_gb_ ihlhdZ.

=em[bgZ ljZgablghc kljmb \ wlhf k_q_gbb jZ\gZ djblbq_kdhc ]em[bg_ (ht = hd).

Hq_\b^gh, qlh ih^ ih^i_jluf iju`dhf gZ^h ihgbfZlv lZdhc iju`hd, \ dhlhjhf

ljZgablgZy kljmy i_j_^ ]Zkbl_e_f mki_\Z_l jZkrbjblvky ^h djblbq_kdhc ]em[bgu

ijb gZebqbb ^hklZlhqgh jZa\blh]h ih\_joghklgh]h \h^h\hjhlZ.

Ih^i_jlu_ iju`db h[jZamxlky \ j_amevlZl_ ^hihegbl_evgh]h \ha^_ckl\by

gZ ihlhd ]Zkbl_e_c wg_j]bb. Wlh \ha^_ckl\b_ oZjZdl_jbam_lky: 1) kh\f_klguf

\ebygb_f gZ ihlhd ]Zkbl_ey wg_j]bb b ^Z\e_gby \h^u \ hl\h^ys_f jmke_;

2) lhevdh j_Zdlb\guf ^_ckl\b_f ]Zkbl_ey, dh]^Z mjh\_gv \h^u \ G; g_ \eby_l gZ

h[jZah\Zgb_ ih^i_jlh]h iju`dZ, ihke_^gb_ gZau\Zxl kZfhh[jZamxsbfbky (jbk.

19.2).

Jbk. 19.2

GZ \h^h[hyo i_j_iZ^Z ij_^mkfZljb\Zxl g_kZfhh[jZamxsb_ky ih^i_jlu_

iju`db (jbk. 19.3).

194

Jbk. 19.3 Z

Jbk. 19.3 [

=_hf_ljbq_kdb_ jZaf_ju we_f_glh\ i_j_iZ^Z dheh^_agh]h lbiZ, Z bf_ggh –

\ukhlu \h^h[hcghc kl_gdb, ]em[bgu \h^h[hcgh]h dheh^pZ, ^ebgu \h^h[h_\

hij_^_eyxlky ]b^jZ\ebq_kdbf jZkq_lhf ih aZ^Zgghfm beb jZkq_lghfm jZkoh^m

\h^u. ?keb hjb_glbjh\Zlvky gZ h[s_ijbagZggmx ko_fm ih^i_jluo iju`dh\ (jbk.

19.4), lh ]b^jZ\ebq_kdbc jZkq_l gZ^h \uihegylv ijb jZkkfhlj_gbb ^\b`_gby

195

\h^u ba \h^h[hcgh]h dheh^pZ, ZgZeh]bqgh]h ^\b`_gbx __ q_j_a \h^hkeb\u aZ

kq_l i_j_iZ^Z mjh\g_c ûZ i_j_^ ]Zkbl_e_f b aZ gbf.

Jbk. 19.4 Z

Jbk. 19.4 [

Kh]eZkgh `_ gh\_crbf bkke_^h\Zgbyf gb`g_]h [v_nZ ^\b`_gb_ \h^u aZ

]Zkbl_e_f, dh]^Z iju`hd gZoh^blky \ ij_^_evghf iheh`_gbb (jbk. 19.3),

ijhbkoh^bl g_ aZ kq_l ij_\jZs_gby ihl_gpbZevghc wg_j]bb ûW \ dbg_lbq_kdmx, Z

aZ kq_l dbg_lbq_kdhc wg_j]bb ljZgablghc kljmb. Wg_j]by kljmb qZklbqgh

^bkkbibjm_lky, Z qZklbqgh aZljZqb\Z_lky gZ kha^Zgb_ i_j\hgZqZevgh]h ^\b`_gby

gZ ihke_iju`dh\hf mqZkld_. I_j_iZ^Z ûZ g_ gZ[ex^Z_lky. Mjh\gb \h^u gZ

]Zkbl_e_ b aZ gbf \ur_, q_f i_j_^ ]Zkbl_e_f.

196

>ey khijy`_gguo ]em[bg ih^i_jluo iju`dh\ aZibku\Zxl l_hj_fm

dhebq_kl\Z ^\b`_gby, gh \ ljZ^bpbhggh_ mjZ\g_gb_ kh]eZkgh gh\hc fh^_eb

iju`dZ gZ^h ^hihegbl_evgh \\_klb qe_gu, mqblu\Zxsb_:

1) j_Zdpbx ]Zkbl_ey;

2) p_gljh[_`gu_ kbeu bg_jpbb;

3) bfimevk lmj[me_glguo gZijy`_gbc;

4) baf_g_gb_ dhebq_kl\Z ^\b`_gby \ h[t_f_ iju`dZ \ aZ\bkbfhklb hl

baf_g_gby kdhjhkl_c \ lhqdZo ih \j_f_gb.

Ijb mq_l_ j_Zdpbb ]Zkbl_ey \ mjZ\g_gb_ \hc^_l \ukhlZ ]Zkbl_ey d – \ukhlZ

kl_gdb Jk beb \ukhlZ \h^h[hcgh]h mklmiZ dheh^pZ d0.

Ij_h[jZah\Zggh_ bkoh^gh_ mjZ\g_gb_, aZibku\Z_fh_ hlghkbl_evgh \lhjhc

khijy`_gghc ]em[bgu g_ihkj_^kl\_ggh m ]Zkbl_ey, bf__l \b^

dhhhh

hhh d

d2d

3

d 14,22

167,0 ��c�c

� cc , (19.1)

]^_ d – \ukhlZ ]Zkbl_ey (\ukhlZ \h^h[hcghc kl_gdb beb \ukhlZ \h^h[hcgh]h

mklmiZ, l._. ]em[bgZ dheh^pZ); hï - i_j\Zy khijy`_ggZy ]em[bgZ, jZ\gZy ]em[bg_

ihlhdZ \ k`Zlhf k_q_gbb hk; hd – djblbq_kdZy ]em[bgZ, \uqbkey_fZy ih nhjfme_

3

2

dg

qh

D , (19.2)

]^_ q – m^_evguc jZkoh^ \

Qq ; b – rbjbgZ ihlhdZ; . – dhwnnbpb_gl, . =

1,05.

=em[bgZ \ k`Zlhf k_q_gbb hk hij_^_ey_lky ba hkgh\gh]h mjZ\g_gby l_hjbb

khijy`_gby [v_nh\, ihemqZ_fh]h gZ hkgh\_ mjZ\g_gby ;_jgmeeb

197

2c

2

2

c02 hg

qh?

M� , (19.3)

]^_ ?0 – ihegZy wg_j]by \ e_\hc qZklb mjZ\g_gby ;_jgmeeb, agZq_gb_ ?0

[m^_l hij_^_eylvky \ jZa^_e_ «H[jZ[hldZ hiulguo ^Zgguo»; 3 - dhwnnbpb_gl

kdhjhklb, mqblu\Zxsbc ihl_jb gZihjZ f_`^m jZkkfZljb\Z_fufb k_q_gbyfb

ihlhdZ, dhlhju_ k\yau\Zxlky mjZ\g_gb_f ;_jgmeeb.

MjZ\g_gb_ (19.3) fh`gh j_rZlv f_lh^hf ihke_^h\Zl_evguo ijb[eb`_gbc.

AgZq_gb_ hk(1) \ i_j\hf ijb[eb`_gbb \uqbkey_lky ih \ujZ`_gbx

0

c(1)2g?

qh

M . (19.4)

AgZq_gb_ hk(2) \h \lhjhf ijb[eb`_gbb

� �c(1)0

c(2)2 hEg

qh

� M

. (19.5)

Dhebq_kl\h ijb[eb`_gbc lZdh\h, qlh[u jZkoh`^_gb_ f_`^m agZq_gbyfb

ihke_^mxs_]h b ij_^r_kl\mxs_]h \uqbke_gbc g_ ij_\urZeh 5%.

Ih mjZ\g_gbx (19.1) fh`gh hij_^_eylv \ukhlm ]Zkbl_ey, _keb ba\_klgZ

\lhjZy khijy`_ggZy ]em[bgZ ih^i_jlh]h iju`dZ gZ \h^h[h_ h˝.

� �

hh

hh

h

h

h

hd cc�

cc��

c�

c 33,017,2

)(2

d

2

dd

22d . (19.6)

MjZ\g_gb_ (19.1) kh^_j`bl ^\Z iZjZf_ljZ – \lhjmx khijy`_ggmx ]em[bgm

h˝ b \ukhlm ]Zkbl_ey d, agZq_gby dhlhjuo gZ^h hij_^_eylv ih wlhfm mjZ\g_gbx.

198

Ihkdhevdm \ jZa^_e_ «P_ev jZ[hlu» mdZau\Z_lky gZ g_h[oh^bfhklv ih^[hjZ

jZaf_jh\ we_f_glh\ fh^_eb, lh ijb \uiheg_gbb jZkq_lh\ ih gZklhys_c jZ[hl_

fh`gh kqblZlv \ukhlm \h^h[hcghc kl_gdb aZ^Zgghc b k mq_lhf __ \_ebqbgu

\uqbkeylv h˝ ih mjZ\g_gbx (19.1).

Fh`gh ij_^\Zjbl_evgh \uqbkeblv agZq_gb_ \lhjhc khijy`_gghc ]em[bgu

gZ i_j\hf \h^h[h_ h˝ ih mjZ\g_gbx ]b^jZ\ebq_kdh]h iju`dZ klZjhc fh^_eb

»»

¼

º

««

¬

ª�¸̧

¹

·¨̈©

§� cc 1815,0

3

c

dc

h

hhh , (19.7)

Z aZl_f, ih^klZ\eyy wlh agZq_gb_ \ mjZ\g_gb_ (19.6), hij_^_eblv lj_[m_fmx

\ukhlm \h^h[hcghc kl_gdb.

Ijb jZkq_l_ ]em[bgu \h^h[hcgh]h dheh^pZ gZ \lhjhc kl_i_gb i_j_iZ^Z \

dZq_kl\_ \lhjhc khijy`_gghc ]em[bgu ijbgbfZ_lky kmffZ [ulh\hc ]em[bgu h/ b

]em[bgu dheh^pZ d0, l._. 0dhh � cc G . Lh]^Z \ujZ`_gb_ ^ey hij_^_e_gby ]em[bgu

dheh^pZ d0 aZibku\Z_lky

d2dd

2c

c

3d

0 33,00,22

hhhhhhh

hd ����� GG , (19.8)

]^_ hk – k`ZlZy ]em[bgZ gZ \h^h[h_ \lhjhc klmi_gb i_j_iZ^Z, _z agZq_gb_

hij_^_ey_lky \ jZa^_e_ «H[jZ[hldZ hiulguo ^Zgguo»; h/ – [ulh\Zy ]em[bgZ

ba\_klgZ ih ^Zgguf baf_j_gbc.

=hjbahglZevgu_ jZaf_ju khhjm`_gby ij_^klZ\e_gu ^ebghc \h^h[h_\. Ba

jbk. 19.1 hq_\b^gh, qlh ^ebgZ \h^h[hy l\ kdeZ^u\Z_lky ba ^ebgu ih^i_jlh]h

iju`dZ li ij b ^Zevghklb hle_lZ kljmb li,

ij ii\ lll � . (19.9)

199

>ebgZ ih^i_jlh]h iju`dZ ijb bkl_q_gbb q_j_a \h^hkeb\u hij_^_ey_lky ih

nhjfme_

P

mH?l 0

0ij i 0,5 E , (19.10)

]^_ � – dhwnnbpb_gl, mqblu\Zxsbc \ebygb_ ]Zkbl_ey gZ ^ebgm iju`dZ, � =

0,7…0,8; m – dhwnnbpb_gl jZkoh^Z \h^hkeb\Z; ^ey \h^h[hcghc kl_gdb

ijyfhm]hevgh]h hq_jlZgby m = 0,42; ^ey \h^hkeb\Z k rbjhdbf ihjh]hf agZq_gb_

m mklZgZ\eb\Z_lky ih kijZ\hqguf ^Zgguf, ijb\h^bfuf \ eZ[hjZlhjghc jZ[hl_

�15; J – \ukhlZ kl_gdb iZ^_gby; G0 – iheguc gZihj gZ \h^hkeb\_

g

VGG

2

2

0

D� , (19.11)

]^_ G – ]_hf_ljbq_kdbc gZihj gZ \h^hkeb\_; V – kj_^gyy kdhjhklv \ k_q_gbb

ihlhdZ i_j_^ \h^hkeb\hf ( \QqhqV , ); Q – hiulguc jZkoh^; \ – rbjbgZ

k_q_gby ihlhdZ.

>ebgZ hle_lZ kljmb li aZ\bkbl hl mkeh\bc bkl_q_gby q_j_a \h^hkeb\u.

Ijb i_j_eb\_ kljmb q_j_a \h^hkeb\ k rbjhdbf ihjh]hf (\oh^gZy qZklv

i_j_iZ^Z)

� �ddi 35,02 hjhl � . (19.12)

Dh]^Z kljmy i_j_eb\Z_lky q_j_a \h^hkeb\ kh kl_gdhc ijZdlbq_kdh]h

ijyfhm]hevgh]h ijhnbey (\h^h[hcgZy kl_gdZ)

� �00i 3,033,1 GjGl � . (19.13)

200

HIBK:GB? HIULGHC MKL:GH<DB

JZ[hlZ ijh\h^blky \ ]b^jZ\ebq_kdhf ehld_ (kf. jZ[hlm �10) gZ fh^_eb

^\moklmi_gqZlh]h i_j_iZ^Z dheh^_agh]h lbiZ (jbk. 19.1).

JZaf_ju fh^_eb aZf_jyxlky \ ijhp_kk_ ijh\_^_gby jZ[hlu.

Ij_^mkfZljb\Z_lky \hafh`ghklv baf_g_gby jZaf_jh\ fh^_eb.

IHJY>HD <UIHEG?GBY J:;HLU

<dexqZ_lky p_gljh[_`guc gZkhk, ih^Zxsbc \h^m \ gZihjguc [Zd, \

dhlhjhf ih^^_j`b\Z_lky ihklhygguc gZihj.

Hldjulb_f j_]mebjmxs_c aZ^\b`db gZ iblZxs_c ljm[_ mklZgZ\eb\Zxlky

jZagu_ jZkoh^u \h^u \ ehld_. GZ[ex^Zxlky k[jhku wlbo jZkoh^h\ ih i_j_iZ^m

[_a ]Zkbl_e_c wg_j]bb b k ]Zkbl_eyfb (k \h^h[hcghc kl_gdhc b \h^h[hcguf

mklmihf). G_h[oh^bfuc mjh\_gv \h^u \ gb`g_f [v_n_ ih^^_j`b\Z_lky k

ihfhsvx aZl\hjZ-`Zexab, mklZgh\e_ggh]h \ dhgp_ ehldZ.

Bkoh^y ba ijbgylh]h \ hiul_ jZkoh^Z gZ fh^_eb khhjm`_gby ih^[bjZxlky

\ukhlZ \h^h[hcghc kl_gdb b ^ebgZ i_j\h]h \h^h[hy, ^ebgZ b ]em[bgZ

\h^h[hcgh]h dheh^pZ gZ \lhjhc klmi_gb ijb mkeh\bb ghjfZevghc jZ[hlu

i_j_iZ^Z – gZ \h^h[hyo klmi_g_c ^he`gu [ulv lhevdh ih^i_jlu_

g_kZfhh[jZamxsb_ky ]b^jZ\ebq_kdb_ iju`db.

Hiulguc jZkoh^ hij_^_eyxl k ihfhsvx \h^hkeb\Z LhfkhgZ (kf. jZ[hlm

�4).

B]hevqZluf mjh\g_f_jhf baf_jyxl hlf_ldb mjh\gy \h^u \ \_jog_f b

gb`g_f [v_nZo, ihjh]Z \oh^ghc qZklb i_j_iZ^Z, \h^h[hcghc kl_gdb, \h^h[h_\,

^gZ hl\h^ys_]h jmkeZ (G;), hlf_ldb k\h[h^ghc ih\_joghklb \h^u \ oZjZdl_jguo

k_q_gbyo i_j_iZ^Z, g_h[oh^bfu_ ^ey hij_^_e_gby ]em[bg b ihkljh_gby wlhc

djb\hc \ ij_^_eZo khhjm`_gby. Ebg_cdhc baf_jyxl ]hjbahglZevgu_ jZaf_ju

i_j_iZ^Z.

201

J_amevlZlu baf_j_gbc aZghkylky \ lZ[ebpm 19.1.

LZ[ebpZ 19.1

�

ii

GZbf_gh\Zgb_ baf_j_gguo oZjZdl_jbklbd,

bo h[hagZq_gb_, jZaf_jghklv

Qbke_ggu_

agZq_gby

oZjZdl_jbklbd

F_jguc \h^hkeb\

1 Hlf_ldZ \_jrbgu m]eZ lj_m]hevgh]h baf_jbl_evgh]h

\h^hkeb\Z, û0, kf

2 Hlf_ldZ mjh\gy \h^u i_j_^ \h^hkeb\hf, û, kf

3 GZihj gZ \h^hkeb\_ G=� - �0, kf

4 JZkoh^ \h^u Q, e/k

5 M^_evguc jZkoh^ \Qq , kf

6 RbjbgZ ihlhdZ (i_j_iZ^Z) \, kf

BamqZ_fuc i_j_iZ^

7 Hlf_ldZ mjh\gy \h^u \ \_jog_f [v_n_, �1, kf

8 Hlf_ldZ \oh^ghc qZklb i_j_iZ^Z, �2, kf

9 Hlf_ldZ \_joZ \h^h[hcghc kl_gdb, �3, kf

10 Hlf_ldZ ^gZ i_j\hc klmi_gb, �4,kf

11 Hlf_ldZ mjh\gy \h^u \ gb`g_f [v_n_, �5, kf

12 Hlf_ldZ ^gZ \ gb`g_f [v_n_, �6, kf

13 Hlf_ldZ ^gZ \h^h[hcgh]h dheh^pZ �7, kf

14 Hlf_ldZ ^gZ ehldZ \ <;, �8, kf

15 Hlf_ldZ k\h[h^ghc ih\_joghklb \h^u gZ ihjh]_

\oh^ghc qZklb:

- gZ^ \oh^guf j_[jhf �9, kf

- gZ^ \uoh^guf j_[jhf �10, kf

GZ \h^h[h_ i_j\hc klmi_gb:

gZ jZkklhygbb l hl kl_gdb iZ^_gby

l1 – kf �11, kf

l2 – kf �12, kf

l3 – kf �13, kf

l4 – kf �14, kf

gZ^ \oh^guf j_[jhf \h^h[hcghc kl_gdb �15, kf

GZ \h^h[h_ \lhjhc klmi_gb:

- gZ^ \uoh^guf j_[jhf \h^h[hcghc kl_gdb �16, kf,

gZ jZkklhygbb l hl kl_gdb iZ^_gby

l5 – kf �17, kf

l6 – kf �18, kf

l7 – kf �19, kf

l8 – kf �20, kf

l9 – kf �21, kf

202

\ gb`g_f [v_n_ gZ jZkklhygbb l hl \h^h[hcgh]h mklmiZ

l10 – kf �21, kf

l11 – kf �22, kf

l12 – kf �23, kf

16 LhesbgZ \h^h[hcghc kl_gdb /, kf

17 >ebgZ i_j\hc klmi_gb l\1, kf

18 >ebgZ \lhjhc klmi_gb, l\2, kf

RbjbgZ i_j_iZ^Z \ jZ\gZ rbjbg_ ehldZ.

AZjbkh\u\Z_lky ijh^hevguc jZaj_a fh^_eb i_j_iZ^Z k bah[jZ`_gb_f

k\h[h^ghc ih\_joghklb ihlhdZ b k h[hagZq_gb_f \k_o g_h[oh^bfuo \ jZ[hl_

hlf_lhd, ]em[bg b jZaf_jh\ fh^_eb.

H;J:;HLD: HIULGUO >:GGUO

1. Ih jZaghklb baf_j_gguo hlf_lhd ih^kqblu\Z_lky gZihj G1 gZ^ ihjh]hf

\oh^ghc qZklb i_j_iZ^Z, \ukhlZ kl_ghd iZ^_gby J1 b J2, \ukhlZ \h^h[hcghc

kl_gdb Jk gZ i_j\hc klmi_gb, ]em[bgZ \h^h[hcgh]h dheh^pZ d0 (\ukhlZ

\h^h[hcgh]h mklmiZ \uoh^ghc qZklb i_j_iZ^Z), [ulh\Zy ]em[bgZ h/ ihlhdZ \

gb`g_f [v_n_, ]em[bgu ihlhdZ h gZ fh^_eb \ k_q_gbyo, mdZaZgguo \ lZ[ebp_ 19.1.

J_amevlZlu \uqbke_gbc aZghkylky \ lZ[ebpm 19.2.

LZ[ebpZ 19.2

�

ii

GZbf_gh\Zgb_ oZjZdl_jbklbd,

jZaf_jghklv

Qbke_ggu_

agZq_gby

1 2 3

I_j\Zy klmi_gv

1 GZihj G1 gZ^ ihjh]hf \oh^ghc qZklb i_j_iZ^Z,

G1 = �1 - �2, kf

2 <ukhlZ kl_gdb iZ^_gby i_j\hc klmi_gb

J1 = �2 - �4, kf

3 <ukhlZ \h^h[hcghc kl_gdb Jk = �3 - �4, kf

4 =em[bgZ ihlhdZ gZ ihjh]_ \oh^ghc qZklb

203

- gZ^ \oh^guf j_[jhf h = �9 - �2, kf

- gZ^ \uoh^guf j_[jhf h = �10 - �2, kf

5 =em[bgZ \h^u gZ \h^h[h_ \ k_q_gbyo, m^Ze_gguo gZ

jZkklhygbyo li hl i_j\hc kl_gdb iZ^_gby:

hl1 = �11 - �4, kf

hl2 = �12 - �4, kf

hl3 = �13 - �4, kf

hl4 = �14 - �4, kf

6 =em[bgZ \h^u gZ^ \oh^guf j_[jhf \h^h[hcghc kl_gdb

h = �15 - �3, kf

<lhjZy klmi_gv

7 <ukhlZ kl_gdb iZ^_gby \lhjhc klmi_gb

J2 = �3 - �7, kf

8 =em[bgZ \h^h[hcgh]h dheh^pZ d0 = �6 - �7, kf

9 ;ulh\Zy ]em[bgZ h/= �5 - �6, kf

10 =em[bgZ ihlhdZ gZ \h^h[h_ \ k_q_gbyo, m^Ze_gguo gZ

jZkklhygbb li hl \lhjhc kl_gdb iZ^_gby:

hl5 = �17 - �7, kf

hl6 = �18 - �7, kf

hl7 = �19 - �7, kf

hl8 = �20 - �7, kf

hl9 = �21 - �7, kf

11 =em[bgZ ihlhdZ \ gb`g_f [v_n_ \ k_q_gbyo gZ

jZkklhygbyo li hl \h^h[hcgh]h mklmiZ dheh^pZ:

hl10 = �21 - �6, kf

hl11 = �22 - �6, kf

hl12 = �23 - �6, kf

< j_amevlZl_ ]b^jZ\ebq_kdbo jZkq_lh\ ih aZ^Zgghfm jZkoh^m Q hij_^_eyxl

^ebgm \h^h[h_\ l\ gZ h[_bo klmi_gyo, \ukhlm \h^h[hcghc kl_gdb Jk, ]em[bgm

\h^h[hcgh]h dheh^pZ d0, ^ey q_]h ihlj_[m_lky \uqbkeylv ]em[bgu hk \ k`Zluo

k_q_gbyo gZ \h^h[hyo b \lhju_ khijy`_ggu_ k gbfb ]em[bgu h˝, djblbq_kdmx

]em[bgm hd, ihegmx m^_evgmx wg_j]bx ?0 \ k_q_gbyo i_j_^ \oh^hf gZ \h^hkeb\u,

l._. \ k_q_gbyo 1-1 b 2-2 (jbk. 19.5), ^ebgu ih^i_jluo iju`dh\ li ij b hle_lZ kljmb

li hl kl_ghd iZ^_gby ijb i_j_eb\_ kljmb q_j_a \h^hkeb\u.

204

Jbk. 19.5

205

AgZq_gb_ djblbq_kdhc ]em[bgu hd \uqbkeyxlky ih nhjfme_ (19.2).

I_j\Zy klmi_gv.

IhegZy m^_evgZy wg_j]by ?01 \ k_q_gbb i_j_^ \oh^hf gZ i_j_iZ^ (k_q_gb_ 1-

1), hlg_k_ggZy d ]hjbahglZevghfm \h^h[hx i_j\hc klmi_gb (jbk. 19.5),

\uqbkey_lky ih nhjfme_

� �> @211

2

11012 GJg

qGJ?

���

D. (19.14)

AgZq_gb_ ]em[bgu \ k`Zlhf k_q_gbb gZ i_j\hf \h^h[h_ hk (k_q_gb_ K-K,

jbk. 19.5) hij_^_ey_lky ba mjZ\g_gby (19.3) ijb ih^klZgh\d_ \ g_]h ?01 \f_klh ?0;

mjZ\g_gb_ (19.3) j_rZ_lky f_lh^hf ihke_^h\Zl_evguo ijb[eb`_gbc – kf.

mjZ\g_gby (19.4), (19.5). Lj_[m_fh_ agZq_gb_ dhwnnbpb_glZ kdhjhklb 3 ijb wlhf

ijbgbfZ_lky ih ebl_jZlmjguf bklhqgbdZf; 3 = 0,95-0,97 [8]. AgZq_gb_ h˝k,

khijy`_gghc k \uqbke_gghc k`Zlhc ]em[bghc hk, hij_^_ey_lky ih nhjfme_ (19.7).

Ihke_ wlh]h \uqbkey_lky \ukhlZ \h^h[hcghc kl_gdb ih nhjfme_ (19.6), \ dhlhjhc

\f_klh hc b h˝ ih^klZ\eyxlky khhl\_lkl\_ggh ihemq_ggu_ hk b h˝k, Z \ukhlZ

]Zkbl_ey d y\ey_lky bkdhfhc \ukhlhc \h^h[hcghc kl_gdb Jk.

>ebgZ ih^i_jlh]h iju`dZ gZ i_j\hf \h^h[h_ hij_^_ey_lky ih nhjfme_

(19.10) ijb ih^klZgh\d_ \ g__ ?01 \f_klh ?0 , J1 \f_klh J , G01 \f_klh G0. AgZq_gb_

ihegh]h gZihjZ G01 \uqbkey_lky ih nhjfme_ (19.11) ijb ih^klZgh\d_ \ g__ G1

\f_klh G b 11 HP

qV

� . AgZq_gb_ dhwnnbpb_glZ jZkoh^Z m \h^hkeb\Z k rbjhdbf

ihjh]hf mklZgZ\eb\Z_lky, dZd mdZaZgh \ur_, ih kijZ\hqguf ^Zgguf,

ijb\h^bfuf \ eZ[hjZlhjghc jZ[hl_ �15. >ebgZ hle_lZ kljmb li gZ i_j\hf

\h^h[h_ \uqbkey_lky ih nhjfme_ (19.12) ijb ih^klZgh\d_ \ g__ J1 \f_klh J .

>ebgZ i_j\h]h \h^h[hy [_a mq_lZ lhesbgu \h^h[hcghc kl_gdb / hij_^_ey_lky ih

nhjfme_ (19.9).

206

<lhjZy klmi_gv.

Hij_^_ey_lky agZq_gb_ iheghc m^_evghc wg_j]bb ?02 \ k_q_gbb i_j_^

\h^h[hcghc kl_gdhc (gZ i_j\hf \h^h[h_, k_q_gb_ 2-2, jbk. 19.5), \ dhlhjhf

]em[bgZ ihlhdZ m`_ ba\_klgZ - h˝k

, (19.15) 02202 GJ? �

]^_ G02 – iheguc gZihj gZ \h^hkeb\_, ij_^klZ\eyxsbf kh[hc \h^h[hcgmx

kl_gdm, hg \uqbkey_lky ih nhjfme_

2

2

02)(2 c

khg

qhG

cc�cc

D. (19.16)

AgZq_gb_ ]em[bgu hk1 \ k`Zlhf k_q_gbb gZ \lhjhf \h^h[h_ (k_q_gb_ Kï - Kï,

jbk. 19.5) hij_^_ey_lky lZd`_ ih mjZ\g_gbyf (19.3), (19.4), (19.5) ijb ih^klZgh\d_

\ gbo ?02 \f_klh ?0. Dhwnnbpb_gl kdhjhklb fh`gh ijbgbfZlv 3 = 0,95 – 0,97.

=em[bgZ \h^h[hcgh]h dheh^pZ d0 hij_^_ey_lky ih nhjfme_ (19.8) ijb

ih^klZgh\d_ \ g__ hk1 \f_klh hk; [ulh\Zy ]em[bgZ h/ ba\_klgZ ih ^Zgguf

baf_j_gbc. >ebgZ ih^i_jlh]h iju`dZ gZ \lhjhf \h^h[h_ hij_^_ey_lky ih

nhjfme_ (19.10) ijb ih^klZgh\d_ \ g__ ?02 \f_klh ?0, J2 \f_klh J , G02 \f_klh G0.

AgZq_gb_ dhwnnbpb_glZ jZkoh^Z \h^h[hcghc kl_gdb m = 0,42. >ebgZ hle_lZ kljmb

li gZ \lhjhf \h^h[h_, dh]^Z kljmy i_j_eb\Z_lky q_j_a \h^h[hcgmx kl_gdm,

\uqbkey_lky ih nhjfme_ (19.13) ijb ih^klZgh\d_ \ g__ G02 \f_klh G0 , J2 \f_klh

J . >ebgZ \lhjh]h \h^h[hy hij_^_ey_lky ih nhjfme_ (19.9) ijb ih^klZgh\d_ \ g__

li b li ij, \uqbke_gguo gZ \lhjhf \h^h[h_.

<uqbkey_lky \lhjZy khijy`_ggZy ]em[bgZ h˝k1 gZ \lhjhf \h^h[h_ ih

nhjfme_ (19.1) ijb ih^klZgh\d_ \ g__ hk1 \f_klh hc b d0 \f_klh d – ^ey

khihklZ\e_gby k hiulghc ]em[bghc.

207

AZl_f khihklZ\eyxlky wdki_jbf_glZevgu_ agZq_gby, hkgh\guo jZaf_jh\

i_j_iZ^Z kh agZq_gbyfb, ih^kqblZggufb ih nhjfmeZf, iml_f gZoh`^_gby

ijhp_glZ hldehg_gby ih \ujZ`_gbx

1001\uq

hi �¸̧¹

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I, % (19.17)

]^_ I – agZq_gb_ ex[h]h bkke_^m_fh]h iZjZf_ljZ; bg^_dk «hi» mdZau\Z_l gZ

hiulgh_ agZq_gb_, bg^_dk «\uq» mdZau\Z_l gZ agZq_gb_ iZjZf_ljZ, \uqbke_ggh]h

ih khhl\_lkl\mxs_c nhjfme_.

J_amevlZlu h[jZ[hldb wdki_jbf_glZevguo ^Zgguo b \uqbke_gby agZq_gbc

bkke_^m_fuo iZjZf_ljh\ aZghkylky \ lZ[ebpm 19.3. Wlb ^Zggu_ iha\heyxl

ZgZebabjh\Zlv jZ[hlm ^\moklmi_gqZlh]h i_j_iZ^Z dheh^_agh]h lbiZ.

LZ[ebpZ 19.3

Qbke_ggu_ agZq_gby

oZjZdl_jbklbd

� GZbf_gh\Zgb_ oZjZdl_jbklbd,

jZaf_jghklv

I klmi_gv II klmi_gv

1 2 3 4

1 M^_evgZy wg_j]by ?0, kf

2 =em[bgZ \ k`Zlhf k_q_gbb, hk, hk1, kf

3 Djblbq_kdZy ]em[bgZ hd, kf

4 <lhjZy khijy`_ggZy ]em[bgZ gZ \h^h[hyo

h˝k b h˝k1, kf

5 <ukhlZ \h^h[hcghc kl_gdb, Jk, kf

6 =em[bgZ \h^h[hcgh]h dheh^pZ, d0, kf - -

7 >ebgZ ih^i_jlh]h ]b^jZ\ebq_kdh]h iju`dZ

li ij, kf

8 >ebgZ hle_lZ kljmb li , kf

9 >ebgZ \h^h[hcgh]h dheh^pZ lk, kf

10 Ijhp_gl hldehg_gby hiulgh]h agZq_gby

\lhjhc khijy`_gghc ]em[bgu h˝ hl

\uqbke_ggh]h agZq_gby 1001\uq c

hi c �¸̧¹

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11 Ijhp_gl hldehg_gby hiulgh]h agZq_gby

\ukhlu \h^h[hcghc kl_gdb Jk hl

\uqbke_ggh]h agZq_gby 1001\uq c

hi c �¸̧¹

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J, %

12 Ijhp_glgh_ hldehg_gb_ hiulghc ]em[bgu

dheh^pZ hl \uqbke_ggh]h agZq_gby

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13 Ijhp_glgh_ hldehg_gb_ hiulgh]h agZq_gby

^ebgu \h^h[hy hl \uqbke_ggh]h

agZq_gby 1001\uq \

hi \ �¸̧¹

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l , %

D ijhlhdhem jZ[hlu ijbeZ]Z_lky jbkmghd fh^_eb i_j_iZ^Z, \uiheg_gguc \

fZkrlZ[_, k bah[jZ`_gb_f k\h[h^ghc ih\_joghklb ihlhdZ \ ij_^_eZo

khhjm`_gby. GZ jbkmgd_ mdZau\Zxlky \k_ hkgh\gu_ jZaf_ju fh^_eb. K\h[h^gZy

ih\_joghklv ihlhdZ kljhblky ih baf_j_gguf hlf_ldZf beb ih \uqbke_gguf

]em[bgZf \ k_q_gbyo.

J:;HL: 20

HIJ?>?E?GB? DHWNNBPB?GL: NBEVLJ:PBB

I?KQ:GH=H =JMGL:

P_ev jZ[hlu. Hij_^_e_gb_ wdki_jbf_glZevguf iml_f dhwnnbpb_glZ

nbevljZpbb i_kqZgh]h ]jmglZ k ihfhsvx ijb[hjZ >Zjkb.

H;SB? K<?>?GBY

>\b`_gb_ `b^dhklb beb ]ZaZ q_j_a ihjbklmx kj_^m gZau\Z_lky

nbevljZpb_c. Bamq_gb_ \hijhkh\ nbevljZpbb ij_^klZ\ey_l [hevrhc

ijZdlbq_kdbc bgl_j_k ^ey j_r_gby rbjhdh]h djm]Z bg`_g_jguo aZ^Zq \

209

jZaebqguo h[eZklyo l_ogbdb: \h^hkgZ[`_gbb – ^ey jZkq_lZ ijblhdZ \h^u d

dheh^pZf b ^j_gZf; ]b^jhl_ogbq_kdhf b f_ebhjZlb\ghf kljhbl_evkl\_ – ^ey

jZkq_lZ jZkoh^h\ b mjh\g_c ]jmglh\uo \h^ ijb hjhr_gbb b hkmr_gbb ihq\,

kljhbl_evkl\_ iehlbg, mkljhckl\_ dhleh\Zgh\ b l.^.

?keb `b^dhklv ijb nbevljZpbb h[jZam_l k\h[h^gmx ih\_joghklv \ ]jmgl_

(gZijbf_j, \ iehlbg_), lh lZdmx nbevljZpbx gZau\Zxl [_agZihjghc.

GZihjgZy nbevljZpby bf__l f_klh \ gZihjguo \h^hghkguo ]hjbahglZo, ]^_

^\b`_gb_ `b^dhklb ijhbkoh^bl aZ kq_l jZaghklb ^Z\e_gbc \ ieZkl_ b kd\Z`bg_

[_a h[jZah\Zgby k\h[h^ghc ih\_joghklb. NbevljZpby fh`_l [ulv lZd`_

eZfbgZjghc b lmj[me_glghc, mklZgh\b\r_cky b g_mklZgh\b\r_cky.

:.>Zjkb bkke_^h\Ze nbevljZpbx \h^u gZ hiulghc mklZgh\d_,

ij_^klZ\eyxs_c kh[hc \_jlbdZevguc khkm^ ihklhyggh]h k_q_gby, aZiheg_gguc

i_kdhf. Q_j_a i_khd ijhimkdZeZkv \h^Z ijb ihklhygghc \h \j_f_gb jZaghklb

gZihjh\. LhesbgZ kehy i_kdZ, _]h njZdpbhgguc khklZ\ b jZaghklv gZihjh\ \

jZaguo hiulZo [ueb jZaebqgu.

;ueh wdki_jbf_glZevgh mklZgh\e_gh, qlh aZ\bkbfhklv jZkoh^Z hl ihl_jv

gZihjZ bf__l ke_^mxsbc \b^

kJQ Z , (20.1)

]^_ k - dhwnnbpb_gl nbevljZpbb `b^dhklb; & – «]_hf_ljbq_kdZy» iehsZ^v

ihi_j_qgh]h k_q_gby h[jZapZ ]jmglZ, \dexqZxsZy iehsZ^v ihj &ihj b iehsZ^v

qZklbp &qZkl (& = &ihj + &qZkl); J – ]b^jZ\ebq_kdbc mdehg, ij_^klZ\eyxsbc

hlghr_gb_ ihl_jv gZihjZ hlj gZ imlb nbevljZpbb d ^ebg_ wlh]h imlb l, lhJ lj .

Kj_^gyy kdhjhklv nbevljZpbb # ih aZdhgm >Zjkb jZ\gZ

kJQ

V Z

. (20.2)

210

Wlh mkeh\gZy kdhjhklv nbevljZpbb, lZd dZd \ ijZdlbq_kdbo aZ^ZqZo m^h[g__

kqblZlv, qlh nbevljZpby ijhbkoh^bl dZd [u q_j_a \k_ k_q_gb_ ]jmglZ, \dexqZy

l\_j^u_ qZklbpu.

NbevljZpby `b^dhklb \ dZ`^hf k_q_gbb ijhbkoh^bl lhevdh q_j_a iehsZ^v

ihj &ihj, ihwlhfm bklbggZy kdhjhklv nbevljZpbb V^ jZ\gZ

ihj

^ ZQ

V . (20.3)

BklbggZy kdhjhklv nbevljZpbb V^ \k_]^Z [hevr_ kdhjhklb nbevljZpbb V b

bo \aZbfhk\yav mklZgZ\eb\Z_lky aZ\bkbfhklvx

mVV ^ , (20.4)

]^_ m – dhwnnbpb_gl ihjbklhklb, qbke_ggh jZ\guc hlghr_gbx h[t_fZ ihj

\ ihjh^_ Wi dh \k_fm h[t_fm W, l._. WWm i .

Dhwnnbpb_gl nbevljZpbb k aZ\bkbl hl \_ebqbgu b nhjfu a_j_g ]jmglZ,

gZebqby ]ebgbkluo qZklbp, iehlghklb b \yadhklb nbevljmxs_c `b^dhklb b _z

l_fi_jZlmju.

AZdhg >Zjkb kijZ\_^eb\ ^ey eZfbgZjgh]h ^\b`_gby, dhlhjh_ rbjhdh

jZkijhkljZg_gh \ ijbjh^guo mkeh\byo.

Ijb lmj[me_glghf j_`bf_ ^\b`_gby gZ[ex^Z_lky hldehg_gb_ hl ebg_cgh]h

aZdhgZ. A^_kv kdhjhklv nbevljZpbb ijyfh ijhihjpbhgZevgZ ]b^jZ\ebq_kdhfm

mdehgm \ kl_i_gb ½.

Kf_rZggh_ eZfbgZjgh-lmj[me_glgh_ ^\b`_gb_ qZs_ \k_]h \ujZ`Z_lky

mjZ\g_gb_f Ijhgb

2\VaVJ � , (20.5)

211

]^_ Z b \ – iZjZf_lju, aZ\bkysb_ hl k\hckl\ ihjbklhc kj_^u b

nbevljmxs_cky `b^dhklb.

Kdhjhklv nbevljZpbb ijb dhlhjhc ijhbkoh^bl gZjmr_gb_ aZdhgZ >Zjkb

gZau\Zxl djblbq_kdhc kdhjhklvx b h[hagZqZxl Vdj. ?z agZq_gb_ fh`gh

hij_^_eblv wdki_jbf_glZevgh ih ]jZnbdm V=f(J) \ lhqd_ _]h aZf_lgh]h

hldehg_gby hl ijyfhc ebgbb [2]. Ke_^h\Zl_evgh, hiulu ijh\h^yl ^h l_o ihj, ihdZ

ijyfZy g_ i_j_c^_l \ djb\mx.

Dhwnnbpb_gl nbevljZpbb ]jmglZ fh`_l [ulv hij_^_e_g:

1) eZ[hjZlhjguf iml_f k ihfhsvx ijb[hjh\ >Zjkb, DZf_gkdh]h, Lbf_,

DZi_pdh]h [1];

2) \ ihe_\uo mkeh\byo \ _]h _kl_kl\_gghf khklhygbb;

3) jZkq_lguf f_lh^hf ih ^Zgguf ]jZgmehf_ljbq_kdh]h khklZ\Z k ihfhsvx

jZkq_lguo nhjfme.

Mqblu\Zy, qlh wfibjbq_kdb_ jZkq_lgu_ nhjfmeu bf_xl madb_ ij_^_eu

ijbf_gbfhklb, bo bkihevah\Zgb_ g_p_e_khh[jZagh, l_f [he__, qlh bf_xlky

^hklZlhqgh ijhklu_ ijb[hju ^ey g_ihkj_^kl\_ggh]h hij_^_e_gby dhwnnbpb_glZ

nbevljZpbb.

HIBK:GB? HIULGHC MKL:GH<DB

Wdki_jbf_glZevgZy mklZgh\dZ – ijb[hj >Zjkb (jbk.20.1) khklhbl ba

\_jlbdZevghc dhehgdb ijyfhm]hevgh]h beb djm]eh]h k_q_gby iehsZ^vx & k

]emobf aZdjuluf ^ghf. < gb`g_c qZklb dhehgdb gZ g_dhlhjhc \ukhl_ hl ^gZ

aZdj_ie_gZ f_lZeebq_kdZy j_r_ldZ, dhlhjZy jZa^_ey_l dhehgdm gZ ^\_ qZklb. <

\_jogxx qZklv aZ]jm`Z_lky ]jmgl, \ gb`g_c – jZkiheZ]Z_lky djZg ^ey

j_]mebjh\Zgby nbevljZpbhggh]h jZkoh^Z.

212

Jbk. 20.1

<_jogyy qZklv dhehgdb bf__l ljb hl\_jklby kh rlmp_jZfb, d dhlhjuf

ih^dexq_gu 3 iv_ahf_ljZ (�1, �2, �3). Kh klhjhgu ]jmglZ hl\_jklby aZdjulu

f_lZeebq_kdhc k_ldhc.

<k_ iv_ahf_lju \u\_^_gu gZ sblhd, gmev rdZeu dhlhjh]h kh\iZ^Z_l k

iehkdhklvx kjZ\g_gby 0-0, jZkiheh`_gghc gb`_ hkgh\Zgby ijb[hjZ. JZkklhygby

f_`^m iv_ahf_ljZfb h^bgZdh\u_ b jZ\gu l.

< \_jog_c qZklb dhehgdb \iZygZ ljm[dZ \ ^ey ih^^_j`Zgby gZ ihklhygghc

\ukhl_ mjh\gy \h^u \ ijb[hj_.

Ih^\h^ \h^u hkms_kl\ey_lky ih ljm[d_ Z. Ijhnbevljh\Z\rZyky \h^Z

keb\Z_lky ih ljm[d_ k q_j_a djZgbd k \ f_jguc khkm^.

213

Ijb ijh\_^_gbb hiulh\, djhf_ ijb[hjZ >Zjkb, g_h[oh^bfh bf_lv:

k_dmg^hf_j; l_jfhf_lj; f_jguc khkm^ h[t_fhf 500 kf3.

IHJY>HD <UIHEG?GBY J:;HLU

1. Ih ljm[d_ Z ba kbkl_fu \h^hkgZ[`_gby ih^Zxl \h^m \ dhehgdm k

bkiulm_fuf ]jmglhf. Ijh\h^yl ijh\_jdm jZ[hlu iv_ahf_ljh\. Ijb aZdjulhf

djZg_ k mjh\gb \h^u \h \k_o lj_o iv_ahf_ljZo ^he`gu gZoh^blvky gZ h^ghc b lhc

`_ hlf_ld_.

2. Ih^]hlh\b\ ijb[hj d jZ[hl_, hldju\Zxl djZg k b ihke_ mklZgh\e_gby

g_baf_ggh]h \h \j_f_gb iheh`_gby mjh\gy \h^u \ iv_ahf_ljZo ijb nbevljZpbb

\h^u q_j_a ]jmgl ijhba\h^yl baf_j_gb_ jZkoh^Z h[t_fguf kihkh[hf ijb ihfhsb

f_jgh]h khkm^Z b k_dmg^hf_jZ.

3. Hij_^_eyxlky ihdZaZgby iv_ahf_ljh\, dhlhju_ khhl\_lkl\_ggh jZ\gu

ihl_gpbZevguf gZihjZf

g

pZG i

ii U� .

4. J_]mebjmxsbf djZgbdhf ihke_^h\Zl_evgh mklZgZ\eb\Zxlky g_kdhevdh

jZaebqguo nbevljZpbhgguo jZkoh^h\, b \k_ baf_j_gby ih\lhjyxlky aZgh\h.

5. < dZ`^hf hiul_ l_jfhf_ljhf hij_^_ey_lky l_fi_jZlmjZ \h^u.

H;J:;HLD: HIULGUO >:GGUO

1. Ih h[t_fm W \ f_jghf khkm^_ b \j_f_gb t ^ey dZ`^h]h hiulZ

ih^kqblu\Z_lky nbevljZpbhgguc jZkoh^ t

WQ b ^Ze__ kj_^gyy kdhjhklv

nbevljZpbb ZQ

V .

214

2. Baf_jyxl ihdZaZgby iv_ahf_ljh\ G1 , G2 , G3 b hij_^_eyxl ihl_jb gZihjZ

gZ i_j\hf mqZkld_ b gZ \lhjhf - 21lj1 HHh � 32lj2 HHh � . AZl_f hij_^_eyxlky

kj_^gyy ihl_jy gZihjZ � � 2/lj2lj1 hhljh � , kj_^gbc ]b^jZ\ebq_kdbc mdehg

l

hJ lj , ]^_ l – imlv nbevljZpbb.

3. Hij_^_ey_lky djblbq_kdZy kdhjhklv nbevljZpbb Vdj, ijb dhlhjhc

ijhbkoh^bl gZjmr_gb_ aZdhgZ >Zjkb ^ey q_]h ih ^Zgguf hiulZ kljhblky ]jZnbd

V=f(J), ]^_ ih hkb hj^bgZl hldeZ^u\Z_lky kdhjhklv V, Z ih hkb Z[kpbkk –

]b^jZ\ebq_kdbc mdehg J. Djblbq_kdZy kdhjhklv hij_^_ey_lky ih ]jZnbdm \ lhqd_

aZf_lgh]h hldehg_gby ]jZnbdZ hl ijyfhc ebgbb.

>_ckl\bl_evgZy kdhjhklv V^, khhl\_lkl\mxsZy Vdj hij_^_ey_lky ba

nhjfmeu m

VV dj^ .

4. Dhwnnbpb_gl nbevljZpbb k ih^kqblu\Z_lky ih ba\_klguf kdhjhklyf

V < Vdj b khhl\_lkl\mxsbf bf ]b^jZ\ebq_kdbf mdehgZf ih nhjfme_ J

Vk .

5. >ey ijb\_^_gby j_amevlZlh\ hiulZ d ihklhygghc l_fi_jZlmj_, gZijbf_j,

d 100K beb dZdhc eb[h ^jm]hc, \uqbkeyxl b mqblu\Zxl l_fi_jZlmjgmx ihijZ\dm

ih nhjfme_ ImZa_cey

. 2000221,00337,01 LLLI ��

Qlh[u ijb\_klb j_amevlZlu hiulZ d g_h[oh^bfhc l_fi_jZlmj_ LIbkd

bkihevamxl aZ\bkbfhklv

nZdl

bkdbkd

LI

LIkk

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215

]^_ kbkd – dhwnnbpb_gl nbevljZpbb ijb\_^_gguc d bkdhfhc l_fi_jZlmj_

Lbkd; k – dhwnnbpb_gl nbevljZpbb, gZc^_gguc ijb nZdlbq_kdhc l_fi_jZlmj_

LnZdl;

LIbkd b LInZdl – l_fi_jZlmjgu_ ihijZ\db, \uqbke_ggu_ khhl\_lkl\_ggh ijb

bkdhfhc l_fi_jZlmj_ Lbkd b nZdlbq_kdhc l_fi_jZlmj_ \h \j_fy hiulZ LnZdl.

6. J_amevlZlu baf_j_gbc b \uqbke_gbc \ghkyl \ lZ[ebpm 20.1.

Ih^kqblZggh_ kj_^g__ hiulgh_ agZq_gb_ dhwnnbpb_glZ nbevljZpbb,

khihklZ\ey_lky kh kijZ\hqguf.

216

LZ[ebpZ 20.1

IhdZaZgby

iv_ahf_ljh\,

G, kf

Ihl_jb gZihjZ,

kf

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hiu-

lZ

Dhe-\h

ijhnb-

evljh\Z

\r_cky

\h^u W, kf

3

<j_fy

t, k_d JZkoh^

t

WQ

kf3/k_d

1 2 3 hlj1

1-2

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nbevl

jZpbb

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kf/k

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nbevl

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kf/k

L_f

i_jZ

lmjZ

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_gl nbevl-

jZpbb ijb

100K

0

01010

LLI

LIkk

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kf/k

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Hij_^_e_gb_ dhwnnbpb_glZ nbevljZpbb i_kqZgh]h ]jmglZ

217

J:;HL: 21

BKKE?>H<:GB? IEHKDHC G:IHJGHC NBEVLJ:PBB IJB

E:FBG:JGHF MKL:GH<B<R?FKY ><B@?GBB IH> HKGH<:GB?F

=B>JHL?OGBQ?KDH=H KHHJM@?GBY F?LH>HF

W=>:

P_ev jZ[hlu: 1. HagZdhfe_gb_ k ijbgpbibZevghc ko_fhc mklZgh\db

W=>: b ijbh[j_l_gb_ ijZdlbq_kdbo gZ\udh\ \ bkihevah\Zgbb mklZgh\db ^ey

ihkljh_gby ]b^jh^bgZfbq_kdhc k_ldb ^\b`_gby nbevljZpbhggh]h ihlhdZ.

2. Ihkljh_gb_ gZ fh^_eb ]b^jh^bgZfbq_kdhc k_ldb ^\b`_gby (iehkdZy

aZ^ZqZ) ijb gZihjghc nbevljZpbb ih^ khhjm`_gb_f.

3. Hij_^_e_gb_ \uoh^guo ]jZ^b_glh\ nbevljZpbhggh]h ihlhdZ.

4. Ihkljh_gb_ wixju kdhjhkl_c nbevljZpbb gZ \uoh^_ ]jmglh\h]h ihlhdZ

\ gb`g_f [v_n_.

5. <uqbke_gb_ m^_evgh]h jZkoh^Z nbevljZpbb ih^ khhjm`_gb_f b

ihkljh_gb_ _]h wixju gZ \uoh^_ \ gb`gbc [v_n.

6. Ihkljh_gb_ wixju \_jlbdZevgh]h ^Z\e_gby (wixju ijhlb\h^Z\e_gby)

b hij_^_e_gb_ kmffZjgh]h ^Z\e_gby gZ hkgh\Zgb_ khhjm`_gby kh klhjhgu

nbevljZpbhggh]h ihlhdZ.

H;SB? K<?>?GBY

NbevljZpbhggu_ aZ^Zqb hlebqZxlky [hevrhc keh`ghklvx bo j_r_gby.

Kms_kl\mxsb_ f_lh^u nbevljZpbhgguo jZkq_lh\ ^Ze_dh g_ \k_]^Z iha\heyxl

^hklZlhqgh lhqgh hij_^_eylv iZjZf_lju ^\b`_gby ]jmglh\uo \h^ \ hkgh\Zgbb

\h^hih^ihjguo khhjm`_gbc b \ h[oh^ bo [_j_]h\uo ijbfudZgbc. Ihwlhfm

iZjZf_lju nbevljZpbhggh]h ihlhdZ ^ey hl\_lkl\_gguo khhjm`_gbc

hij_^_eyxl fh^_ebjh\Zgb_f. Ij_^eh`_gguc G.G.IZ\eh\kdbf

wdki_jbf_glZevguc f_lh^ we_dljh]b^jh^bgZfbq_kdbo ZgZeh]bc (f_lh^ W=>:)

218

y\ey_lky gZb[he__ h[sbf, ijhkluf b m^h[guf ba ijbf_gy_fuo \ gZklhys__

\j_fy f_lh^h\ bkke_^h\Zgby klZpbhgZjghc nbevljZpbb iml_f fh^_ebjh\Zgby.

F_lh^ W=>: hkgh\Zg gZ fZl_fZlbq_kdhc b nbabq_kdhc ZgZeh]bb f_`^m

eZfbgZjghc nbevljZpb_c \ ihjbklhc kj_^_ b ^\b`_gb_f we_dljbq_kdh]h lhdZ \

ijh\h^ys_c kj_^_.

>ey gZ]ey^ghklb \ lZ[ebp_ 21.1 ij_^klZ\e_gu we_f_glu ZgZeh]bb

iZjZf_ljh\ nbevljZpbhggh]h ihlhdZ b we_dljbq_kdh]h lhdZ \ ijh\h^gbd_.

We_f_glu ZgZeh]bb

LZ[ebpZ 21.1

NbevljZpbhgguc ihlhd We_dljbq_kdbc lhd

Iv_ahf_ljbq_kdbc (ihl_gpbZevguc)

gZihj G, f

We_dljbq_kdbc ihl_gpbZe U, \

Dhwnnbpb_gl nbevljZpbb D, f/k M^_evgZy we_dljhijh\h^bfhklv K, Hf-

1, f

-1

Kdhjhklv nbevljZpbb u, f/k Iehlghklv lhdZ i, :/f2

AZdhg >Zjkb l

GDb

ww

� , ]^_ l – ^ebgZ

imlb nbevljZpbb (ebgby lhdZ), f

AZdhg HfZ l

UCi

ww

� , ]^_ l – ^ebgZ

ijh\h^gbdZ we_dljbq_kdh]h lhdZ

(ebgbb lhdZ), f

NbevljZpbhgguc jZkoh^ Q, f3/k KbeZ lhdZ I, :

MjZ\g_gb_ ih\_joghklb (ebgbb)

jZ\guo gZihjh\ G = const

MjZ\g_gb_ ih\_joghklb ebgbb jZ\gh]h

we_dljbq_kdh]h ihl_gpbZeZ U = const

<h^hg_ijhgbpZ_fZy ih\_joghklv

(ebgby lhdZ) n

G

ww

=0, ]^_ n – ghjfZev d

ih\_joghklb

BaheypbhggZy ih\_joghklv (ebgby

lhdZ)

n

U

ww

=0, ]^_ n – ghjfZev d ih\_joghklb

NbevljZpbhggh_ khijhlb\e_gb_

mqZkldZ fh^_eb, k/f2

ZK

lN

' , ]^_ & -

iehsZ^v k_q_gby ihlhdZ, f2

We_dljbq_kdh_ khijhlb\e_gb_

ijh\h^gbdZ, Hf ZC

lR

' , ]^_ & -

iehsZ^v k_q_gby ijh\h^gbdZ, f2

MjZ\g_gb_ EZieZkZ ^ey gZihjZ

2

2

2

2

2

2

z

H

y

H

x

H

w

w�

w

w�

w

w=0

MjZ\g_gb_ EZieZkZ ^ey

we_dljbq_kdh]h ihl_gpbZeZ

2

2

2

2

2

2

z

U

y

U

x

U

w

w�

w

w�

w

w=0

GZihjgZy nmgdpby (bgl_]jZe)

mjZ\g_gby EZieZkZ � �zyxfH ,, Nmgdpby ihl_gpbZeZ (bgl_]jZe)

mjZ\g_gby EZieZkZ � �zyxfU ,,

219

Ba lZ[ebpu \b^gh, qlh wd\bihl_gpbZevguf ih\_joghklyf we_dljbq_kdh]h

ihey khhl\_lkl\mxl ih\_joghklb jZ\gh]h gZihjZ nbevljZpbhggh]h ihlhdZ b

kh\iZ^Zxl ebgbb lhdh\, Z ijhp_kk ^\b`_gby we_dljbq_kdh]h lhdZ \

we_dljhijh\h^ys_c kj_^_ b ijhl_dZgb_ eZfbgZjgh]h nbevljZpbhggh]h ihlhdZ

\ ihjbklhc kj_^_ hibku\Zxlky mjZ\g_gbyfb h^gh]h b lh]h `_ \b^Z. Wlh

k\b^_l_evkl\m_l h ijbgpbibZevghc \hafh`ghklb j_r_gby aZ^Zq nbevljZpbb

iml_f bkke_^h\Zgby khhl\_lkl\mxs_]h we_dljbq_kdh]h ihey \ ijh\h^gbd_,

ij_^klZ\eyxs_f kh[hc fh^_ev h[eZklb nbevljZpbb k ZgZeh]bqgufb

]jZgbqgufb mkeh\byfb. IZjZf_lju `_ bkke_^m_fh]h we_dljbq_kdh]h ihey gZ

fh^_eb g_ljm^gh ijZdlbq_kdb ihemqblv k bkihevah\Zgb_f mklZgh\db W=>:,

iha\heyxs_c ihkljhblv k_ldm ^\b`_gby we_dljbq_kdh]h lhdZ. WlZ k_ldZ

y\ey_lky ]jZnbq_kdbf \ujZ`_gb_f mjZ\g_gby EZieZkZ b khklhbl ba ebgbc

jZ\gh]h ihl_gpbZeZ, wd\b\Ze_glgh]h gZihjm nbevljZpbhggh]h ihlhdZ

(wd\bihl_gpbZe_c) b ebgbc lhdZ. K_ldZ, oZjZdl_jbamxsZy ^\b`_gb_

we_dljbq_kdh]h lhdZ lZd`_, ij_^klZ\ey_l kh[hc ]b^jh^bgZfbq_kdmx k_ldm

eZfbgZjgh]h mklZgh\b\r_]hky ^\b`_gby iehkdh]h nbevljZpbhggh]h ihlhdZ.

Wd\bihl_gpbZevgu_ ebgbb b ebgbb lhdZ, y\eyxsb_ky bahebgbyfb

khijy`_gguo ihl_gpbZevghc nmgdpbb 3 b nmgdpbb lhdZ % \ g_ hkh[uo lhqdZo

ihey i_j_k_dZxlky ih^ ijyfuf m]ehf, l._. ebgbb 3 = const b % = const h[jZamxl

hjlh]hgZevgmx k_ldm ^\b`_gby, jbk. 21.1, \.

Ijb we_dljhfh^_ebjh\Zgbb fh`gh kljhblv ebrv ihe_ ihl_gpbZevghc

nmgdpbb 3, l._. hij_^_eylv gZ lhdhijh\h^ys_c fh^_eb lhqdb jZ\gh]h

ihl_gpbZeZ (jZ\gh]h gZihjZ), ih dhlhjuf aZl_f ijh\h^ylky wd\bihl_gpbZeb,

jbk. 21.1, [. < lh `_ \j_fy, f_lh^ W=>: iha\hey_l ihemqblv b kbkl_fm ebgbc

lhdZ, _keb bkihevah\Zlv k\hckl\h \aZbfhaZf_gy_fhklb ebgbc jZ\guo

ihl_gpbZeh\ b ebgbc lhdZ. >ey wlh]h gZ^h gZ fh^_eb baf_gblv ]jZgbqgu_

mkeh\by, l._. lhdhih^\h^ysb_ f_lZeebq_kdb_ rbgu b baheypbhggu_

ih\_joghklb ihf_gylv f_klZfb, jbk. 21.1, Z.

220

Jbk. 21.1

< wlhf kemqZ_ j_rZ_lky h[jZlgZy aZ^ZqZ, \ dhlhjhc wd\bihl_gpbZevgu_

ebgbb 3 = const y\eyxlky ebgbyfb lhdZ % = const bkoh^ghc (ijyfhc) aZ^Zqb.

H^gZdh ihkljh_gb_ ebgbc lhdZ f_lh^hf W=>: y\ey_lky k l_ogbq_kdhc klhjhgu

aZ^Zq_c [he__ keh`ghc, q_f ihkljh_gb_ ebgbc jZ\guo gZihjh\ \ k\yab k l_f,

qlh ihgZ^h[blky ba]hlh\eylv rbgu \_kvfZ keh`gh]h hq_jlZgby,

khhl\_lkl\mxs_]h hq_jlZgbx \h^hg_ijhgbpZ_fh]h dhglmjZ h[eZklb

nbevljZpbb. <\b^m wlh]h gZ ijZdlbd_ j_^dh h[jZsZxlky d ihkljh_gbx ebgbc

lhdZ f_lh^hf W=>:, Z kljhyl bo ]jZnbq_kdbf kihkh[hf ihke_ ihkljh_gby

wd\bihl_gpbZe_c bgkljmf_glZevguf iml_f.

221

Ijb ]jZnbq_kdhf ihkljh_gbb ebgbc lhdZ bf_xl \ \b^m, qlh \ bahljhiguo

]jmglZo ebgbb lhdZ b ebgbb jZ\guo gZihjh\ ^he`gu [ulv \aZbfgh

hjlh]hgZevgufb; ebgbb lhdZ, jZkiheh`_ggu_ [eb`_ d ih^a_fghfm dhglmjm

khhjm`_gby, ih k\h_c nhjf_ ijb[eb`Zxlky d hq_jlZgbx dhglmjZ, Z ebgbb lhdZ,

jZkiheh`_ggu_ m \h^hmihjZ bf_xl nhjfm, [ebadmx d hq_jlZgbx \h^hmihjZ.

@_eZl_evgh bf_lv hdhgqZl_evgmx k_ldm nbevljZpbb d\Z^jZlbqghc, l._.

khklhys_c ba djb\hebg_cguo d\Z^jZlh\, jbk. 21.1,\. >ey kh[ex^_gby wlh]h

mkeh\by g_h[oh^bfh, qlh[u kj_^gb_ ebgbb \ dZ`^hf d\Z^jZl_ [ueb jZ\gu.

>bZ]hgZeb de_lhd k_ldb nbevljZpbb ^he`gu ^Z\Zlv hjlh]hgZevgmx k_ldm.

DZkZl_evgu_ d ebgbyf jZ\guo gZihjh\, hdZgqb\Zxsboky \ m]eZo

\h^hg_ijhgbpZ_fh]h dhglmjZ khhjm`_gby, y\eyxlky [bkk_dljbkZfb wlbo m]eh\.

Ke_^m_l hlf_lblv, qlh ijb h^ghjh^ghf ]jmgl_ hq_jlZgb_

]b^jh^bgZfbq_kdhc k_ldb aZ\bkbl lhevdh hl dhgnb]mjZpbb fh^_ebjm_fhc

h[eZklb nbevljZpbhggh]h ihlhdZ b g_ aZ\bkbl hl ^_ckl\mxs_]h gZihjZ b

dhwnnbpb_glZ nbevljZpbb ]jmglZ.

F_lh^hf W=>: \uihegyxlky gZb[he__ keh`gu_ bkke_^h\Zgby iehkdbo,

ieZgh\uo b ijhkljZgkl\_gguo, gZihjguo b [_agZihjguo, mklZgh\b\rboky b

g_mklZgh\b\rboky nbevljZpbhgguo ihlhdh\ \ h^ghjh^guo, g_h^ghjh^guo,

bahljhiguo b Zgbahljhiguo ]jmglZo. Ijhba\h^ylky ihkljh_gby k_lhd l_q_gby b

hij_^_e_gby nbevljZpbhgguo jZkoh^h\, kdhjhkl_c, ]jZ^b_glh\,

iv_ahf_ljbq_kdbo gZihjh\, ^_ij_kkbhgguo ih\_joghkl_c, \_ebqbgu

ijhlb\h^Z\e_gby nbevljZpbhggh]h ihlhdZ gZ ih^a_fguc dhglmj

]b^jhkhhjm`_gbc b ^j. Hl^_evgu_ ba gZa\Zgguo aZ^Zq mdZaZgu \ jZa^_e_ «P_ev

jZ[hlu» b gZoh^yl k\h_ j_r_gb_ ih oh^m \uiheg_gby jZ[hlu.

IJBGPBI J:;HLU MKL:GH<DB W=>:

< hkgh\m ijb[hjZ W=>: iheh`_g fhkl khijhlb\e_gby MblklhgZ, dhlhjuc

ihdZaZg gZ jbk. 21.2 , Z, Z ijbgpbibZevgZy ko_fZ ijb[hjZ – gZ jbk. 21.2, [.

222

Bgl_]jZlhj W=>:-9/60 khklhbl ba iblZxs_c p_ib (bklhqgbd lhdZ,

ihgb`Zxsbc ljZgknhjfZlhj, \uijyfbl_ev) b baf_jbl_evghc p_ib (^_ebl_ev

gZijy`_gby 5 beb ]jZ^mbjh\Zgguc ihl_gpbhf_lj, bg^bdZlhj-]Zev\Zghf_lj 6,

b]eZ-smi 7 b fh^_ev bkke_^m_fhc h[eZklb nbevljZpbb 2, \uiheg_ggmx ba

we_dljhijh\h^ghc [mfZ]b).

Jbk. 21. 2

>ey hkms_kl\e_gby fhklh\hc baf_jbl_evghc ko_fu d ^_ebl_ex

gZijy`_gby 5 iZjZee_evgh ih^kh_^bgyxl fh^_ev 2, Z ih^\b`ghc dhglZdl K

^_ebl_ey gZijy`_gby q_j_a bg^bdZlhj-]Zev\Zghf_lj 6 b b]em-smi 7 kh_^bgyxl

k fh^_evx. < lhqd_ : fhklZ khijhlb\e_gbc we_dljbq_kdbc lhd jZa^_ey_lky gZ

^\_ \_l\b, koh^ysb_ky \ lhqd_ <. ?keb b]em-smi mklZgh\blv \ lhqd_ D fh^_eb k

ihl_gpbZehf, jZ\guf ihl_gpbZem gZ ih^\b`ghf dhglZdl_ K ^_ebl_ey

gZijy`_gby, lh bg^bdZlhj-]Zev\Zghf_lj 6 ihdZ`_l ghev. AgZy khijhlb\e_gby

R1 b R2 gZ ^_ebl_e_, agZq_gb_ ijb\_^_ggh]h ihl_gpbZeZ \ lhqd_ D gZoh^yl ih

nhjfme_

223

RRU r 1 , (21.1)

]^_ R – ihegh_ khijhlb\e_gb_ ^_ebl_ey R = R1 + R2.

GZ \oh^ghf b \uoh^ghf mqZkldZo fh^_eb nbevljZpbhggh]h ihlhdZ, \

k_q_gbyo dhlhjuo gZihju ihklhyggu, mklZgZ\eb\Zxl rbgu R1 b R2 ^ey

khh[s_gby bf we_dljbq_kdbo ihl_gpbZeh\ U1 b U2. LZd dZd U1 � U2 (U1 > U2), lh

\ we_dljhijh\h^ys_c fh^_eb \hagbdZ_l we_dljbq_kdbc lhd, ijbq_f

we_dljbq_kdbc ihl_gpbZe \ ij_^_eZo fh^_eb iZ^Z_l hl \_ebqbgu U1 ^h

\_ebqbgu U2.

IHJY>HD IJH<?>?GBY HIULH<

Ba]hlZ\eb\Z_lky we_dljhijh\h^ysZy fh^_ev bkke_^m_fhc h[eZklb

nbevljZpbb (\h^hijhgbpZ_fh]h hkgh\Zgby khhjm`_gby). Ijb wlhf \g_rgb_

]jZgbpu gZlmju b fh^_eb ^he`gu [ulv ]_hf_ljbq_kdb ih^h[gu b gZ ]jZgbpZo

h[eZklb nbevljZpbb gZlmju gZihj b we_dljbq_kdbc ihl_gpbZe fh^_eb ^he`gu

[ulv ZgZeh]bqgufb.

>ebgZ fh^_ebjm_fhc h[eZklb iehkdh]h gZihjgh]h nbevljZpbhggh]h

ihlhdZ ijb g_[hevrhc fhsghklb t \h^hijhgbpZ_fh]h ieZklZ, jbk. 21.3, Z, [,

gZagZqZxl ba mkeh\by

, (21.2) � tll 4...30 � �

]^_ l0 – ^ebgZ ]hjbahglZevghc ijh_dpbb g_ijhgbpZ_fhc qZklb ih^a_fgh]h

dhglmjZ khhjm`_gby.

Ijb [hevrhc fhsghklb \h^hijhgbpZ_fh]h ieZklZ (t :�) h[eZklv

nbevljZpbb h]jZgbqb\Z_lky ihemhdjm`ghklvx, jbk. 21.3, \,], k p_gljhf \ lhqd_

0,5 l0. JZ^bmk r ^he`_g [ulv g_ f_g__ 1,5 l0 beb 3S0 (S0 – ^ebgZ \_jlbdZevghc

ijh_dpbb ih^a_fgh]h dhglmjZ, \dexqZy b rimgl).

224

?keb g_h[oh^bfh fh^_ebjh\Zlv h[eZklv [_agZihjghc nbevljZpbb, jbk.

21.4, Z, [, lh ^ebgZ

tbl 4� , (21.3)

]^_ b – rbjbgZ iehlbgu ih ih^hr\_ ^h gZqZeZ ^j_gZ`Z.

Ijb ]em[hdhf aZe_]Zgbb \h^hmihjZ h[eZklv nbevljZpbb kgbam

h]jZgbqb\Z_lky ebgb_c, jZkiheh`_gghc gZ ]em[bg_ t

bt 5,2 beb Ht 5 ; (21.4)

\ jZkq_l_ ijbgbfZ_lky [hevr__ agZq_gb_ t ba \uqbke_gguo.

225

\)

])

Jbk. 21.3

GZ ebkl_ we_dljhijh\h^ghc [mfZ]b \ aZ^Zgghf fZkrlZ[_

]_hf_ljbq_kdh]h ih^h[by \uq_jqb\Zxl, Z aZl_f \uj_aZxl bkke_^m_fmx h[eZklv

nbevljZpbb. Ijb wlhf g_ ba]hlZ\eb\Zxl fh^_ev iehsZ^vx f_g__ 200 kf2, lZd

dZd gZ fZeuo fh^_eyo j_amevlZlu bkke_^h\Zgby [m^ml oZjZdl_jbah\Zlvky

226

[óevrbfb ih]j_rghklyfb b d lhfm `_ mkeh`gy_lky j_ZebaZpby ]jZgbqguo

mkeh\bc.

Jbk. 21.4

Ih ]jZgbqguf ebgbyf jZ\gh]h gZihjZ – ih ih\_joghklb ]jmglh\ \

\_jog_f b gb`g_f [v_nZo, ]^_ ^he`gu [ulv ijbdj_ie_gu khhl\_lkl\mxsb_

rbgu, g_h[oh^bfh hklZ\blv aZiZk [mfZ`gh]h djZy rbjbghc 3-4 ff ^ey

ih^dexq_gby rbg. Rimgl fh^_ebjm_lky \ \b^_ \uj_aZ khhl\_lkl\mxs_c

]em[bgu rbjbghc 1…1,5 ff.

=jZgbpu, gZ dhlhjuo [m^ml mklZgZ\eb\Zlvky lhdhih^\h^ysb_ rbgu,

\uq_jqb\Zxlky q_jguf ]jZnblguf dZjZg^Zrhf ^ey memqr_gby dhglZdlZ

f_`^m rbgZfb b we_dljhijh\h^ghc [mfZ]hc.

227

>ey ba]hlh\e_gby fh^_eb (h^ghjh^ghc ih ijh\h^bfhklb) \u[bjZxl

khjlZ [mfZ]b kh kj_^gbf agZq_gb_f khijhlb\e_gby gZ d\Z^jZl R� = 400…20000

Hf. Fh^_ev, ba]hlh\e_ggZy ba gbadhhfghc [mfZ]b, fh`_l i_j_]j_\Zlvky.

I_j_^ gZqZehf jZ[hlu gZ mklZgh\d_ W=>: -9/60 g_h[oh^bfh

hagZdhfblvky k l_ogbq_kdbf hibkZgb_f ijb[hjZ b bgkljmdpb_c ih

wdkiemZlZpbb _]h.

=hlh\Zy fh^_ev ihf_sZ_lky \ jZ[hq_c qZklb kl_g^Z bgl_]jZlhjZ gZ f_klh

dZjlhgZ g_kdhevdh [hevr_]h jZaf_jZ, q_f kZfZ fh^_ev. GZ g__ gZdeZ^u\Zxl

rbgu b iehlgh ijb`bfZxl aZ`bfZfb. AZ`bfu g_ kjZam aZ`bfZxl ^h dhgpZ, Z

ihkl_i_ggh, l._. i_j_oh^y hl h^gh]h aZ`bfZ d ^jm]hfm g_kdhevdh jZa \^hev

^Zgghc rbgu. >Ze__ k ihfhsvx dhffmlZpbhgguo rgmjh\ rbgm \_jog_]h

[v_nZ, khhl\_lkl\mxsmx gZihjm G = 100%, b rbgm gb`g_]h [v_nZ (G = 0%)

ih^kh_^bgyxl d khhl\_lkl\mxsbf ]g_a^Zf ijb[hjZ W=>:. Smi ih^kh_^bgyxl

d ]g_a^m «b]eZ». AZl_f \dexqZxl lmf[e_j «k_lv» b «]Zev\Zghf_lj» b lZdbf

h[jZahf rbgZf R1 b R2 khh[sZxl we_dljbq_kdb_ ihl_gpbZeu U1 b U2.

IjbklmiZy d ijh\_^_gbx hiulZ, ij_^\Zjbl_evgh ijh\_jyxl gme_\u_

ihdZaZgby klj_edb ]Zev\Zghf_ljZ ijb aZ^Zgghc jZaghklb ihl_gpbZeh\. >ey

wlh]h rdZeu ^_dZ^u b j_hohj^Z klZ\yl \ iheh`_gby «0» ijb \dexq_gbb

]Zev\Zghf_ljZ \ iheh`_gb_ «gbadZy qm\kl\bl_evghklv ]Zev\Zghf_ljZ». B]ehc-

smihf ke_]dZ ijbdZkZxlky d rbg_ R2 k ihl_gpbZehf «0%» (G;). ?keb klj_edZ

]Zev\Zghf_ljZ gZ baf_jbl_evghf mkljhckl\_ ijb wlhf g_ hldehgy_lky \

klhjhgm, lh fh`gh \dexqblv \ukhdmx qm\kl\bl_evghklv ]Zev\Zghf_ljZ. Ijb

hldehg_gbb klj_edb hl gmey gZ^h kdhfi_gkbjh\Zlv g_khhl\_lkl\b_ ihl_gpbZeZ

gmex ieZ\guf \jZs_gb_f \ h^gm beb ^jm]mx klhjhgm jmqdb «J_]meylhj 0%».

Ihke_ ijh\_jdb ihl_gpbZeZ «0%» ijbklmiZxl d ijh\_jd_ ihl_gpbZeZ

«100%» gZ rbg_ R1 (<;). >ey wlh]h rdZem i_j_dexqZl_ey ^_dZ^ klZ\yl gZ

^_e_gb_ «9», Z rdZem j_hohj^Z ^_e_gb_f k pbnjhc «10» - ijhlb\ mdZaZl_ey.

=Zev\Zghf_lj i_j_dexqZ_lky gZ gbadmx qm\kl\bl_evghklv, b]ehc ijbdZkZxlky

d rbg_ R1 – 100%. Ihl_gpbZe j_]mebjmxl k ihfhsvx ihl_gpbhf_ljZ

228

«J_]meylhj 100%». AZl_f i_j_oh^yl gZ \ukhdmx qm\kl\bl_evghklv

]Zev\Zghf_ljZ b mklZgZ\eb\Zxl ihl_gpbZe [he__ lhqgh.

Ihke_ mklZgh\db ihl_gpbZeh\ «0%» b «100%» gZ rbgZo fh^_eb

ijhba\h^yl [he__ lhqgmx ih^]hgdm ijhf_`mlhqguo agZq_gbc ihl_gpbZeh\ gZ

fh^_eb k ^_ebl_ey gZijy`_gby \ khhl\_lkl\bb k «Bgkljmdpb_c ih wdkiemZlZpbb

mklZgh\db W=>:-9/60».

Ihke_ j_ZebaZpbb b ijh\_jdb ]jZgbqguo mkeh\bc i_j_oh^yl d

gZoh`^_gbx wd\bihl_gpbZevguo lhq_d \gmljb ihey fh^_ebjm_fhc h[eZklb

nbevljZpbb ^ey ijh\_^_gby ih gbf khhl\_lkl\mxsbo wd\bihl_gpbZe_c (ebgbc

jZ\guo gZihjh\). >ey hlukdZgby k ihfhsvx b]eu-smiZ gZ fh^_eb lhq_d,

ijbgZ^e_`Zsbo hij_^_e_gghc wd\bihl_gpbZeb, gZ^h mklZgh\blv rdZem

i_j_dexqZl_ey ^_dZ^ gZ ^_e_gb_, khhl\_lkl\mxs__ ^Zgghfm ihl_gpbZem, Z

rdZem j_hohj^Z – gZ ^_e_gb_ «0». H[uqgh ihegh_ iZ^_gb_ ihl_gpbZeZ gZ

fh^_eb ijbgbfZxl aZ 100% beb aZ 1 b \ aZ\bkbfhklb hl g_h[oh^bfhc lhqghklb

j_r_gby aZ^Zqb ^_eyl gZ 5, 10 beb 20 qZkl_c. < gZklhys_c jZ[hl_ jZaghklv

ihl_gpbZeh\ (gZihj) jZa^_ey_lky gZ 10 qZkl_c b ihwlhfm \ ijhp_kk_ hiulZ gZ

bkke_^m_fhf ebkl_ we_dljhijh\h^ghc [mfZ]b klZ\yl lhqdb, ijbgZ^e_`Zsb_

ihl_gpbZeZf 90%, 80%,…, 10%. Lhqdb dZ`^hc wd\bihl_gpbZeb gZoh^yl b]ehc

ijb iheh`_gbb klj_edb ]Zev\Zghf_ljZ, hl\_qZxs_fm gme_\hfm hlkq_lm. Ihbkd

lhq_d wd\bihl_gpbZeb gZqbgZ_lky gZ ih^a_fghf dhglmj_ nexl[_lZ, ^ey q_]h

ijh\h^yl hkljb_f b]eu \^hev wlh]h dhglmjZ b ke_^yl aZ ihdZaZgb_f

]Zev\Zghf_ljZ LhqdZ nbdkbjm_lky gZ we_dljhijh\h^ghc [mfZ]_ e_]dbf

gZ`Zlb_f b]eu, aZl_f aZdj_iey_lky p\_lguf dZjZg^Zrhf. <lhjmx lhqdm

bkdhfhc ebgbb gZoh^yl \[ebab i_j\hc b l.^. Ihke_^gyy lhqdZ wd\bihl_gpbZeb

e_`bl gZ ]jZgbp_ fh^_eb. DZ`^mx wd\bihl_gpbZev (jZ\ghgZihjgmx ebgbx)

kljhyl ih 5-8 lhqdZf. Kh_^bgyy wlb lhqdb ieZ\ghc djb\hc, ihemqZxl ebgbx

jZ\gh]h ihl_gpbZeZ beb ebgbx ijb\_^_ggh]h gZihjZ hr = const, jbkm_fmx

p\_lguf dZjZg^Zrhf. =jZgbqgu_ ebgbb, hl\_qZxsb_ ihl_gpbZeZf 100% b 0%,

ijh\h^yl ih djZyf rbg R1 b R2. <k_ ihkljh_ggu_ lZdbf h[jZahf ebgbb

229

gZ^ibku\Zxl khhl\_lkl\mxsbfb agZq_gbyfb ijb\_^_gguo gZihjh\ hr (hr1=1.0,

hr2 =0.9, hr3 = 0.8, … , hrn = 0) beb ^_ckl\bl_evguo gZihjh\ G, k\yaZgguo k hr

aZ\bkbfhklvx

, (21.5) 2r hZhG �

]^_ - jZaghklv mjh\g_c \h^u \ \_jog_f b gb`g_f [v_nZo; h1 b h2 -

]em[bgu \ \_jog_f b gb`g_f [v_nZo, hlkqblZggu_ hl iehkdhklb kjZ\g_gby,

gZijbf_j, hl ebgbb ^gZ.

21 hhZ �

< blh]_ fh^_ev bkke_^m_fhc h[eZklb nbevljZpbb jZa^_ey_lky ebgbyfb

jZ\gh]h gZihjZ gZ ^_kylv ihykh\. IZ^_gb_ ^_ckl\mxs_]h gZihjZ \ ij_^_eZo

dZ`^h]h ihykZ khklZ\bl 0,1z.

?keb ih^a_fguc dhglmj khhjm`_gby bf__l lhqdb i_j_ehfZ, lh ihy\ey_lky

gZ^h[ghklv \ hij_^_e_gbb ihl_gpbZeZ \ gbo. K wlhc p_evx hkljb_ b]eu

mklZgZ\eb\Zxl \ jZkkfZljb\Z_fhc lhqd_, gh kgZqZeZ i_j_dexqZl_ev ^_dZ^

klZ\yl \ iheh`_gb_, khhl\_lkl\mxs__ [eb`Zcr_c kijZ\Z wd\bihl_gpbZeb, b,

\jZsZy jmqdm j_hohj^Z, ^h[b\Zxlky, qlh[u klj_edZ ]Zev\Zghf_ljZ ^Z\ZeZ

gme_\hc hlkq_l. : ^Ze__ ^_eZxl hlkq_l ih j_hohj^m b gZoh^yl bkdhfuc

ihl_gpbZe \ mdZaZgghc lhqd_.

Fh^_ev bkke_^m_fhc h[eZklb nbevljZpbb k aZdj_ie_ggufb ebgbyfb

jZ\gh]h gZihjZ k ihfhsvx dhibjh\Zevghc [mfZ]b i_j_ghkblky k

we_dljhijh\h^ghc [mfZ]b gZ fbeebf_ljh\mx.

H;J:;HLD: HIULGUO >:GGUO

<k_ \uqbke_gby agZq_gbc iZjZf_ljh\ nbevljZpbhggh]h ihlhdZ

\uihegyxlky ih bkoh^guf ^Zgguf, ijb\_^_gguf \ lZ[ebp_ 21.2.

230

Bkoh^gu_ ^Zggu_

LZ[ebpZ 21.2

Fh^_ev

h[eZklb

nbevljZpbb

ih^

nexl[_lhf

khhjm`_gby

FZkrlZ[

h[eZklb

nbevljZpbb

1:…

=em[bgZ

\h^u \

<; h1, f

=em[bgZ

\h^u \

G; h2, f

GZihj gZ

khhjm`_gbb

Z, f

Dhwnnbpb_gl

nbevljZpbb

]jmglZ D, f/k

\u^Z_lky ^ey

jZ[hlu

ba]hlh\e_ggZy

fh^_ev

1. GZ fh^_eb h[eZklb nbevljZpbb, ij_^klZ\e_gghc gZ fbeebf_ljh\hc

[mfZ]_ k ijh\_^_ggufb ebgbyfb jZ\gh]h gZihjZ, ijhba\h^blky ]jZnbq_kdh_

(hl jmdb) ihkljh_gb_ ebgbc lhdZ. Ijb wlhf bf_xl \ \b^m \ur_ijb\_^_ggu_

k\hckl\Z ]b^jh^bgZfbq_kdhc k_ldb ^\b`_gby b ijZ\beZ ihkljh_gby wlhc k_ldb.

Ihkljh_ggZy lZdbf h[jZahf ]b^jh^bgZfbq_kdZy k_ldZ bf__l \b^ – jbk. 21.5.

Jbk. 21.5

231

2. >ey hij_^_e_gby \uoh^guo ]jZ^b_glh\ J ihyk ^Z\e_gby \ ahg_ \uoh^Z

ihlhdZ \ gb`gbc [v_n jZa[b\Zxl gZ [he__ f_edb_ ihykZ (imgdlbjgZy

wd\bihl_gpbZev gZ jbk. 21.5). Ijbf_gbl_evgh d ihke_^g_fm f_edhfm ihykm b

gZoh^yl kj_^gb_ \ yq_cd_ k_ldb \uoh^gu_ ]jZ^b_glu ih nhjfme_

\uo

\uokj

l

Gj

'

' , (21.6)

]^_ ûG – iZ^_gb_ gZihjZ \ ij_^_eZo jZkkfZljb\Z_fhc yq_cdb, kgbfZ_fh_

k ]b^jh^bgZfbq_kdhc k_ldb; ûl – kj_^g__ jZkklhygb_ f_`^m wd\bihl_gpbZeyfb

\ ij_^_eZo yq_cdb, baf_jy_fh_ ih ebgbb lhdZ, ijhoh^ys_c q_j_a k_j_^bgm

yq_cdb (imgdlbjgu_ ebgbb lhdZ).

J_amevlZlu hij_^_e_gby \uoh^guo ]jZ^b_glh\ gZ ih\_joghklb ^gZ

gb`g_]h [v_nZ ij_^klZ\e_gu \ lZ[ebp_ 21.3.

<uoh^gu_ ]jZ^b_glu b kdhjhklb nbevljZpbb

LZ[ebpZ 21.3

� e_gl 1 2 3 4 5 6 7 8

ûl\uo, f

\uo\uokj lGj '' /

kjkj.e KJu , f/k

Ihke_ \uqbke_gby kj_^gbo \uoh^guo ]jZ^b_glh\ \h \k_o yq_cdZo

\uoh^gh]h ihykZ k_ldb kljhyl ih ^Zgguf lZ[ebpu 21.3 bo wixjm k p_evx

ijh\_jdb f_klghc nbevljZpbhgghc ijhqghklb ]jmglZ gZ \uoh^_

nbevljZpbhggh]h ihlhdZ. <uoh^gu_ ]jZ^b_glu g_ ^he`gu ij_\urZlv agZq_gb_

djblbq_kdh]h ]jZ^b_glZ, hij_^_ey_fh]h ih KGbI. >ey ihkljh_gby wlhc wixju

\uqbke_ggu_ \uoh^gu_ ]jZ^b_glu \ \u[jZgghf fZkrlZ[_ hldeZ^u\Zxlky ih

\_jlbdZeyf, ijhoh^ysbf q_j_a khhl\_lkl\mxsb_ lhqdb ^gZ gb`g_]h [v_nZ.

Wlb lhqdb y\eyxlky lhqdZfb i_j_k_q_gby ebgbb ^gZ G; k ebgbyfb lhdZ,

ijhoh^ysbfb q_j_a k_j_^bgm \uoh^guo yq__d k_ldb (kf. jbk. 21.5). Wlb ebgbb

232

lhdZ ^hihegbl_evgh _s_ gZ^h ijh\_klb hl jmdb (gZ jbk. 21.5 njZ]f_glu bo

ihdZaZgu imgdlbjgufb hlj_adZfb).

3. <uqbkeyxlky kj_^gb_ kdhjhklb nbevljZpbb gZ \uoh^_ ]jmglh\h]h

ihlhdZ \ gb`gbc [v_n ih nhjfme_ >Zjkb \ l_o `_ \uoh^guo yq_cdZo k_ldb,

dhlhju_ bkihevah\Zebkv \ur_ ^ey hij_^_e_gby ]jZ^b_glh\

kjDJu kj , (21.7)

]^_ D – dhwnnbpb_gl nbevljZpbb, _]h agZq_gb_ aZ^Z_lky \ jZ[hl_.

<uqbke_ggu_ agZq_gby kj_^gbo \uoh^guo kdhjhkl_c nbevljZpbb gZ

ih\_joghklb ^gZ gb`g_]h [v_nZ ij_^klZ\e_gu \ lZ[ebp_ 21.3. Ih wlbf ^Zgguf

kljhyl wixjm \uoh^guo kdhjhkl_c nbevljZpbb, ijb wlhf \uqbke_ggu_

kdhjhklb \ \u[jZgghf fZkrlZ[_ hldeZ^u\Zxlky gZ l_o `_ \_jlbdZeyo, dhlhju_

bkihevah\Zebkv ^ey ihkljh_gby wixju ]jZ^b_glh\. Gh fZkrlZ[u gZ

dhhj^bgZlguo hkyo kdhjhklb b ]jZ^b_glZ ^he`gu [ulv lZdbfb, qlh[u wixjZ

kdhjhkl_c jZaf_sZeZkv \ur_ wixju \uoh^guo ]jZ^b_glh\.

4. Hij_^_eyxl m^_evguc nbevljZpbhgguc jZkoh^, l._. jZkoh^ gZ _^bgbpm

rbjbgu h[eZklb nbevljZpbb. Wlhl jZkoh^ q _klv kmffZ m^_evguo jZkoh^h\ qe,

ijhoh^ysbo ih dZ`^hc e_gl_. M^_evguc jZkoh^ dZ`^hc e_glu qe hij_^_eyxl

]jZnhZgZeblbq_kdbf kihkh[hf ih \ujZ`_gbx

1ekj.ee Suq ' , (21.8)

]^_ ukj.e – kj_^gyy kdhjhklv nbevljZpbb gZ \uoh^_ ]jmglh\h]h ihlhdZ \

gb`gbc [v_n ih ^Zgghc e_gl_; agZq_gby ukj.e ijb\_^_gu \ lZ[ebp_ 21.3; bo

lZd`_ fh`gh [jZlv k ihkljh_gghc wixju \uoh^guo kdhjhkl_c; ûSe – rbjbgZ

e_glu ih ^gm gb`g_]h [v_nZ, hij_^_ey_lky ih q_jl_`m, jbk. 21.5.

J_amevlZlu hij_^_e_gby m^_evgh]h nbevljZpbhggh]h jZkoh^Z

ij_^klZ\e_gu \ lZ[ebp_ 21.4.

233

JZkq_l m^_evgh]h nbevljZpbhggh]h jZkoh^Z q

LZ[ebpZ 21.4

� e_gl Kj_^gyy \uoh^gZy

kdhjhklv e_glu

ukj.e

RbjbgZ e_glu gZ

\uoh^_

]jmglh\h]h

ihlhdZ,f

M^_evguc jZkoh^

e_glu qe, f3/k·f

1

2

3

4

5

q=�qe

AZl_f ih ^Zgguf lZ[ebpu 21.4, hldeZ^u\Zy \ fZkrlZ[_ gZjZklZxsmx

kmffm m^_evguo jZkoh^h\ ih e_glZf kijZ\Z hl khhl\_lkl\mxs_c e_glu, kljhyl

wixjm m^_evguo jZkoh^h\.

Iheguc nbevljZpbhgguc jZkoh^ ih^ khhjm`_gb_f _klv ijhba\_^_gb_

m^_evgh]h jZkoh^Z q gZ ^ebgm \k_]h khhjm`_gby. Ijhba\_^_gb_ iehsZ^b wixju

\uoh^guo kdhjhkl_c gZ ^ebgm khhjm`_gby lZd`_ ^Z_l iheguc nbevljZpbhgguc

jZkoh^ ih^ khhjm`_gb_f.

5. >ey hij_^_e_gby kbeu ^Z\e_gby nbevljZpbhggh]h ihlhdZ gZ nexl[_l

khhjm`_gby kljhyl wixjm \_jlbdZevgh]h ^Z\e_gby (wixjm ijhlb\h^Z\e_gby)

ihlhdZ gZ hkgh\Zgb_ khhjm`_gby. < wlbo p_eyo ih^a_fguc dhglmj khhjm`_gby

ijh_dlbjm_lky gZ ]hjbahglZevgmx ebgbx, gZ dhlhjhc hlf_qZxlky lhqdb baehfZ

dhglmjZ b lhqdb i_j_k_q_gby ebgbc jZ\gh]h gZihjZ k dhglmjhf. <h \k_o wlbo

lhqdZo \uqbkey_lky \_jlbdZevgh_ ^Z\e_gb_ ih nhjfme_

� mhZhgj r ��� 2U , g/f2

(21.9)

]^_ ! – iehlghklv \h^u; hr - ijb\_^_gguc gZihj beb qbkeh,

ihdZau\Zxs__, dZdmx qZklv ^_ckl\mxs_]h gZihjZ Z khklZ\ey_l ebgby jZ\gh]h

234

gZihjZ, ijhoh^ysZy q_j_a ^Zggmx lhqdm; h2 - ]em[bgZ \ gb`g_f [v_n_; m –

aZ]em[e_gb_ lhqdb ih^ ^ghf gb`g_]h [v_nZ.

J_amevlZlu jZkq_lZ \_jlbdZevgh]h ^Z\e_gby \ lhqdZo nex[_lZ

ij_^klZ\e_gu \ lZ[ebp_ 21.5.

AgZq_gby \_jlbdZevgh]h ^Z\e_gby nbevljZpbhggh]h ihlhdZ

\ oZjZdl_jguo lhqdZo nex[_lZ

LZ[ebpZ 21.5

� lhq_d 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Ijb\_^_ggu

c gZihj hr

AZ]em[e_gb_

lhqdb m, f

=em[bgZ \

G;, f

>Z\e_gb_ j,

IZ

JZkklhygb_

f_`^m

\_jlbdZeyf

b, f

IehsZ^v

wixju

ijhlb\h^Z\

e_gby

f_`^m

\_jlbdZeyf

b ûW, g/f

¦' WW

<uqbke_ggu_ agZq_gby ^Z\e_gby, hleh`_ggu_ \ fZkrlZ[_ ih^

khhl\_lkl\mxsbfb lhqdZfb gZ ijh_dpbb dhglmjZ hkgh\Zgby, iha\heyxl

ihkljhblv wixjm \_jlbdZevgh]h ^Z\e_gby nbevljZpbhggh]h ihlhdZ gZ

hkgh\Zgb_ khhjm`_gby (gZ jbk. 21.5 wixjZ ijhlb\h^Z\e_gby aZrljboh\ZgZ).

WixjZ ijhlb\h^Z\e_gby oZjZdl_jbam_l kmffZjgh_ ^Z\e_gb_, ijboh^ys__ky gZ

1 ih].f. ^ebgu khhjm`_gby. ?_ iehsZ^v jZ\gZ kbe_ ^Z\e_gby gZ iehsZ^v

235

hkgh\Zgby khhjm`_gby rbjbghc 1 f. WlZ kbeZ ijhoh^bl q_j_a p_glj ly`_klb

wixju ijhlb\h^Z\e_gby.

>ey hij_^_e_gby j_amevlbjmxs_c kbeu J\, ^_ckl\mxs_c gZ hkgh\Zgb_

khhjm`_gby, gZ^h mfgh`blv iehsZ^v wixju ijhlb\h^Z\e_gby gZ ^ebgm

khhjm`_gby \

W\J\ , g (21.10)

J_amevlZlu hij_^_e_gby iehsZ^b wixju ijhlb\h^Z\e_gby ij_^klZ\e_gu

\ lZ[ebp_ 21.5.

J:;HL: 22

BKKE?>H<:GB? ;?KPBJDMEYPBHGGH=H H;L?D:GBY L?E:

IEHKDBF IHL?GPB:EVGUF IHLHDHF F?LH>HF

W=>:

P_ev jZ[hlu: 1. Ihkljh_gb_ ]b^jh^bgZfbq_kdhc k_ldb ^\b`_gby ijb

[_kpbjdmeypbhgghf h[l_dZgbb aZ^Zggh]h ijhnbey k ihfhsvx bgl_]jZlhjZ

W=>:-9/60.

2. Hij_^_e_gb_ ihey jZkij_^_e_gby kdhjhkl_c b ^Z\e_gbc ijb h[l_dZgbb

ijhnbey iml_f ih^kq_lZ dhwnnbpb_glh\ kdhjhkl_c b ^Z\e_gbc \ lhqdZo

h[l_dZ_fh]h ijhnbey, Z lZd`_ agZq_gbc kdhjhkl_c b ^Z\e_gbc \ gbo.

3. Ihkljh_gb_ ]jZnbdh\ baf_g_gby dhwnnbpb_glh\ ^Z\e_gby Kpi ih ohj^_

h[l_dZ_fh]h djueh\h]h ijhnbey beb ih jZa\_jld_ djm]h\h]h ijhnbey hl^_evgh

^ey \_jog_c b gb`g_c _]h iheh\bgu.

236

4. Ihkljh_gb_ ]jZnbdh\ baf_g_gby dhwnnbpb_glZ kdhjhklb �i \^hev lj_o

wd\bihl_gpbZe_c, ijhoh^ysbo \ eh[h\hc, kj_^bgghc b dhjfh\hc qZklyo

h[l_dZ_fh]h ijhnbey ^ey \_jog_c b gb`g_c _]h iheh\bgu.

H;SB? K<?>?GBY

Iehkdh_ ihl_gpbZevgh_ l_q_gb_

AgZqbl_evgh_ qbkeh l_ogbq_kdbo aZ^Zq fh`gh j_rZlv, ij_^iheZ]Zy

^\b`_gb_ iehkdbf, lh _klv lZdbf, \ dhlhjhf \k_ iZjZf_lju l_q_gby h^bgZdh\u

\ koh^kl\_gguo lhqdZo iZjZee_evguo f_`^m kh[hc iehkdhkl_c b baf_gyxlky

lhevdh \ gZijZ\e_gbb ^\mo hk_c dhhj^bgZl.

Ihl_gpbZevgh_ l_q_gb_ – wlh [_a\boj_\h_ l_q_gb_, ijb dhlhjhf \ ihlhd_

hlkmlkl\m_l \jZs_gb_ `b^dbo qZklbp, Z ^himkdZ_lky lhevdh bo ihklmiZl_evgh_

^\b`_gb_ b ^_nhjfZpby. Fh^_ev ihl_gpbZevgh]h ^\b`_gby mijhsZ_l j_r_gb_

p_eh]h jy^Z ijbdeZ^guo aZ^Zq ]b^jhf_oZgbdb. GZijbf_j, ijb h[l_dZgbb l_e

[_a]jZgbqguf ihlhdhf, l_q_gb_ ijb[eb`_ggh ijbgbfZ_lky [_a\boj_\uf

ih\kx^m, aZ bkdexq_gb_f ih]jZgbqgh]h kehy b ]b^jh^bgZfbq_kdh]h ke_^Z.

Ih]jZgbqguc kehc – kjZ\gbl_evgh madZy h[eZklv l_q_gby `b^dhklb beb

]ZaZ, ijbe_]ZxsZy d ih\_joghklb h[l_dZ_fh]h l_eZ, \ ij_^_eZo dhlhjhc kbeu

\gmlj_gg_]h lj_gby khbaf_jbfu k kbeZfb ^Z\e_gby b bg_jpbb b kdhjhklv

baf_gy_lky hl gmey gZ ih\_joghklb l_eZ (mkeh\b_ ijbebiZgby) ^h g_dhlhjh]h

agZq_gby u0, oZjZdl_jgh]h ^ey \g_rg_c, hlghkbl_evgh ih]jZgbqgh]h kehy,

h[eZklb l_q_gby.

=b^jh^bgZfbq_kdbc ke_^ – wlh lZd`_ hlghkbl_evgh g_[hevrZy h[eZklv

l_q_gby, gZ[ex^Z_fZy aZ dhjfh\hc qZklvx h[l_dZ_fh]h l_eZ \gba ih ihlhdm,

]^_ kdhjhklv ih^lhjfh`_ggh]h l_ehf ihlhdZ ihkl_i_ggh \hkklZgZ\eb\Z_lky ^h

agZq_gby u0 \g_rg_c h[eZklb l_q_gby.

Ijb ihl_gpbZevghf beb [_a\boj_\hf l_q_gbb m]eh\Zy kdhjhklv

\jZs_gby qZklbp `b^dhklb hlghkbl_evgh k\hbo f]gh\_gguo hk_c = 0 b __

237

dhfihg_glu o = m = z = 0. ?keb jZkkfZljb\Z_lky iehkdh_ l_q_gb_,

oZjZdl_jbam_fh_ kbkl_fhc dhhj^bgZl O b M, lh \ wlhf kemqZ_

02

1 ¸̧

¹

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§

w

w�

w

w :

y

u

x

uxy

z

beb (22.1)

0 w

w�

w

w

y

u

x

uxy

.

<ujZ`_gb_ (22.1) y\ey_lky mkeh\b_f ihl_gpbZevgh]h ^\b`_gby,

hibku\Z_fh]h kdZeyjghc nmgdpb_c ihl_gpbZeZ kdhjhklb 3(o,m), qZklgu_

ijhba\h^gu_ dhlhjhc hij_^_eyxl \_dlhju dhfihg_glh\ kdhjhklb

°°¿

°°¾

½

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ww

yu

xu

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Djhf_ lh]h, ^ey ex[h]h iehkdh]h l_q_gby g_k`bfZ_fhc `b^dhklb

^he`gh \uihegylvky ^bnn_j_gpbZevgh_ mjZ\g_gb_ g_jZaju\ghklb, bf_xs__

\b^

0 w

w�

ww

y

u

x

u yx . (22.3)

MjZ\g_gb_ (22.3) ihdZau\Z_l, qlh kms_kl\m_l g_dhlhjZy kdZeyjgZy

nmgdpby lhdZ %(o,y), dhlhjZy m^h\e_l\hjy_l mkeh\byf

238

°°¿

°°¾

½

ww

ww

xu

yu

y

x

\

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(22.4)

<ujZ`Zy dhfihg_glu kdhjhklb \ mjZ\g_gbb (22.3) kh]eZkgh jZ\_gkl\Z

(22.2), ihemqbf mjZ\g_gb_ EZieZkZ ^ey nmgdpbb ihl_gpbZeZ kdhjhklb 3

02

2

2

2

w

w�

w

w

yx

MM . (22.5)

MjZ\g_gb_ EZieZkZ fh`gh aZibkZlv b ^ey nmgdpbb lhdZ %. Ih^klZ\eyy

(22.4) \ (22.1), ihemqbf

02

2

2

2

w

w�

w

w

yx

\\. (22.6)

AZ^ZqZ h[ h[l_dZgbb l_eZ iehkdbf ihl_gpbZevguf ihlhdhf g_k`bfZ_fhc

`b^dhklb k\h^blky d j_r_gbx h^gh]h ba mjZ\g_gbc (22.5), (22.6) ijb

hij_^_e_gguo ]jZgbqguo mkeh\byo. J_r_gb_ mjZ\g_gbc EZieZkZ

ZgZeblbq_kdbf kihkh[hf ijb ijhba\hevguo ]jZgbqguo mkeh\byo ^h\hevgh

keh`gh b g_ \k_]^Z \uihegbfh. Kms_kl\mxl [he__ ijhklu_ b ^hklZlhqgh

lhqgu_ ^ey ijZdlbq_kdbo jZkq_lh\ kihkh[u ]jZnbq_kdbo j_r_gbc mjZ\g_gby

EZieZkZ \ \b^_ ihkljh_gby ]b^jh^bgZfbq_kdbo k_lhd.

=b^jh^bgZfbq_kdZy k_ldZ ^\b`_gby ihlhdZ

=b^jh^bgZfbq_kdZy k_ldZ y\ey_lky ]jZnbq_kdbf \ujZ`_gb_f mjZ\g_gby

EZieZkZ b ij_^klZ\ey_l kh[hc ^\_ kbkl_fu hjlh]hgZevguo ^jm] ^jm]m ebgbc:

ebgbc jZ\gh]h ihl_gpbZeZ kdhjhklb (wd\bihl_gpbZevguo ebgbc) 3 = const b

ebgbc lhdZ % = const – ebgbc gZdeZ^u\Z_fuo gZ bkke_^m_fmx h[eZklv iehkdh]h

239

ihl_gpbZevgh]h l_q_gby `b^dhklb. =b^jh^bgZfbq_kdZy k_ldZ aZf_gy_l

\_dlhjgh_ ihe_ jZkij_^_e_gby iZjZf_ljh\ l_q_gby kdZeyjguf, dhlhjh_ [he__

m^h[gh ijb j_r_gbb aZ^Zq.

L_hjby ihl_gpbZevgh]h ^\b`_gby ^hdZau\Z_l hjlh]hgZevghklv b

d\Z^jZlbqghklv kljh_gby ]b^jh^bgZfbq_kdhc k_ldb. Wlh agZqbl, qlh \_dlhj

kdhjhklb gZijZ\e_g ih ghjfZeb d wd\bihl_gpbZeb, l._. k_f_ckl\Z ebgbc 3 =

const b % = const – hjlh]hgZevgu, b yq_cdb k_ldb ij_^klZ\eyxl \ h[s_f kemqZ_

djb\hebg_cgu_ d\Z^jZlu (jbk. 22.1).

Jbk. 22.1

<\_^_f h[hagZq_gby: ûn – jZkklhygb_ f_`^m ^\mfy khk_^gbfb

wd\bihl_gpbZeyfb \^hev ebgbb lhdZ; ûs – jZkklhygb_ f_`^m ^\mfy khk_^gbfb

ebgbyfb lhdZ \^hev wd\bihl_gpbZeb; û3 – jZaghklv agZq_gbc ihl_gpbZeZ

kdhjhklb gZ khk_^gbo wd\bihl_gpbZeyo; û% - jZaghklv agZq_gbc nmgdpbc lhdZ

gZ khk_^gbo ebgbyo lhdZ. Lh]^Z ^ey dZ`^hc yq_cdb ]b^jh^bgZfbq_kdhc k_ldb

kijZ\_^eb\h khhlghr_gb_

240

sn '

'

'' \M

. (22.7)

G_h[oh^bfh hlf_lblv, qlh gb h^gZ ba ebgbc k_ldb g_ gZqbgZ_lky b g_

aZdZgqb\Z_lky \gmljb h[eZklb l_q_gby, Z fh`_l gZqbgZlvky b aZdZgqb\Zlvky

eb[h gZ ]jZgbp_ h[eZklb l_q_gby, eb[h ij_^klZ\eylv kh[hc aZfdgmlmx djb\mx.

H^ghbf_ggu_ ebgbb k_ldb g_ fh]ml i_j_k_dZlvky gb]^_, djhf_ hkh[uo b

djblbq_kdbo lhq_d – lhq_d, \ dhlhjuo kdhjhklv jZ\gZ khhl\_lkl\_ggh

[_kdhg_qghklb beb gmex. D k\hckl\Zf ]b^jh^bgZfbq_kdhc k_ldb ke_^m_l

hlg_klb __ h[jZlbfhklv, aZdexqZxsmxky \ lhf, qlh dZ`^hc k_ld_

khhl\_lkl\mxl ^\Z \hafh`guo l_q_gby, dh]^Z wd\bihl_gpbZeu h^gh]h l_q_gby

kem`Zl ebgbyfb lhdZ ^jm]h]h b gZh[hjhl.

M^_evguc jZkoh^ f_`^m ^\mfy ebgbyfb lhdZ ihklhyg_g b fh`_l [ulv

hij_^_e_g aZ\bkbfhklvx

ii susuq '� '� 00 . (22.8)

Hlkx^Z kdhjhklv ui \ ex[hc lhqd_ i h[eZklb l_q_gby jZ\gZ

i

is

suu

'

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0 , (22.9)

]^_ u0 – h[uqgh ba\_klgZy kdhjhklv ihlhdZ «gZ [_kdhg_qghklb»; ûs0 b ûsi

– jZkklhygb_ ih wd\bihl_gpbZeyf f_`^m \u[jZggufb ebgbyfb lhdZ «gZ

[_kdhg_qghklb» b \ hdj_klghklb jZkkfZljb\Z_fhc lhqdb i.

AZqZklmx [hevrbc ijZdlbq_kdbc bgl_j_k ij_^klZ\ey_l hij_^_e_gb_ g_

kZfhc kdhjhklb ui , Z [_ajZaf_jgh]h dhwnnbpb_glZ kdhjhklb �i , dhlhjuc

oZjZdl_jbam_lky hlghr_gb_f

241

i

ii

s

s

u

u

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AgZy \_ebqbgm ^Z\e_gby «gZ [_kdhg_qghklb» j0, fh`gh hij_^_eblv

^Z\e_gb_ \ bgl_j_kmxs_c gZk lhqd_ i k ihfhsvx mjZ\g_gby ;_jgmeeb

� 2i

20

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i � (22.11)

JZkij_^_e_gb_ ^Z\e_gby \^hev h[l_dZ_fh]h l_eZ h[uqgh oZjZdl_jbam_lky

\_ebqbghc – dhwnnbpb_glhf ^Z\e_gby Kp, dhlhjuc hij_^_ey_lky dZd

hlghr_gb_ jZaghklb ^Z\e_gbc \ ^Zgghc lhqd_ gZ ih\_joghklb l_eZ \

[_kdhg_qghklb d ^bgZfbq_kdhfm ^Z\e_gbx g_\hafms_ggh]h ihlhdZ

2

20

0

u

ppC i

piU

� (22.12)

beb k mq_lhf (22.11) dhwnnbpb_gl ^Z\e_gby

2

2

0 11 ii

pis

sC [� ¸̧

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LZdbf h[jZahf, ]b^jh^bgZfbq_kdZy k_ldZ iha\hey_l hij_^_eblv ihe_

jZkij_^_e_gby kdhjhkl_c b ^Z\e_gbc, ke_^h\Zl_evgh, \uqbkeblv kbeu

\aZbfh^_ckl\by ihlhdZ b l_eZ b j_rblv jy^ ^jm]bo \hijhkh\.

MjZ\g_gb_ ;_jgmeeb gZibkZgh [_a mq_lZ m^_evghc wg_j]bb iheh`_gby \\b^m __ kjZ\gbl_evghc fZehklb; \

mjZ\g_gbb wg_j]by hlg_k_gZ d _^bgbp_ h[t_fZ

242

WE?DLJH=B>JH>BG:FBQ?KD:Y :G:EH=BY (W=>:)

< ^Zgghc jZ[hl_ jZkkfZljb\Z_lky ZgZeh]by, kms_kl\mxsZy f_`^m

iehkdbf ihl_gpbZevguf l_q_gb_f g_k`bfZ_fhc `b^dhklb b l_q_gb_f

we_dljbq_kdh]h lhdZ \ iehkdhc ijh\h^ys_c kj_^_ (\ we_dljhijh\h^ghc [mfZ]_),

hkgh\ZggZy gZ mjZ\g_gbb EZieZkZ, dhlhjuf hibku\Z_lky dZ`^h_ ba mdZaZgguo

nbabq_kdbo y\e_gbc. GZibr_f mjZ\g_gb_ EZieZkZ ^ey we_dljbq_kdh]h

ihl_gpbZeZ U \ iehkdhf ijh\h^gbd_.

02

2

2

2

w

w�

w

w

y

U

x

U. (22.14)

KjZ\gb\Zy (22.14) k (22.5) b (22.6), \b^bf, qlh kms_kl\m_l ZgZeh]by f_`^m

we_dljbq_kdbf ihl_gpbZehf, ihl_gpbZehf kdhjhklb b nmgdpb_c lhdZ.

Ke_^m_l ih^q_jdgmlv, qlh ih^h[gZy ZgZeh]by y\e_gbc lj_[m_l

h^bgZdh\h]h fZl_fZlbq_kdh]h \ujZ`_gby ]jZgbqguo mkeh\bc.

LZdbf h[jZahf, f_lh^ we_dljh]b^jh^bgZfbq_kdhc ZgZeh]bb iha\hey_l

aZf_gblv bkke_^m_fmx h[eZklv iehkdh]h ihl_gpbZevgh]h l_q_gby `b^dhklb

fh^_evx k l_q_gb_f we_dljbq_kdh]h lhdZ \ iehkdhf ijh\h^gbd_, qlh

agZqbl_evgh mijhsZ_l ba]hlh\e_gb_ kZfhc fh^_eb h[eZklb l_q_gby b ih\urZ_l

lhqghklv baf_j_gby hij_^_ey_fuo iZjZf_ljh\.

HIBK:GB? MKL:GH<DB

Bgl_]jZlhj W=>:-9/60 khklhbl ba lj_o [ehdh\: iblZl_evgh]h mkljhckl\Z

IM, baf_jbl_evgh]h mkljhckl\Z BM b ihl_gpbhf_ljbq_kdbo ^_ebl_e_c

gZijy`_gby I>G.

IblZl_evgh_ mkljhckl\h IM \ hkgh\ghf khklhbl ba ihgb`Zxs_]h

ljZgknhjfZlhjZ b ba \uijyfbl_e_c lhdZ.

243

Baf_jbl_evgh_ mkljhckl\h BM ijbgpbibZevgh khklhbl ba

]jZ^mbjh\Zggh]h ihl_gpbhf_ljZ, ]Zev\Zghf_ljZ – bg^bdZlhjZ gme_\h]h lhdZ

beb jZ\gh\_kby fhklZ, dhglZdlghc b]eu b fh^_eb bkke_^m_fhc h[eZklb

lhq_gby, \uiheg_gghc ba we_dljhijh\h^ghc [mfZ]b.

Ihl_gpbhf_ljbq_kdb_ ^_ebl_eb gZijy`_gby I>G g_h[oh^bfu ^ey

j_ZebaZpbb ]jZgbqguo mkeh\bc ijb j_r_gbb hl^_evguo l_ogbq_kdbo aZ^Zq.

GZ jbk. 22.2 ihdZaZgZ ijbgpbibZevgZy we_dljbq_kdZy ko_fZ bgl_]jZlhjZ,

dhlhjZy ij_^klZ\ey_l kh[hc q_luj_oie_qguc fhkl (fhklbd MblklhgZ).

Jbk. 22.2

244

IHJY>HD IJH<?>?GBY J:;HLU

Ih^]hlh\bl_evgu_ jZ[hlu

1. <u[bjZ_lky fZkrlZ[ fh^_eb (ijhnbey) b gZagZqZ_lky kdhjhklv u0 b

^Z\e_gb_ j0 \ g_\hafms_gghf ihlhd_ «gZ [_kdhg_qghklb», l._. gZ ]jZgbp_

fh^_ebjm_fhc h[eZklb l_q_gby.

2. <uj_aZ_lky ba we_dljhijh\h^ghc [mfZ]b fh^_ebjm_fZy h[eZklv

l_q_gby \ \b^_ ijyfhm]hevgbdZ ijb bkke_^h\Zgbb h[l_dZgby \ulygmlh]h

djueh\h]h ijhnbey, beb \ \b^_ d\Z^jZlZ ijb h[l_dZgbb djm]h\h]h ijhnbey.

Ijbq_f klhjhgu ijyfhm]hevgbdZ jZ\gu, ijbf_jgh 10-lb b 5-lb ohj^Zf, Z

klhjhgu d\Z^jZlZ - 10-lb ^bZf_ljZf djm]h\h]h ijhnbey (ohj^hc gZau\Z_lky

ijyfZy, kh_^bgyxsZy ^\_ gZb[he__ m^Ze_ggu_ ^jm] hl ^jm]Z lhqdb ijhnbey).

MdZaZggu_ jZaf_ju fh^_ebjm_fhc h[eZklb iha\heyxl kqblZlv gZ __ ]jZgbpZo

ihlhd g_\hafms_gguf, l._. lZdbf, dZdbf hg gZ[ex^Z_lky «gZ [_kdhg_qghklb».

LZd dZd bkdjb\e_gb_ ebgbc lhdZ ijb h[l_dZgbb l_eZ gZ[ex^Z_lky \

hdj_klghklyo _]h, lh gZ jZkklhygbb, ijb[ebabl_evgh jZ\ghf q_luj_f-iylb

ohj^Zf, \hafmsZxs__ \ebygb_ h[l_dZ_fh]h ijhnbey i_j_klZ_l kdZau\Zlvky.

>jm]bfb keh\Zfb, ijhlb\hiheh`gu_ klhjhgu ijyfhm]hevgbdZ (d\Z^jZlZ)

fh^_ebjm_fhc h[eZklb fh`gh ijbgylv ihiZjgh aZ ebgbb lhdZ b

wd\bihl_gpbZeb.

3. <uj_aZ_lky ba f_lZeebq_kdhc nhev]b fh^_ev ijhnbey \ ijbgylhf

fZkrlZ[_ (k kh[ex^_gb_f ]_hf_ljbq_kdh]h ih^h[by) b gZde_b\Z_lky

we_dljhijh\h^guf de__f \ p_glj_ fh^_ebjm_fhc h[eZklb l_q_gby lZd, qlh[u

_]h ohj^Z h[jZah\ZeZ k gZijZ\e_gb_f ^ebgghc klhjhgu ijyfhm]hevgbdZ

aZ^Zgguc m]he ZlZdb.

4. I_j_^ gZqZehf jZ[hlu gZ mklZgh\d_ g_h[oh^bfh hagZdhfblvky k

L_ogbq_kdbf hibkZgb_f b k Bgkljmdpb_c ^ey ijh\_^_gby bkke_^h\Zgbc gZ

bgl_]jZlhj_ W=>:-9/60.

J_p_il ijb]hlh\e_gby we_dljhijh\h^gh]h de_y: de_c ;N-2 – 30 ] (h^bg lx[bd), kibjl j_dlbnbdZl – 25 fe,

kZ`Z ]Zah\Zy – 3-4 ]

245

J_ZebaZpby ]jZgbqguo mkeh\bc

1. Ihkljh_gb_ ]b^jh^bgZfbq_kdhc k_ldb j_dhf_g^m_lky gZqbgZlv k

gZg_k_gby gZ h[eZklv l_q_gby ebgbc lhdZ. Ijb wlhf we_dljbq_kdbc ihl_gpbZe

U y\ey_lky ZgZeh]hf nmgdpbb lhdZ %.

>ey ebgbc lhdZ % = const, qlh gZ we_dljbq_kdhc fh^_eb jZ\ghp_ggh

U=const.

GZ jbk. 22.3 ihdZaZgZ bkke_^m_fZy h[eZklv l_q_gby, \uj_aZggZy \ nhjf_

ijyfhm]hevgbdZ ba we_dljhijh\h^ghc [mfZ]b. Ijbq_f klhjhgu

ijyfhm]hevgbdZ 2-3 b 1-4 ij_^klZ\eyxl kh[hc ebgbb lhdZ «gZ [_kdhg_qghklb».

>ey j_ZebaZpbb ]jZgbqguo mkeh\bc U = const g_h[oh^bfh gZ klhjhgu 2-3 b 1-

4 gZeh`blv f_lZeebq_kdb_ rbgu, ijh\h^bfhklv dhlhjuo agZqbl_evgh \ur_

ijh\h^bfhklb we_dljhijh\h^ghc [mfZ]b, qlh iha\hey_l g_ mqblu\Zlv iZ^_gb_

we_dljbq_kdh]h ihl_gpbZeZ \^hev rbgu, l._. kqblZlv ihl_gpbZe gZ g_c U =

const.

Jbk. 22.3

H[l_dZ_fuc ijhnbev lZd`_ y\ey_lky h^ghc ba ebgbc lhdZ, ihwlhfm hg

^he`_g bf_lv, dZd b rbgu, \ukhdmx ijh\h^bfhklv, qlh ^hklb]Z_lky gZde_cdhc

246

gZ we_dljhijh\h^gmx [mfZ]m h[l_dZ_fh]h ijhnbey, \uiheg_ggh]h ba

f_lZeebq_kdhc nhev]b. Lh]^Z gZ g_f we_dljbq_kdbc ihl_gpbZe U = const, qlh b

j_Zebam_l ]jZgbqgu_ mkeh\by gZ dhglmj_ h[l_dZ_fh]h lhdZ.

Klhjhgu 1-2 b 3-4 ijb ihkljh_gbb ]b^jh^bgZfbq_kdhc k_ldb

ij_^klZ\eyxl kh[hc wd\bihl_gpbZeb «gZ [_kdhg_qghklb», ^ey dhlhjuo 0 ww

n

\

beb 0 ww

n

U, qlh jZ\ghkbevgh hlkmlkl\bx ghjfZevghc khklZ\eyxs_c lhdZ gZ

]jZgbpZo 1-2 b 3-4. >jm]bfb keh\Zfb, ebgbb 1-2 b 3-4 ^he`gu [ulv

lhdhg_ijh\h^bfufb, qlh e_]dh hkms_kl\ey_lky h[j_adhc we_dljhijh\h^ghc

[mfZ]b \^hev mdZaZgguo ebgbc.

2. Ijb ihkljh_gbb k ihfhsvx bgl_]jZlhjZ W=>: kbkl_fu

wd\bihl_gpbZevguo ebgbc we_dljbq_kdbc ihl_gpbZe U y\ey_lky ZgZeh]hf

nmgdpbb ihl_gpbZeZ kdhjhkl_c 3. Ke_^h\Zl_evgh, ^ey wd\bihl_gpbZeb 3 = const

beb U = const. Ihke_^g__ j_Zebam_lky gZdeZ^dhc rbg gZ klhjhgu

ijyfhm]hevghc h[eZklb l_q_gby 1-2 b 3-4 (jbk. 22.4).

Jbk. 22.4

247

>ey klhjhg 2-3 b 1-4 ]jZgbqgu_ mkeh\by 0 ww

s

M beb 0

ww

s

U, qlh

^hklb]Z_lky h[j_adhc we_dljhijh\h^ghc [mfZ]b ih wlbf ebgbyf. Djhf_ lh]h,

h[l_dZ_fuc ijhnbev ^ey wd\bihl_gpbZe_c y\ey_lky ^bwe_dljbdhf, ihwlhfm

ijhnbev gZ we_dljhijh\h^ghc [mfZ]_ g_h[oh^bfh ZddmjZlgh \uj_aZlv.

Ihkljh_gb_ ]b^jh^bgZfbq_kdhc k_ldb ^\b`_gby ihlhdZ

1. DZd m`_ hlf_qZehkv, ihkljh_gb_ k_ldb j_dhf_g^m_lky gZqbgZlv k

gZg_k_gby ebgbc lhdZ, ^ey q_]h we_dljbq_kdZy fh^_ev bkke_^m_fhc h[eZklb

ihlhdZ kh[bjZ_lky ih ko_f_, ijb\_^_gghc gZ jbk. 22.3. Ih^\h^ylky d rbgZf

ihl_gpbZeu, jZ\gu_ 0 b 100%. Ijb wlhf gZ h[l_dZ_fhf ijhnbe_

mklZgZ\eb\Z_lky g_dhlhjh_ agZq_gb_ we_dljbq_kdh]h ihl_gpbZeZ Ud,

oZjZdl_jbamxs_]h ebgbx lhdZ, ijhoh^ysmx q_j_a djblbq_kdmx lhqdm D (jbk.

22.3). >ey baf_j_gby agZq_gby wlh]h ihl_gpbZeZ dZkZxlky dhglZdlghc b]ehc

ijhnbey b, baf_gyy khijhlb\e_gb_ gZ ]jZ^mbjh\Zgghf ihl_gpbhf_lj_

(j_hohj^_), ^h[b\Zxlky hlkmlkl\by lhdZ \ p_ib ]Zev\Zghf_ljZ. Hlukdb\Zxlky

dhglZdlghc b]ehc gZ we_dljhijh\h^ghc [mfZ]_ lhqdb k lZdbf `_ ihl_gpbZehf,

dhlhju_ iha\heyxl ihkljhblv ebgbx lhdZ, ijhoh^ysmx q_j_a djblbq_kdmx

lhqdm D. <u[jZ\ rZ] \ 5 beb 10%, ^ey baf_g_gby we_dljbq_kdh]h ihl_gpbZeZ \

h[_ klhjhgu hl ihl_gpbZeZ Ud hlukdb\Zxlky dhglZdlghc b]ehc lhqdb

hklZevguo ebgbc lhdZ.

2. >ey ihkljh_gby wd\bihl_gpbZevguo ebgbc we_dljbq_kdZy fh^_ev

kh[bjZ_lky ih ko_f_, mdZaZgghc gZ jbk. 22.4. KgZqZeZ hlukdb\Zxlky dhglZdlghc

b]ehc lhqdb wd\bihl_gpbZeb, ijhoh^ys_c q_j_a djblbq_kdmx lhqdm D. K wlhc

p_evx, dZkZykv b]ehc lhqdb D, baf_jyxl agZq_gby ihl_gpbZeZ \ g_c, aZl_f

hlukdb\Zxl lhqdb ^jm]bo wd\bihl_gpbZe_c k l_f `_ rZ]hf, qlh b ^ey ebgbc

lhdZ.

248

H;J:;HLD: HIULGUO >:GGUO

JZkq_l jZkij_^_e_gby kdhjhkl_c b ^Z\e_gbc

1. Ih ihkljh_gghc ]b^jh^bgZfbq_kdhc k_ld_ ijhba\h^blky jZkq_l

dhwnnbpb_glh\ kdhjhkl_c b ^Z\e_gbc ih nhjfmeZf (22.10) b (22.13).

2. AgZy agZq_gb_ iZjZf_ljh\ g_\hafms_ggh]h ihlhdZ u0, j0, !0,

jZkkqblu\Zxlky kdhjhklb b ^Z\e_gby \ lhqdZo h[l_dZ_fh]h ijhnbey ih

nhjfmeZf (22.9) b (22.11).

3. Kljhylky gZ ohj^_ h[l_dZ_fh]h djueh\h]h ijhnbey beb gZ jZa\_jld_

djm]eh]h ijhnbey ]jZnbdb baf_g_gby dhwnnbpb_glZ ^Z\e_gby Cji hl^_evgh ^ey

\_jog_c b gb`g_c iheh\bgu ijhnbey.

4. >ey hp_gdb \hafms_gbc, \ghkbfuo ijhnbe_f \ ihlhd, kljhylky

]jZnbdb baf_g_gby dhwnnbpb_glh\ kdhjhklb �i \^hev lj_o wd\bihl_gpbZe_c,

ijhoh^ysbo q_j_a beb \[ebab djblbq_kdhc b hkh[hc lhq_d khhl\_lkl\_ggh \

eh[h\hc b dhjfh\hc qZklyo, b q_j_a lhqdm \ kj_^bgghc qZklb ijhnbey ^ey

\_jog_c b gb`g_c iheh\bgu.

J_amevlZlu jZkq_lZ aZghkylky \ lZ[ebpu 23.1 b 23.2.

LZ[ebpZ 22.1

JZkklhygb_

f_`^m ebgbyfb

lhdZ

Dhwnnbpb_glu Kdhjhklv \ lhqd_

ijhnbey,

ui f/k

�

lhq_d

gZ

ijhnbe_

«gZ

[_kdhg_qgh

hl

lhqdb

ijhnbey ^h

[eb`Zcr_c

ebgbb

lhdZ,

kdhjhklb

,

� i

^Z\e_gby,

Cp

i

>Z\e_gb_

\ lhqd_

ijhnbey,

ji, dIZ

IZjZf_lju

g_\hafms_ggh-

]h ihlhdZ

u0=…f/k

j0=…dIZ

!=…d]/f3

249

LZ[ebpZ 22.2

JZkklhygb_ f_`^m ebgbyfb

lhdZ

�

wd\bihl_gpbZeb i � ebgbb

lhdZ,

j «gZ

[_kdhg_qghklb»,

ûs0, kf

khk_^gbfb

ûsj-(j+1)

Dhwnnbpb_glu

kdhjhklb

� �1

0

��'

'

js

s

j

[

J:;HL: 23

BKKE?>H<:GB? H;L?D:GBY L?E: IJB G:EBQBB PBJDMEYPBB

IEHKDBF IHL?GPB:EVGUF IHLHDHF F?LH>HF W=>:

P_ev jZ[hlu: 1. Ihkljh_gb_ ]b^jh^bgZfbq_kdhc k_ldb ^\b`_gby ijb

h[l_dZgbb djueh\h]h ijhnbey iehkdbf ihl_gpbZevguf ihlhdhf k gZebqb_f

pbjdmeypbb k ihfhsvx bgl_]jZlhjZ W=>:-9/60.

2. Hij_^_e_gb_ dhwnnbpb_glZ ih^t_fghc kbeu ih nhjfme_

G.?.@mdh\kdh]h b ih jZkij_^_e_gbx ^Z\e_gbc gZ ih\_joghklb ijhnbey.

H;SB? K<?>?GBY

Ijb h[l_dZgbb l_e ihl_gpbZevguf ihlhdhf kbeZ khijhlb\e_gby,

kh]eZkgh iZjZ^hdkm Wce_jZ->´:eZf[_jZ, ihemqZ_lky jZ\ghc gmex. Ihwlhfm ^ey

hij_^_e_gby kbeh\h]h \aZbfh^_ckl\by ihlhdZ k h[l_dZ_fuf l_ehf gm`gh gZ

ihl_gpbZevgh_ l_q_gb_ \hdjm] jZkkfZljb\Z_fh]h l_eZ gZeh`blv

pbjdmeypbhgguc ihlhd hl lhq_qguo \boj_c, jZkiheh`_gguo \gmljb beb ih

ih\_joghklb l_eZ, Z kZfm _]h ih\_joghklv jZkkfZljb\Zlv dZd aZfdgmlmx ebgbx

lhdZ 3= const, \gmljb dhlhjhc kms_kl\m_l l_q_gb_ `b^dhklb.

250

Ihl_gpbZevghklv l_q_gby (hlkmlkl\b_ \jZs_gby qZklbp) \ h[eZklb \g_

dhglmjZ l_eZ ijb wlhf g_ [m^_l gZjmrZlvky, b kh]eZkgh ijbgpbim

kmi_jihabpbb, lZdb_ iehkdb_ ihlhdb fh`gh gZdeZ^u\Zlv ^jm] gZ ^jm]Z.

Ijb h[l_dZgbb k gZebqb_f pbjdmeypbb djueh\h]h ijhnbey

(pbebg^jbq_kdh]h l_eZ k aZdjm]e_gghc i_j_^g_c b aZhklj_gghc aZ^g_c

djhfdZfb) ]eZ\guc \_dlhj kbe ^Z\e_gby [m^_l gZijZ\e_g i_ji_g^bdmeyjgh

kdhjhklb gZ[_]Zxs_]h ihlhdZ (kdhjhklb «gZ [_kdhg_qghklv») u0, lh _klv ijb

lZdhf ih^oh^_ eh[h\h_ khijhlb\e_gb_ Jo hklZ_lky jZ\guf gmex, Z ih^t_fgZy

kbeZ Jm hij_^_ey_lky ih nhjfme_ G.?.@mdh\kdh]h

=uJm 0U , (23.1)

]^_ Jm – ih^t_fgZy kbeZ, ^_ckl\mxsZy gZ _^bgbpm ^ebgu djueh\h]h

ijhnbey ijb h[l_dZgbb iehkdbf ihl_gpbZevguf ihlhdhf g_k`bfZ_fhc

`b^dhklb, ! – iehlghklv `b^dhklb, = – pbjdmeypby \_dlhjZ kdhjhklb ih

dhglmjm, ho\Zlu\Zxs_fm ijhnbev. Pbjdmeypb_c = \_dlhjZ kdhjhklb u ih

g_dhlhjhfm dhglmjm S gZau\Z_lky dhglmjguc bgl_]jZe

� �³ ³ �� s s

zyxs dzudyudxudsu= . (23.2)

Ba nhjfmeu G.?.@mdh\kdh]h ke_^m_l, qlh ijbqbghc ihy\e_gby

ih^t_fghc kbeu y\eyxlky \bojb, f_jhc bgl_gkb\ghklb dhlhjuo y\ey_lky

pbjdmeypby kdhjhklb. Ijb gZagZq_gbb \_ebqbgu pbjdmeypbb kdhjhklb, ^Zxs_c

agZq_gb_ ih^t_fghc kbeu, ^hklZlhqgh ohjhrh kh\iZ^Zxs__ k j_Zevguf ^ey

^Zggh]h ijhnbey, bkoh^yl ba ihklmeZlZ @mdh\kdh]h-QZieu]bgZ, kh]eZkgh

dhlhjhfm bklbgghc \_ebqbghc pbjdmeypbb y\ey_lky lZ, ijb dhlhjhc kdhjhklv \

lhqd_ aZhklj_gby h[l_dZ_fh]h ijhnbey bf__l dhg_qgh_ agZq_gb_. Ijb

ihl_gpbZevghf h[l_dZgbb djueh\h]h ijhnbey [_a pbjdmeypbb, ^Z`_ ijb fZeuo

m]eZo ZlZdb, lhqdZ koh^Z g_ kh\iZ^Z_l k hkljhc djhfdhc ijhnbey. Ijb wlhf

251

ihlhd h]b[Z_l aZ^gxx djhfdm ijhnbey b kdhjhklv \ lhqd_ aZhklj_gby

l_hj_lbq_kdb jZ\gZ [_kdhg_qghklb, qlh nbabq_kdb g_j_Zevgh. Ijb ihkljh_gbb

]b^jh^bgZfbq_kdhc k_ldb l_q_gby ^ey kemqZy h[l_dZgby l_eZ k pbjdmeypb_c

lhqdZ koh^Z ihlhdZ ^he`gZ jZkiheZ]Zlvky gZ hkljhc djhfd_ ijhnbey, ijb wlhf

kdhjhklv \ lhqd_ aZhklj_gby [m^_l bf_lv dhg_qgh_ agZq_gb_.

Ijb ihkljh_gbb ]b^jh^bgZfbq_kdhc k_ldb l_q_gby ke_^m_l bf_lv \ \b^m,

qlh ijb ihl_gpbZevghf ^\b`_gbb ihl_gpbZe kdhjhklb 3 y\ey_lky h^ghagZqghc

nmgdpb_c, ijb h[l_dZgbb k pbjdmeypb_c ihl_gpbZe kdhjhklb fgh]hagZq_g b

baf_gy_lky gZ \_ebqbgm pbjdmeypbb = ihke_ dZ`^h]h h[oh^Z dhglmjZ. Ihwlhfm

g_h[oh^bfh ijb\_klb fgh]hk\yagmx h[eZklv ^\b`_gby `b^dhklb d

h^ghk\yaghc fh^_eb h[eZklb l_q_gby gZ ijb[hj_ W=>:, ijh\h^y jZaj_a ih

wd\bihl_gpbZeb, gZqbgZxs_cky gZ h[l_dZ_fhf dhglmj_, ijb wlhf agZq_gby

ihl_gpbZeZ ih jZagu_ klhjhgu jZaj_aZ [m^ml hlebqZlvky gZ \_ebqbgm

pbjdmeypbb.

IHKLJH?GB? =B>JH>BG:FBQ?KDHC K?LDB L?Q?GBY

H[l_dZ_fuc ijhnbev ba]hlZ\eb\Z_lky ba nhev]b b ijbde_b\Z_lky d

we_dljhijh\h^ghc [mfZ]_ we_dljhijh\h^guf de__f. D ijhnbex ijbiZb\Z_lky

ijh\h^gbd kh rl_ik_evghc \bedhc, ih^dexqZ_fuc d h^ghfm ba

ihl_gpbhf_ljbq_kdbo ^_ebl_e_c gZijy`_gby. H[eZklv l_q_gby \uj_aZ_lky ba

we_dljhijh\h^ghc [mfZ]b b ih^dexqZ_lky ^ey ihkljh_gby ebgbb lhdZ % = const

d bgl_]jZlhjm W=>: (jbk. 23.1) ZgZeh]bqgh kemqZx [_kpbjdmeypbhggh]h

h[l_dZgby.

Pbjdmeypby gZ fh^_eb hkms_kl\ey_lky ih^Zq_c gZ dhglmj g_dhlhjh]h

agZq_gby Un ihl_gpbZeZ hl ^_ebl_ey gZijy`_gby. Kh]eZkgh ihklmeZlm

@mdh\kdh]h-QZieu]bgZ \_ebqbgZ pbjdmeypbb ^he`gZ [ulv lZdhc, qlh[u ihlhd

koh^be k ijhnbey \ lhqd_ aZhklj_gby ih dZkZl_evghc d dhglmjm. Ihwlhfm,

ij_`^_ q_f gZqZlv ihkljh_gb_ ebgbb lhdZ, gm`gh ih^h[jZlv agZq_gb_

ihl_gpbZeZ Un gZ ijhnbe_ ke_^mxsbf h[jZahf. Ijb ^Zgghf Un kljhyl

252

g_[hevrhc (3-5 kf) mqZklhd ebgbb lhdZ ijb[eb`Zykv d ijhnbex. ?keb ebgby %

= %n \uc^_l gZ dhglmj g_ \ lhqd_ aZhklj_gby, lh baf_gyxl agZq_gb_ Un b

ih\lhjyxl ihkljh_gb_. AZ gme_\h_ ijb[eb`_gb_ fh`gh [jZlv agZq_gb_ Un ijb

Jbk. 23.1

[_kpbjdmeypbhgghf h[l_dZgbb, lh _klv lh agZq_gb_, dhlhjh_ Z\lhfZlbq_kdb

mklZgh\blky gZ dhglmj_, dh]^Z gZ g_]h g_ ih^Zgh ^hihegbl_evgh_ gZijy`_gb_.

Ih^h[jZ\ Un, kljhyl \kx ebgbx lhdZ % = %n, ihke_ q_]h hklZevgu_ ebgbb lhdZ k

\u[jZgguf rZ]hf 5 beb 10% kljhylky lZd `_, dZd \ eZ[hjZlhjghc jZ[hl_ 22

ijb [_kpbjdmeypbhgghf h[l_dZgbb.

Ijb ihkljh_gbb wd\bihl_gpbZe_c 3 = const ^ey kemqZy h[l_dZgby k

pbjdmeypb_c g_h[oh^bfh mqblu\Zlv g_h^ghagZqghklv ihl_gpbZeZ 3. GZb[he__

m^h[guf kihkh[hf ihkljh_gby wd\bihl_gpbZe_c y\ey_lky ijbf_g_gguc \

jZ[hl_ ?.B.Iylb]hjkdhc b :.B Kfheyd «Bkke_^h\Zgb_ f_lh^hf W=>:

h[l_dZgby l_e iehkdbf ihl_gpbZevguf ihlhdhf».-FWB,1975.

Ih gZc^_gghc ebgbb lhdZ % = %n fh^_ev jZaj_aZ_lky b ijhnbev \f_kl_ k

ijbde__ghc nhev]hc \uj_aZ_lky. H[_ ihemq_ggu_ h[eZklb g_aZ\bkbfh

253

ih^dexqZxlky d bgl_]jZlhjm W=>: ^ey ihkljh_gby wd\bihl_gpbZe_c 3 = const

(jbk. 23.2) ZgZeh]bqgh kemqZx [_kpbjdmeypbhggh]h h[l_dZgby.

Jbk. 23.2

<gZqZe_ kljhylky wd\bihl_gpbZeb ^ey \_jog_c h[eZklb lZdbf h[jZahf,

qlh[u hgb ijhoh^beb q_j_a lhqdb : b H. JZkiheh`b\ f_`^m lhqdZfb : b H

p_eh_ qbkeh rZ]h\, ihemqbf \_ebqbgm rZ]Z ^ey \_jog_c h[eZklb

n

UUU OA\

� ' , (23.3)

]^_ n – p_eh_ qbkeh, \u[jZggh_ lZd, qlh[u ûU\ ihemqbeky [ebadbf d

rZ]m, k dhlhjuf ihkljh_gu ebgbb lhdZ (5 beb 10%). Ihkljh_gb_

wd\bihl_gpbZe_c gZqbgZ_lky k lhq_d : beb H b aZl_f \ h[_ klhjhgu k rZ]hf

ûU\.

< gb`g_c h[eZklb gZ mqZkldZo \g_ ijhnbey <ï:ï b HïKï wd\bihl_gpbZeb

^he`gu y\eylvky ijh^he`_gb_f wd\bihl_gpbZe_c \_jog_c h[eZklb. Lh]^Z

ijbjZ\gb\Zy qbkeh rZ]h\ gZ mqZkldZo <: b <ï:ï, ihemqbf \_ebqbgm rZ]Z ^ey

gb`g_c qZklb h[eZklb l_q_gby

254

BA

ABg U

U

UU

U

UU '

�

c� '

c '

100

100

0

0 . (23.4)

K wlbf rZ]hf kljhyl wd\bihl_gpbZeb \e_\h hl lhqdb :ï b \ijZ\h hl lhqdb

Hï. GZ mqZkld_ :ïHï ijb ihkljh_gbb k rZ]hf ûUg, \ h[s_f kemqZ_, fh`_l

meh`blvky g_p_eh_ qbkeh rZ]h\.

J:KQ?L IH>T?FGHC KBEU

Ih^t_fgZy kbeZ h[uqgh \ujZ`Z_lky \ \b^_

2

20u

SKJ mm U�� , (23.5)

]^_ Cm – dhwnnbpb_gl ih^t_fghc kbeu, S – oZjZdl_jgZy iehsZ^v, dhlhjZy

^ey iehkdhc aZ^Zqb [m^mqb hlg_k_gZ d _^bgbp_ rbjbgu \ujZablky S = l , ]^_ l –

ohj^Z ijhnbey.

<ujZ`Zy \_ebqbgm ih^t_fghc kbeu ih nhjfme_ G.?.@mdh\kdh]h,

ihemqbf ^ey dhwnnbpb_glZ ih^t_fghc kbeu

0

20

2

2

lu

=

ul

JK

mm

U

. (23.6)

GZ we_dljbq_kdhc fh^_eb h[eZklb l_q_gby ZgZeh]hf pbjdmeypbb [m^_l

kdZqhd we_dljbq_kdh]h ihl_gpbZeZ U ijb lZdhf `_ h[oh^_ dhglmjZ ijhnbey,

dhlhjuc ijhbkoh^bl ijb i_j_oh^_ q_j_a wd\bihl_gpbZev, ijh\_^_ggmx q_j_a

lhqdm :ï. Ke_^m_l bf_lv \ \b^m, qlh agZq_gby we_dljbq_kdbo ihl_gpbZeh\ gZ

h^ghc wd\bihl_gpbZeb \ \_jog_c b gb`g_c h[eZklyo [m^ml hlebqZlvky.

255

Pbjdmeypby kdhjhklb, jZ\gZy kdZqdm we_dljbq_kdh]h ihl_gpbZeZ, \ujZablky \

\b^_

¸̧¹

·¨̈©

§�

cc

O

OAA

U

UUU

L==

100

0 . (23.7)

Dhwnnbpb_gl ih^t_fghc kbeu hij_^_ey_lky lZd

¸̧¹

·¨̈©

§�

�

cc

O

OAAy

U

UUU

l

LK

50. (23.8)

<b^gh, qlh ^ey hij_^_e_gby dhwnnbpb_glZ ih^t_fghc kbeu fh`gh g_

kljhblv \kx k_ldm, Z ^hklZlhqgh ihkljhblv ebgbx lhdZ % = %n, \^hev g__

\uihegblv jZaj_a h[eZklb gZ ^\_ qZklb b, ih^dexqb\ bo d ijb[hjm, baf_jblv

we_dljbq_kdb_ ihl_gpbZeu \ lhqdZo :, :ï b H, Hï.

>ey khihklZ\e_gby fh`gh hij_^_eblv Cm ih jZkij_^_e_gbx ^Z\e_gbc gZ

dhglmj_

� � � �dxK

lul

dLynjj

KL

PL

i

m ³³

�

1

2

,cos

20

0

U

, (23.9)

lh _klv Cm [m^_l jZ\gh iehsZ^b ]jZnbdZ \ dhhj^bgZlZo CJ, l

x. Dhwnnbpb_gl

^Z\e_gby KJ gZoh^blky ih ]b^jh^bgZfbq_kdhc k_ld_ l_q_gby lZd `_, dZd b ijb

[_kpbjdmeypbhgghf h[l_dZgbb.

>ey fZl_fZlbq_kdhc h[jZ[hldb wdki_jbf_glZevguo ^Zgguo ij_^eZ]Z_lky

lZ[ebqgZy nhjfZ aZibk_c.

256

LZ[ebpZ 23.1

JZkklhygb_ f_`^m ebgbyfb lhdZ � lhq_d

gZ

ijhnbe_

Hlghkbl_ev-

gh_ jZkklhy-

gb_ l

x

«gZ [_kdh-

g_qghklb»,

ûs0, kf

hl lhqdb ijh-

nbey ^h [eb`Zc-

r_c ebgbb lhdZ,

ûsi, kf

Dhwnnbpb_gl

^Z\e_gby 2

01 ¸̧¹

·¨̈©

§

''

� i

pis

sK

Ijbf_-

qZgb_

>ebgZ

fh^_eb

L=…

>ebgZ

ohj^u

ijhnb-

ey

l=…

AgZq_-

gb_

we_dljb

q_kdh]h

ihl_gpb

ZeZ \

oZjZd-

l_jguo

lhqdZo:

UA=…

UAï=…

UO=…

UOï=…

J:;HL: 24

IHKLJH?GB? :WJH>BG:FBQ?KDHC L?GB A>:GBY

P_ev jZ[hlu. 1. Bamq_gb_ jZkij_^_e_gby ^Z\e_gby (Zwjh^bgZfbq_kdh]h

dhwnnbpb_glZ) ih ih\_joghklb a^Zgby.

2. Ihkljh_gb_ wixju ]hjbahglZevghc khklZ\eyxs_c kdhjhklb \_ljh\h]h

ihlhdZ, h[l_dZxs_]h a^Zgb_ ^ey lj_o \_jlbdZevguo k_q_gbc.

3. Ihkljh_gb_ Zwjh^bgZfbq_kdhc l_gb a^Zgby.

257

H;SB? K<?>?GBY

Ijb ijh_dlbjh\Zgbb a^Zgbc b khhjm`_gbc ^ey j_r_gby aZ^Zq ZwjZpbb `b-

ehc aZkljhcdb b ijhfure_gguo a^Zgbc g_h[oh^bfh mqblu\Zlv ^_ckl\b_ \_ljZ

gZ we_f_glu aZkljhcdb.

Hkh[_ggh agZqbl_evguf \_ljh\uf \ha^_ckl\byf ih^\_j`_gu \ukhdb_ a^Z-

gby b khhjm`_gby. Ba-aZ \_ljh\h]h \ha^_ckl\by \hagbdZ_l bgnbevljZpby \ha^m-

oZ \ ihf_s_gbb, qlh ijb\h^bl d m\_ebq_gbx l_iehihl_jv abfhc. AZ a^Zgb_f,

\ke_^kl\b_ hlju\Z ihlhdZ h[jZam_lky aZklhcgZy h[eZklv K-K (jbk.24.1) k

\boj_\uf ^\b`_gb_f, gZau\Z_fZy Zwjh^bgZfbq_kdhc l_gvx. Lmj[me_glguc

h[f_g \ wlhc h[eZklb k \g_rg_c kj_^hc hdZau\Z_lky g_^hklZlhqguf, ihwlhfm \

ij_^_eZo Zwjh^bgZfbq_kdhc l_gb g_^himklbf \u[jhk aZ]jyag_ggh]h \ha^moZ.

Jbk. 24.1

>Z\e_gb_ \_ljZ gZ khhjm`_gb_ \ujZ`Z_lky q_j_a ^bgZfbq_kdh_ ^Z\e_gb_

k\h[h^gh]h \_ljh\h]h ihlhdZ

258

j = d ! ¸¸¹

·¨¨©

§f

2

2u

, (24.1)

]^_ d – Zwjh^bgZfbq_kdbc dhwnnbpb_gl; u� - kdhjhklv \_ljZ gZ \ukhl_;

! – iehlghklv \ho^moZ.

>ey a^Zgby, bf_xs_]h nhjfm iZjZee_e_ibi_^Z, jZkiheh`_ggh]h

ghjfZevgh d ihlhdm, gZ eh[h\hc (gZ\_lj_gghc) klhjhg_ d = (0,7…0,8), gZ

luevghc klhjhg_ d = (0,2…0,3). Iheh`bl_evgh_ agZq_gb_ Zwjh^bgZfbq_kdh]h

dhwnnbpb_glZ hl-deZ^u\Z_lky \gmljb dhglmjZ khhjm`_gby, Z hljbpZl_evgh_

agZq_gb_ – kgZjm`b dhglmjZ (jbk.24.2).

Jbk. 24.2

F_oZgbaf h[jZah\Zgby Zwjh^bgZfbq_kdhc l_gb ke_^mxsbc.

KqblZ_lky, qlh lhqdZ hlju\Z ih]jZgbqgh]h kehy hl kl_gdb a^Zgby y\ey_lky

gZqZehf hlju\gh]h l_q_gby, ]^_ ih f_j_ m^Ze_gby hl a^Zgby kdhjhklb m[u\Zxl.

Fh`gh \u^_eblv ebgbx gme_\uo kdhjhkl_c H – H (jbk.24.1), \hdjm] dhlhjhc

ijhbkoh^bl pbjdmeypby qZklbp. Wlh l_q_gb_ ghkbl g_mklhcqb\uc oZjZdl_j.

H[jZah\Z\rb_ky \bojb hlghkylky \gba ih l_q_gbx, gZ bo f_kl_ \hagbdZxl

gh\u_. FZkkh\uc h[f_g k \g_rgbf ihlhdhf a^_kv g_\_ebd. Hkgh\ghc ihlhd,

h[l_dZxsbc h[eZklv Zwjh^bgZfbq_kdhc l_gb, fh`gh jZkkfZljb\Zlv dZd

ihl_gpbZevgh_ h[l_dZgb_ g_dhlhjh]h l_eZ h\Zevghc nhjfu.

AgZy kdhjhklv gZ ]jZgbp_ Zwjh^bgZfbq_kdhc l_gb a^Zgby

259

ux = ur ijb y = h,

]^_ h - \ukhlZ Zwjh^bgZfbq_kdhc l_gb (jbk.24.1), fh`gh \uqbkeblv

jZkij_^_e_gb_ kdhjhkl_c \ p_gljZevghc qZklb l_gb ih nhjfme_

ux = ur ¸¸¹

·¨¨©

§�¸

¹

ᬩ

§3

1

2

32

h

y (24.2)

H[jZlgZy kdhjhklv m hkgh\Zgby fh`_l [ulv ihemq_gZ ba nhjfmeu (24.2)

ijb y = 0 ug = - 3

1 ur , (24.3)

Z ebgby gme_\uo kdhjhkl_c H – H (jbk.1) ( ijb ux = 0) jZkiheZ]Z_lky gZ

\ukhl_

y0 = 0,58h (24.4)

Ijb h[l_dZgbb a^Zgby rbjbghc

o < 2,5 Ga^ (24.5)

Zwjh^bgZfbq_kdZy l_gv jZkijhkljZgy_lky hl aZ\_lj_gghc klhjhgu a^Zgby gZ

jZkklhygb_

l = 6 Ga^ , (24.6)

Z \ukhlZ l_gb khklZ\ey_l y = (1,8…2) Ga^ hl ih\_joghklb a_feb.

260

HIBK:GB? HIULGHC MKL:GH<DB

HiulgZy mklZgh\dZ khklhbl ba hk_\h]h \_glbeylhjZ, kha^Zxs_]h ihlhd

\ha^moZ, fh^_eb a^Zgby, \ l_e_ dhlhjhc \uiheg_gu dZgZeu, \u\_^_ggu_ \ gb`-

gbc __ lhj_p b kh_^bg_ggu_ j_abgh\ufb reZg]Zfb kh rlmp_jZfb. D rlmp_jZf

ih^kh_^bgy_lky fbdjhfZghf_lj.

>ey baf_j_gby kdhjhkl_c bkihevam_lky kdhjhklgZy ljm[dZ, aZdj_ie_ggZy

gZ ih^\b`ghf rlZlb\_, h[_ki_qb\Zxs_f __ i_j_f_s_gb_ \ ]hjbahglZevghc b

\_jlbdZevghc iehkdhklyo b hij_^_e_gb_ dhhj^bgZl lhqdb, \ dhlhjhc baf_jy_lky

kdhjhklv. Dhgkljmdpby rlZlb\Z iha\hey_l bkihevah\Zlv ^ey baf_j_gby

kdhjhklb ihlhdZ \f_klh kdhjhklghc ljm[db lZd`_ b l_jfhZg_fhf_lj, rdZeZ

j_]bkljbjmxs_]h ijb[hjZ dhlhjh]h ij_^\Zjbl_evgh lZjbjm_lky b iha\hey_l

hij_^_eblv \_ebqbgm kdhjhklb [_a dZdh]h-eb[h i_j_kq_lZ beb j_]bkljbjh\Zlv

__ gZ ^bZ]jZffghc e_gl_.

IHJY>HD <UIHEG?GBY J:;HLU

1. <dexqZxl hk_\hc \_glbeylhj.

2. K ihfhsvx fbdjhfZghf_ljZ, ihhq_j_^gh ih^dexqZ_fh]h d dZ`^hfm ba

rlmp_jh\, hij_^_eyxl jZkij_^_e_gb_ ^Z\e_gby ih dhglmjm a^Zgby.

3. K ihfhsvx kdhjhklghc ljm[db beb l_jfhZg_fhf_ljZ hij_^_eyxl

kdhjhklv ih^oh^Z b kdhjhklb \ 4 – 5 lhqdZo dZ`^hc ba lj_o \_jlbdZevguo

iehkdhkl_c (gZ^ a^Zgb_f, \ kj_^g_c b dhg_qghc qZklyo Zwjh^bgZfbq_kdhc l_gb).

>ey wlh]h kdhjhklgmx ljm[dm ijb ihfhsb ih^\b`gh]h rlZlb\Z i_j_f_sZxl \

gm`gmx lhqdm ijhkljZgkl\Z b nbdkbjmxl __ dhhj^bgZlu b ihdZaZgby fbdjhfZ-

ghf_ljZ.

261

H;J:;HLD: HIULGUO >:GGUO

1. Ih aZf_j_gguf ihdZaZgbyf fbdjhfZghf_ljZ h ff kibjlh\h]h klhe[Z

\uqbkeyxl ^Z\e_gb_ j \h \k_o lhqdZo dhglmjZ a^Zgby

j = !kigh’,

]^_ !ki - iehlghklv kibjlZ; hc - ijb\_^_ggh_ ihdZaZgb_

fbdjhfZghf_ljZ, jZ\gh_ nh ; n - ihijZ\hqguc dhwnnbpb_gl fbdjhfZghf_ljZ.

2. Ih nhjfme_ (24.1) \uqbkey_lky jZkij_^_e_gb_ Zwjh^bgZfbq_kdh]h

dhwnnbpb_glZ d ih dhglmjm a^Zgby.

3. Ih ihdZaZgbyf fbdjhfZghf_ljZ \uqbkey_lky hkj_^g_ggZy kdhjhklv \

aZ^Zgguo lhqdZo \ha^mrgh]h ihlhdZ ih nhjfme_

UUkighu 2 .

4. K mq_lhf nhjfmeu (24.5) hij_^_ey_lky fZdkbfZevgZy \ukhlZ b ^ebgZ

Zwjh^bgZfbq_kdhc l_gb.

Hiulgu_ ^Zggu_ b j_amevlZlu \uqbke_gbc k\h^ylky \ lZ[ebpm.

LZ[ebpZ 24.1.

>Z\e_gb_ ih dhglmjm a^Zgby Kdhjhklv \ lhqdZo gZ \_jlbdZeb

Dhhj^bgZlu

lhqdb

IhdZaZgby

fbdjhfZghb_ljZ

�

lhqdb

h

ff.ki.kl.

h

f.ki.kl.

j

IZ

D

O

kf

M

kf

h

ff.ki.kl.

h’

f.ki.kl

u

f/k

1 2 3 4 5 6 7 8 9 10

Ih j_amevlZlZf \uqbke_gbc \ ijbgylhf fZkrlZ[_ kljhylky wixju

jZkij_^_e_gby ^Z\e_gby ih dhglmjm a^Zgby (jbk.24.2) b wixju kdhjhkl_c

262

(jbk.24.1), gZghkblky ebgby H – H gme_\uo kdhjhkl_c b ]jZgbpu

Zwjh^bgZfbq_kdhc l_gb b jZkl_dZgby \ha^mrgh]h ihlhdZ (jbk.24.1).

J:;HL: 25

HIJ?>?E?GB? IHL?JV >:<E?GBY < =:AHIJH<H>?

P_ev jZ[hlu. 1. Hiulgh_ hij_^_e_gb_ ihl_jv ^Z\e_gby \ ]Zahijh\h^_.

2. Hij_^_e_gb_ dhwnnbpb_glZ ]b^jZ\ebq_kdh]h lj_gby � b ihkljh_gb_

aZ\bkbfhklb � = f (Re).

H;SB? K<?>?GBY

Ih^ZqZ ]ZaZ ih ljm[Zf (ijbjh^guc b bkdmkkl\_gguc ]Za, \ha^mo, iZj)

rbjhdh jZkijhkljZg_gh \ kh\j_f_gghc l_ogbd_. Ih kjZ\g_gbx k dZi_evgufb

`b^dhklyfb ^\b`_gb_ ]Zah\ ih ljm[Zf bf__l k\hb hkh[_gghklb ba-aZ jZaebqby

\ nbabq_kdbo k\hckl\Zo. < i_j\mx hq_j_^v wlb hlebqby \uau\Zxlky e_]dhc

k`bfZ_fhklvx ]ZaZ ijb g_agZqbl_evguo baf_g_gbyo ^Z\e_gby, lh]^Z dZd

dZi_evgu_ `b^dhklb ijZdlbq_kdb g_k`bfZ_fu \ [hevrhf ^bZiZahg_ ^Z\e_gbc.

Kljhbl_evgufb ghjfZfb b ijZ\beZfb (KGbI), gZijbf_j, ^ey ]hjh^kdbo

kbkl_f ]ZahkgZ[`_gby mklZgh\e_gu ke_^mxsb_ dZl_]hjbb ^Z\e_gby ]ZaZ:

gbadh]h – g_ [he__ 5o103 IZ; kj_^g_]h – hl 5o10

3 IZ ^h 0,3 FIZ b \ukhdh]h – hl

0,3 FIZ ^h 1,2 FIZ. Ijb wlhf `beu_ b h[s_kl\_ggu_ a^Zgby, mqj_`^_gby,

f_edb_ ijhfure_ggu_ ihlj_[bl_eb ih^dexqZxl d jZkij_^_ebl_evguf

]Zahijh\h^Zf gbadh]h ^Z\e_gby, ]Zahf \ukhdh]h ^Z\e_gby iblZxl

ijhfure_ggu_ ij_^ijbylby. JZkij_^_ebl_evgu_ ]Zahijh\h^u gbadh]h

^Z\e_gby ij_^klZ\eyxl kh[hc aZfdgmlmx fgh]hdhevp_\mx k_lv,

ho\Zlu\Zxsmx \kx l_jjblhjbx jZchgZ, kgZ[`Z_fh]h ]Zahf. LZd dZd

ihlj_[e_gb_ ]ZaZ hlebqZ_lky g_jZ\ghf_jghklvx, lh ]Zahijh\h^u kbkl_f

263

jZkij_^_e_gby jZkkqblu\Zxl gZ fZdkbfZevguc qZkh\hc jZkoh^, hij_^_-

e_gguc ih kh\f_s_gghfm kmlhqghfm ]jZnbdm jZa[hjZ ]ZaZ ihlj_[bl_eyfb, beb

ijb hlkmlkl\bb _]h gZ jZkq_lguc qZkh\hc jZkoh^, hij_^_ey_fuc jZaebqgufb

f_lh^Zfb.

J:KQ?LGU? A:<BKBFHKLB >EY BAHL?JFBQ?KDH=H

><B@?GBY =:A: < LJM;?

Ijb ^\b`_gbb k`bfZ_fh]h ]ZaZ mjZ\g_gb_ g_jZaju\ghklb !V& = konst

^ey ]Zahijh\h^Z ihklhyggh]h k_q_gby &=const ijbgbfZ_l \b^ mkeh\by

ihklhygkl\Z fZkkh\hc kdhjhklb !V = const. Gh ^Z\e_gb_ j ih ^ebg_

]Zahijh\h^Z mf_gvrZ_lky, Z agZqbl mf_gvrZ_lky b iehlghklv ]ZaZ !.

Ke_^h\Zl_evgh, kdhjhklv ^\b`_gby ]ZaZ # \hajZklZ_l. LZdbf h[jZahf, \ ljm[_

ihklhyggh]h k_q_gby ^\b`_gb_ g_k`bfZ_fhc `b^dhklb (! = const) [m^_l

jZ\ghf_jguf, Z k`bfZ_fhc `b^dhklb (]ZaZ) (! � const) – mkdhj_gguf.

Ijb bahl_jfbq_kdhf ^\b`_gbb L = const ^bgZfbq_kdbc dhwnnbpb_gl \yadhklb

� hklZ_lky ijZdlbq_kdb ihklhygguf ih ^ebg_ ljm[u, Z, ke_^h\Zl_evgh, g_

f_gy_lky b qbkeh J_cghev^kZ Re = P

UVd. LZdbf h[jZahf, ijb bahl_jfbq_kdhf

^\b`_gbb k`bfZ_fh]h ]ZaZ dhwnnbpb_gl ]b^jZ\ebq_kdh]h lj_gby �=f(Re,d

d w )

hklZ_lky ihklhygguf, g_kfhljy gZ baf_g_gb_ \^hev ]Zahijh\h^Z kj_^g_c

kdhjhklb ^\b`_gby V b _]h iehlghklb !. <_ebqbgZ dhwnnbpb_glZ

]b^jZ\ebq_kdh]h lj_gby � hij_^_ey_lky ba l_o `_ khh[jZ`_gbc, qlh b ijb

^\b`_gbb g_k`bfZ_fhc `b^dhklb (kf. eZ[. jZ[hlm «Hij_^_e_gb_

dhwnnbpb_glZ ]b^jZ\ebq_kdh]h khijhlb\e_gby ijb ^\b`_gbb `b^dhklb \

ljm[hijh\h^_»).

264

NhjfmeZ >Zjkb-<_ck[ZoZ kijZ\_^eb\Z lhevdh ^ey we_f_glZjgh]h

mqZkldZ dl ]Zahijh\h^Z, \ ij_^_eZo dhlhjh]h fh`gh ij_g_[j_qv baf_g_gb_f

iehlghklb ]ZaZ b kdhjhklb _]h ^\b`_gby.

- dp= �2

2V

d

dlU (25.1)

Bgl_]jbjmy (25.1) k mq_lhf ihklhygkl\Z fZkkh\hc kdhjhklb ! V = !1 V1 b

mjZ\g_gby DeZci_jhgZ

RT=Uj

, (25.2)

]^_ R – m^_evgZy ]Zah\Zy ihklhyggZy, ^ey \ha^moZ R = 287 (>`/d]) u

0D; T– l_fi_jZlmjZ ]ZaZ \ ]jZ^mkZo D_ev\bgZ; j - Z[khexlgh_ ^Z\e_gb_;

! – iehlghklv ]ZaZ;

ihemqbf aZ\bkbfhklv ^ey d\Z^jZlbqgh]h i_j_iZ^Z ^Z\e_gbc

�

1

22

21

2j

jj �

d

l !1

2

21V

, (25.3)

dhlhjmx fh`gh ij_h[jZah\Zlv d \b^m

j1 – j 2=

1

2

2

j

j'�

u �d

l!1

2

21V

. (25.4)

265

:gZeba nhjfmeu (25.4) ihdZau\Z_l, qlh hgZ hlebqZ_lky hl nhjfmeu

>Zjkb-<_ck[ZoZ fgh`bl_e_f, k\yaZgguf k i_j_iZ^hf ^Z\e_gby, dhlhjuf ijb

fZeuo ûj/j1 fh`gh ij_g_[j_qv.

LZdbf h[jZahf, ijb ]b^jZ\ebq_kdhf jZkq_l_ ]Zahijh\h^h\ jZaebqZxl ^\Z

kemqZy: fZeuo hlghkbl_evguo i_j_iZ^h\ ^Z\e_gby (ûj/jkj< 5%) b [hevrbo

i_j_iZ^Zo ^Z\e_gby (ûj/jkj > 5%). Bf__lky \ \b^m i_j_iZ^ ûp f_`^m

^Z\e_gbyfb \ gZqZevghf j1 b dhg_qghf j2 k_q_gbyo, hlg_k_gguc d kj_^g_fm

^Z\e_gbx j kj= 0,5 ( j1 + j2 ).

Ijb fZeuo hlghkbl_evguo i_j_iZ^Zo ^Z\e_gby (h[uqgh ]Zahijh\h^u

gbadh]h b kj_^g_]h ^Z\e_gby) ij_g_[j_]Zxl k`bfZ_fhklvx ]ZaZ b jZkq_l ijbg-

pbibZevgh g_ hlebqZ_lky hl jZkq_lh\ ^ey g_k`bfZ_fhc `b^dhklb ! = const.

Ke_^m_l mqblu\Zlv, qlh h[uqgh a^_kv jZkkfZljb\Zxl g_ gZihju Z ^Z\e_gby,

ihwlhfm mjZ\g_gb_ >.;_jgmeeb aZibku\Z_lky \ ke_^mxs_f \b^_:

!gz1 +p1 + ! ¸¸¹

·¨¨©

§

2

21V

= !gz2 +p2 + ! jV

'�¸¸¹

·¨¨©

§

2

22 , (25.5)

Z nhjfmeZ >Zjkb-<_ck[ZoZ

ûj = !gh = �d

l !

2

2V. (25.6)

Ijb [hevrbo i_j_iZ^Zo ^Z\e_gby (h[uqgh ]Zahijh\h^u \ukhdh]h

^Z\e_gby) jZkq_lu ijhba\h^yl k mq_lhf k`bfZ_fhklb ]ZaZ, bkihevamy nhjfmem

(25.3) b mjZ\g_gb_ >.;_jgmeeb ^ey bahl_jfbq_kdh]h ijhp_kkZ

gz1 +RTlnP1 + 2

21V

= gz2 +RTlnP2 +2

22V

+ gh. (25.7)

266

Ihl_jb \ f_klguo khijhlb\e_gbyo mqblu\Zxl k ihfhsvx wd\b\Ze_glghc

^ebgu lw, l._. f_klgh_ khijhlb\e_gb_ mkeh\gh aZf_gy_lky mqZkldhf ljm[hijh\h-

^Z k lZdbfb `_ ihl_jyfb lw =(�/�)d ; lh]^Z jZkq_lgZy ^ebgZ \hajZklZ_l

lj = l +� lw .

Ke_^m_l bf_lv \ \b^m, qlh ijb jZkq_l_ ]Zahijh\h^h\ aZqZklmx \\h^blky

ihgylb_ m^_evgh]h khijhlb\e_gby lj_gby Rl = ûj/l , l._. khijhlb\e_gb_ 1

ih].f ]Zahijh\h^Z.

HIBK:GB? HIULGHC MKL:GH<DB

Fgh]hklmi_gqZluc dhfij_kkhj 1 (jbk.25.1) q_j_a j_kb\_j 3 ih^Z_l ]Za \

]Zahijh\h^ 4, \ gZqZe_ dhlhjh]h bf__lky mkljhckl\h 2 ^ey hl\h^Z qZklb ]ZaZ, Z \

dhgp_ ]Zahijh\h^Z mklZgh\e_g jhlZf_lj 5. GZ j_kb\_j_ 3 b ih dhgpZf hiulgh]h

mqZkldZ ]Zahijh\h^Z 4 bf_xlky rlmp_ju ^ey ih^dexq_gby ^Zlqbdh\ ^Z\e_gby.

Jbk. 25.1

IHJY>HD IJH<?>?GBY J:;HLU

1. <dexqZxl dhfij_kkhj 1 b k ihfhsvx ^jhkk_ebjmxs_]h mkljhckl\Z 2

mklZgZ\eb\Zxl hij_^_e_gguc jZkoh^ \ha^moZ.

2. Baf_jyxl ^Z\e_gb_ b l_fi_jZlmjm \ j_kb\_j_ 3 k ihfhsvx U –h[jZa-

gh]h \h^ygh]h iv_ahf_ljZ b l_jfhf_ljZ.

267

3. K ihfhsvx gZdehggh]h kibjlh\h]h fbdjhfZghf_ljZ baf_jyxl ihl_-

jb ^Z\e_gby gZ hiulghf mqZkld_ ]Zahijh\h^Z 4.

4. K ihfhsvx jhlZf_ljZ 5 hij_^_eyxl jZkoh^ \ha^moZ.

Ijb jZaebqguo jZkoh^Zo ijhba\h^yl 5 – 6 hiulh\.

H;J:;HLD: HIULGUO >:GGUO

1. Ih aZf_j_gguf \ j_kb\_j_ 3 j b t ba mjZ\g_gby khklhygby (mjZ\g_gby

DeZci_jhgZ) hij_^_eyxl iehlghklv \ha^moZ !.

2. GZoh^yl ihl_jb ^Z\e_gby ûphi \ hiulghf ]Zahijh\h^_.

3. <uqbkeyxl qbkeh J_cghev^kZ Re b dhwnnbpb_gl ]b^jZ\ebq_kdh]h

lj_gby �.

4. <uqbkeyxl qbkeh J_cghev^kZ QVd

Re b dhwnnbpb_gl

]b^jZ\ebq_kdh]h lj_gby O\uq ih nhjfme_ ;eZabmkZ 25,0\uqRe

3164,0 O .

5. K mq_lhf hlghkbl_evgh]h i_j_iZ^Z ^Z\e_gby ûj/j \uqbkeyxl ihl_jb

^Z\e_gby ûj\uq b kjZ\gb\Zxl k hiulgufb ûjhi . Ijb wlhf, _keb ûj/j > 0,05,

lh ûj\uq hij_^_eyxl ih nhjfme_ (25.4), Z, _keb ûj/j < 0,05, lh ûj\uq - ih

nhjfme_ (25.6)

AgZq_gby iehlghklb \h^u b kibjlZ, dbg_fZlbq_kdh]h dhwnnbpb_glZ \ya-

dhklb � \ha^moZ ijbgbfZxl ih kijZ\hqgbdm, Zlfhkn_jgh_ ^Z\e_gb_

hij_^_eyxl ih [Zjhf_ljm.

J_amevlZlu baf_j_gbc b \uqbke_gbc aZghkylky \ lZ[ebpm 1.

268

LZ[ebpZ 25.1

HIULU

<_ebqbgu

?^.

baf_j_-

gby 1 2 3 4 5

1. Bkoh^gu_ iZjZf_lju:

- l_fi_jZlmjZ

- ihdZaZgby

iv_ahf_ljZ

- ^Z\e_gb_

- iehlghklv \ha^moZ

0D

h\

f.\h^.kl

j , IZ ! , d]/f

3

2. Ihl_jb ^Z\e_gby

- lki

- k * lki

- ûjhi

f.ki.kl.

f.ki.kl.

IZ

3. Hij_^_e_gb_ jZkoh^Z

- Z

- Q

- V – kdhjhklv

- Re – qbkeh

J_cghev^kZ

- �hi

- �\uq - ûj\uq

f3/qZk

f/k

J:;HL: 26

I:J:F?LJBQ?KDB? BKIUL:GBY P?GLJH;?@GH=H G:KHK:

P_ev jZ[hlu: ihkljh_gb_ oZjZdl_jbklbd b hij_^_e_gb_ hilbfZevguo

agZq_gbc ih^Zqb, gZihjZ b fhsghklb p_gljh[_`gh]h gZkhkZ.

H;SB? K<?>?GBY

=jZnbq_kdZy aZ\bkbfhklv gZihjZ G, fhsghklb N b DI> gZkhkZ � hl _]h

ih^Zqb Q ijb ihklhygghc qZklhl_ \jZs_gby, iehlghklb b \yadhklb `b^dhc

kj_^u gZau\Z_lky oZjZdl_jbklbdhc gZkhkZ. Ijb wlhf aZ\bkbfhklv H = f(Q)

269

gZau\Z_lky gZihjghc, Z N = f(Q) b � = f(Q) – wg_j]_lbq_kdhc oZjZdl_jbklbdhc

gZkhkZ. BkiulZgby ih mklZgh\e_gbx oZjZdl_jZ aZ\bkbfhkl_c H = f(Q) , N = f(Q)

b � = f(Q) gZau\Zxlky iZjZf_ljbq_kdbfb. H[uqgh hgb ijh\h^ylky \

aZ\h^kdbo eb[h eZ[hjZlhjguo mkeh\byo gZ ki_pbZevgh h[hjm^h\Zgguo kl_g^Zo

\ khhl\_lkl\bb k =HKL 6134-87 «GZkhku ^bgZfbq_kdb_. F_lh^u bkiulZgbc».

OZjZdl_jbklbdb(Z) gZkhkZ bkihevamxlky ^ey kh]eZkh\Zgbb _]h jZ[hlu k k_lvx, Z

lZd`_ ^ey ih^[hjZ h[hjm^h\Zgby b mklZgh\e_gbb mkeh\bc _]h fhglZ`Z b

wdkiemZlZpbb.

< dZq_kl\_ ijbf_jZ gZ jbk. 26.1 ijb\_^_gu oZjZdl_jbklbdb (gZihjgZy b

wg_j]_lbq_kdZy) p_gljh[_`gh]h gZkhkZ fZjdb D 90/20 (gZkhk dhgkhevgh]h lbiZ

k ih^Zq_c Q = 90 f3/q b gZihjhf G = 20 f) ijb n = 2900 h[/fbg [2].

Jbk. 26.1

270

K��Ih^Zq_c (h[t_fghc) gZkhkZ Q (f3/k, f

3/qZk) gZau\Z_lky hlghr_gb_

h[t_fZ ih^Z\Z_fhc `b^dhc kj_^u dh \j_f_gb.

GZihjhf gZkhkZ G gZau\Z_lky jZaghklv m^_evguo wg_j]bc gZ \uoh^_

(k_q_gb_ “g”, jbk. 26.2) b \oh^_ (k_q_gb_ “\”, kf. lZf `_) \ gZkhk, \ujZ`_ggZy

\ukhlhc klhe[Z ih^Z\Z_fhc `b^dhklb.

Jbk. 26.2

< khhl\_lkl\bb k =HKL17398-72 gZihj G hij_^_ey_lky ih aZ\bkbfhklb

g

JG

U , (26.1)

271

]^_ J – ^Z\e_gb_ gZkhkZ; ! – iehlghklv `b^dhc kj_^u; g – mkdhj_gb_

k\h[h^gh]h iZ^_gby.

>ey hij_^_e_gby ^Z\e_gby gZkhkZ bkihevam_lky \ujZ`_gb_

� \g

2\

2g

\g2

ZZgVV

jjj ���

�� UU �, (26.2)

]^_ jg b j\ – khhl\_lkl\_ggh ^Z\e_gby gZ \uoh^_ (k_q_gb_ ”g”, jbk 26.2) b \oh^_

(k_q_gb_ “\”, jbk. 26.2) \ gZkhk (^Z\e_gby gZ]g_lZgby b \kZku\Zgby); Vg b V\ –

kdhjhklb `b^dhc kj_^u gZ \uoh^_ b \oh^_ \ gZkhk; Zg b Z\ – \ukhlu p_gljh\

ly`_klb k_q_gbc \uoh^Z b \oh^Z \ gZkhk.

IjbgbfZy, qlh ^Z\e_gby jg b j\ baf_jyxlky khhl\_lkl\_ggh fZghf_ljhf 1

b \Zdmmf_ljhf 2 (ijbf_g_gb_ \Zdmmf_ljZ ij_^mkfZljb\Z_lky ^ey kemqZy

kha^Zgby \ZdmmfZ gZ \oh^_ \ gZkhk).) b mqblu\Zy, qlh \Zdmmf y\ey_lky

hljbpZl_evguf ba[ulhqguf ^Z\e_gb_f, \ujZ`_gb_ (26.1) k mq_lhf (26.2) ihke_

g_keh`guo ij_h[jZah\Zgbc ijbgbfZ_l \b^

2g

2\

2g

0\ZdfZgVV

hhhG�

��� , (26.3)

]^_ hfZg b h\Zd - khhl\_lkl\_ggh ihdZaZgby fZghf_ljZ 1 b \Zdmmf_ljZ 2,

\ujZ`_ggu_ \ f_ljZo klhe[Z i_j_dZqb\Z_fhc `b^dhklb Vg b V\ bf_xl lh`_

agZq_gb_, qlh b \ \ujZ`_gbb (26.2); h0 – jZkklhygb_ ih \_jlbdZeb f_`^m

hlf_ldhc iheh`_gby fZghf_ljZ b lhqdhc ih^dexq_gby \Zdmmf_ljZ (kf. jbk.

26.2).

<ujZ`_gb_ (26.3), ijb mkeh\bb jZ\_gkl\Z ^bZf_ljh\ \kZku\Zxs_c b

gZ]g_lZl_evghc ebgbc (dg = d\ ), beb ijb g_agZqbl_evghc (ih kjZ\g_gbx k

gZihjhf G) jZaghklb kdhjhklguo gZihjh\ (V2g – V

2\) /2g, fh`gh aZibkZlv \

ke_^mxs_f \b^_:

272

0\ZdfZg hhhG �� . (26.4)

Ihe_agZy fhsghklv gZkhkZ Ni - fhsghklv, khh[sZ_fZy gZkhkhf

ih^Z\Z_fhc `b^dhc kj_^_

Ni = !gQH = 1000

jQ d<l , (26.5)

]^_ j – ^Z\e_gb_, 2f

g ; Q – ih^ZqZ

k

f3

.

Fhsghklvx gZkhkZ N gZau\Z_lky fhsghklv, ihlj_[ey_fZy gZkhkhf

N = MÜ&, (26.6)

]^_ M – djmlysbc fhf_gl gZ \Zem gZkhkZ, Gf; & – m]eh\Zy kdhjhklv

\jZs_gby \ZeZ, k-1

.

=HKL 6134-87 ^himkdZ_l hij_^_e_gb_ fhsghklb gZkhkZ N iml_f

baf_j_gby fhsghklb ijb\h^ys_]h we_dljh^\b]Zl_ey (W>) k ihke_^mxsbf

mq_lhf _]h DI> ijb jZ[hl_ gZ aZ^Zgghf j_`bf_. < wlhf kemqZ_ \ujZ`_gb_ ^ey

jZkq_lZ N bf__l \b^

N = �^\ Ü�i Ü Wwe d<l , (26.7)

]^_ �^\ – DI> W>, hij_^_ey_fuc ih ]jZnbdm aZ\bkbfhklb _]h hl gZ]jmadb

W>; �i - DI> i_j_^Zqb; ijb g_ihkj_^kl\_gghf kh_^bg_gbb gZkhkZ k W> �i = 1;

Wwe – fhsghklv, ihlj_[ey_fZy W> ba k_lb, d<l.

Hlghr_gb_ fhsghkl_c Ni b N gZau\Z_lky DI> gZkhkZ

N

Nia . (26.8)

273

OZjZdl_jbklbdb gZkhkZ, ihemq_ggu_ ^ey hij_^_e_gghc qZklhlu \jZs_gby

\ZeZ n, fh]ml [ulv i_j_kqblZgu gZ ex[mx ^jm]mx qZklhlm \jZs_gby n1 ih

nhjfmeZf l_hjbb ih^h[by

; ;

3

11

2

1111¸̧¹

·¨̈©

§ ¸̧

¹

·¨̈©

§

n

n

N

N

n

n

H

H

n

n

Q

Q . (26.9)

HIBK:GB? HIULGHC MKL:GH<DB

Wdki_jbf_glZevgZy mklZgh\dZ (jbk. 26.3) \dexqZ_l ke_^mxsb_ hkgh\gu_

we_f_glu: gZkhk, we_dljh^\b]Zl_ev, \kZku\Zxsmx b gZ]g_lZl_evgmx ebgbb,

gZihjguc [Zd, baf_jbl_evgmx ZiiZjZlmjm.

Jbk. 26.3

274

GZkhk 1 kh_^bg_g k we_dljh^\b]Zl_e_f 2 ijb ihfhsb mijm]hc fmnlu. GZ

\kZku\Zxs_c ebgbb 3 gZkhkZ kfhglbjh\Zgh ijb_fgh_ mkljhckl\h 4, khklhys__

ba h[jZlgh]h deZiZgZ b ij_^hojZgbl_evghc k_ldb. Djhf_ lh]h, gZ \kZku\Zxs_c

ebgbb mklZgh\e_gZ j_]mebjmxsZy aZ^\b`dZ 5. GZ gZ]g_lZl_evghc ebgbb 6

mklZgh\e_gu j_]mebjmxsZy aZ^\b`dZ 7 b jZkoh^hf_j (ljm[Z <_glmjb) 8.

GZihjguc [Zd 9, bkihevam_fuc ^ey ijb_fZ \h^u, hihjh`gy_lky ijb ihfhsb

keb\ghc ljm[u 10, kgZ[`_gghc aZ^\b`dhc 11.

>ey ih^^_j`Zgby ihklhyggh]h gZihjZ b ij_^mij_`^_gby i_j_iheg_gby \

[Zd_ bf__lky ohehklhc k[jhk, khklhysbc ba ljm[u 12 b dhgbq_kdhc \hjhgdb 13.

Baf_jbl_evgZy ZiiZjZlmjZ \dexqZ_l \Zdmmff_lj 14, fZghf_lj 15,

^bnn_j_gpbZevguc fZghf_lj 16, ijbkh_^bg_gguc d jZkoh^hf_jm 8. Baf_j_gb_

qZklhlu \jZs_gby \ZeZ jZ[hq_]h dhe_kZ hkms_kl\ey_lky k ihfhsvx

we_dljhggh]h lZohf_ljZ 17. Hij_^_e_gb_ fhsghklb gZkhkZ N ijhba\h^blky

dhk\_gguf iml_f – ih ih^\_^_gghc fhsghklb we_dljbq_kdh]h lhdZ d h[fhldZf

we_dljh^\b]Zl_ey. >ey baf_j_gby wlhc fhsghklb bkihevam_lky lj_onZaguc

\Zllf_lj 18.

IHJY>HD <UIHEG?GBY J:;HLU

1. I_j_^ aZimkdhf kl_g^Z \ jZ[hlm hldju\Z_lky aZ^\b`dZ 7 gZ

gZ]g_lZl_evghc ebgbb 6 b ijhba\h^blky aZiheg_gb_ gZkhkZ 1 \h^hc.

2. <dexqZ_lky gZkhk. >ey bkdexq_gby i_j_]jmadb we_dljh^\b]Zl_ey i_j_^

imkdhf gZkhkZ ijhba\h^yl aZdjulb_ aZ^\b`db 7.

3. Ijb aZdjulhc aZ^\b`d_ 7 kgbfZxlky ihdZaZgby \Zdmmff_ljZ 14,

fZghf_ljZ 15, ^bnfZghf_ljZ 16, lZohf_ljZ 17, \Zllf_ljZ 18.

4. Iml_f ihke_^h\Zl_evgh]h hldjulby aZ^\b`db 7 mklZgZ\eb\Z_lky 7…9

^jm]bo j_`bfh\ jZ[hlu gZkhkZ b ^ey dZ`^h]h ba gbo ijhba\h^yl l_ `_ aZf_ju,

qlh [ueb i_j_qbke_gu \ i.3.

275

5. >ey ihemq_gby gZ^_`guo j_amevlZlh\ j_dhf_g^m_lky ih\lhjblv hiulu

ihke_^h\Zl_evgh \ h[jZlghf ihjy^d_ (^h ihegh]h aZdjulby aZ^\b`db 7). <k_

j_amevlZlu baf_j_gbc \ghkylky \ lZ[ebpm 26.1. (< ijb\_^_gghf \b^_ lZ[e. 26.1

ij_^mkfZljb\Z_l hij_^_e_gb_ gZihjZ gZkhkZ ih \ujZ`_gbx 26.4).

6. Ihke_ ijh\_^_gby bkiulZgbc ijhba\h^blky hldexq_gb_ gZkhkZ 1 b

\Zllf_ljZ 18.

Ijbf_qZgby: FZjdZ gZkhkZ –

>bZf_lj \kZku\Zxs_c ebgbb d< =

>bZf_lj gZ]g_lZl_evghc ebgbb dg =

<_jlbdZevgh_ jZkklhygb_ f_`^m hlf_ldhc iheh`_gby

fZghf_ljZ b lhqdhc ih^dexq_gby \Zdmmf_ljZ h0 =

DI> we_dljh^\b]Zl_ey �^\ =

H;J:;HLD: HIULGUO >:GGUO

1. Ih jZaghklb h ihdZaZgbc ^bnn_j_gpbZevgh]h fZghf_ljZ,

ih^dexq_ggh]h d jZkoh^hf_jm <_glmjb, b ih lZjbjh\hqghfm ]jZnbdm Q = f(h)

hij_^_ey_lky ih^ZqZ gZkhkZ Q (e/k).

2. Ih nhjfme_ (26.4) jZkkqblu\Z_lky gZihj G, jZa\b\Z_fuc gZkhkhf (f).

3. Ih nhjfme_ (26.5) hij_^_ey_lky ihe_agZy fhsghklv gZkhkZ Ni (d<l).

4. Ih nhjfme_ (26.7) k bkihevah\Zgb_f ]jZnbq_kdhc aZ\bkbfhklb DI>

we_dljh^\b]Zl_ey hl ih^\_^_gghc d g_fm fhsghklb, hij_^_ey_lky fhsghklv

gZkhkZ N (d<l).

5. Ih nhjfme_ (26.8) hij_^_ey_lky iheguc DI> gZkhkZ �. <k_ j_amevlZlu

jZkq_lZ \ghkylky \ lZ[e. 26.1.

6. GZ hkgh\Zgbb j_amevlZlh\ \uqbke_gbc, ihemq_gguo ^ey aZ^Zgghc

qZklhlu \jZs_gby n jZ[hq_]h dhe_kZ, kljhyl gZihjgmx (G = f(Q)) b

wg_j]_lbq_kdmx (N = f(Q), � = f(Q)) oZjZdl_jbklbdb gZkhkZ. Ijb ihkljh_gbb

276

]jZnbdh\ oZjZdl_jbklbd ke_^m_l hjb_glbjh\Zlvky gZ h[jZa_p, ijb\_^_gguc gZ

jbk. 26.1.

7. GZ ]jZnbdZo mklZgZ\eb\Zxlky hilbfZevgu_ agZq_gby iZjZf_ljh\ (gZihjZ

(Hhil), ih^Zqb (Qhil), fhsghklb (Nhil) gZkhkZ, khhl\_lkl\mxsb_ j_`bfm jZ[hlm

k fZdkbfZevguf DI> �fZo. A^_kv `_ ihdZau\Z_lky jZ[hqbc bgl_j\Ze

wdkiemZlZpbb gZkhkZ, \ jZfdZo dhlhjh]h \_ebqbgZ fZdkbfZevgh]h DI> �fZo

kgb`Z_lky g_ [he__, q_f gZ 10%.

8.Ijb g_h[oh^bfhklb ihkljh_gby oZjZdl_jbklbd gZkhkZ ^ey ^jm]hc qZklhlu

\jZs_gby n, ijhba\h^yl i_j_kq_l iZjZf_ljh\ Q, H, N ih nhjfmeZf ih^h[by

(26.9).

277

LZ[ebpZ 27.1

Hij_^_e_gb_

ih^Zqb gZkhkZ

Hij_^_e_gb_ gZihjZ gZkhkZ Hij_^_e_gb_

fhsghklb gZkhkZ

IhdZaZgby

\Zdmmf_ljZ

IhdZaZgby

fZghf_ljZ

� hiulZ

IhdZaZg

by

^bnfZg

h-f_ljZ

h

Ih^Zq

Z

gZkhkZ

Q h\Zd j hfZg

GZ-

ihj

G

Ihe_a

gZy

fhsgh

klv

gZkhkZ

Nn

IhdZaZgby

\Zllf_ljZ

Wwe

Fhsghk

lv

gZkhkZ

N

DI>

gZkhkZ

JZaf_j-

ghklv

f.\h^.kl. e/k ff.jl.kl f.\h^.kl. d]k/kf2 f.\h^.kl. f d<l d<l d<l %

1

2

3

4

5

6

278

J:;HL: 27

D:<BL:PBHGGU? BKIUL:GBY P?GLJH;?@GH=H G:KHK:

P_ev jZ[hlu.1. >_fhgkljZpby gZ eZ[hjZlhjghf kl_g^_ \g_rgbo

ijbagZdh\ \hagbdgh\_gby dZ\blZpbb ijb jZ[hl_ p_gljh[_`gh]h gZkhkZ.

2. Ihkljh_gb_ dZ\blZpbhgghc oZjZdl_jbklbdb b hij_^_e_gb_ ^himklbfuo

agZq_gbc dZ\blZpbhggh]h aZiZkZ b \ukhlu \kZku\Zgby gZkhkZ.

H;SB? K<?>?GBY

DZ\blZpb_c gZau\Z_lky y\e_gb_ \kdbiZgby `b^dhklb ijb ihgb`_gbb

^Z\e_gby ^h ^Z\e_gby gZkus_gguo iZjh\ i_j_dZqb\Z_fhc `b^dhklb.

<kdbiZgb_ `b^dhklb khijh\h`^Z_lky h[jZah\Zgb_f dZ\_jg (iZjh\uo b ]Zah\uo

imauj_c), dhlhju_ m\e_dZxlky ihlhdhf \ h[eZklv ih\ur_ggh]h ^Z\e_gby, ]^_

ijhbkoh^bl bo dhg^_gkZpby. Ijb dhg^_gkZpbb bf__l f_klh ^\b`_gb_ qZklbp

`b^dhklb k \hajZklZxs_c kdhjhklvx d p_gljm dZ\_jgu. Ijb ^hklb`_gbb

p_gljZ dZ\_jgu ijhbkoh^bl khm^Zj_gb_ qZklbp, khijh\h`^Z_fh_ j_adbf

ih\ur_gb_f ^Z\e_gby (]b^jZ\ebq_kdbc m^Zj). Ih^ ^_ckl\b_f ]b^jZ\ebq_kdbo

m^Zjh\, ijhl_dZxsbo k \ukhdhc qZklhlhc, ijhbkoh^bl f_klgh_ jZajmr_gb_

(wjhaby) jZ[hq_c ih\_joghklb gZkhkgh]h dhe_kZ, qlh y\ey_lky gZb[he__

hiZkguf ke_^kl\b_f dZ\blZpbb.

IjZ\bevgZy mklZgh\dZ gZkhkZ hlghkbl_evgh mjh\gy jZ[hq_c `b^dhklb \

[Zd_, \u[hj jZaf_jh\ b iZjZf_ljh\ ihlhdZ \h \kZku\Zxs_f ljm[hijh\h^_

^he`gu h[_ki_qb\Zlv jZ[hlm gZkhkZ \ [_kdZ\blZpbhgghf j_`bf_.

>ey bkdexq_gby dZ\blZpbb g_h[oh^bfh qlh[u Z[khexlgh_ ^Z\e_gb_ gZ

\oh^_ \ gZkhk j\o [ueh \ur_ ^Z\e_gby gZkus_gguo iZjh\ jg.i. i_j_dZqb\Z_fhc

`b^dhklb.

279

GZ hkgh\Zgbb mjZ\g_gby >.;_jgmeeb aZ\bkbfhklv ^ey hij_^_e_gby

^Z\e_gby j\o bf__l \b^

(27.1) lj.\k2\\0\o 2/// hgVHgpgj ��� UU

]^_ j0 - Z[khexlgh_ ^Z\e_gb_ \ ijb_fghf j_a_j\mZj_ (qZs_ \k_]h jZ\gh

Zlfhkn_jghfm ^Z\e_gbx); G\ – \ukhlZ \kZku\Zgby; V\ - kdhjhklv `b^dhklb gZ

\oh^_ \ gZkhk; hlj.\k - ihl_jb gZihjZ \h \kZku\Zxs_c ebgbb.

Ba mjZ\g_gby (27.1) \b^gh, qlh ih\ur_gb_ \ukhlu \kZku\Zgby G\ b

ihl_jv gZihjZ hlj.\k ijb\h^bl d kgb`_gbx ^Z\e_gby j\o gZ \oh^_ \ gZkhk. Ijb

^hklZlhqgh [hevrbo agZq_gbyo \ukhlu \kZku\Zgby b khijhlb\e_gby

\kZku\Zxs_c ebgbb ^Z\e_gb_ gZ \oh^_ \ gZkhk klZgh\blky gZklhevdh fZeuf,

qlh klZgh\blky jZ\guf ^Z\e_gbx gZkus_gguo iZjh\ jg.i, ijb dhlhjhf

\hagbdZ_l dZ\blZpby.

K.K.Jm^g_\uf [ueh ij_^eh`_gh ^ey hij_^_e_gby ghjfZevguo mkeh\bc

jZ[hlu gZkhkZ bkihevah\Zlv ihgylby ^himkdZ_fh]h dZ\blZpbhggh]h aZiZkZ

(>DA) ûh. Ih^ >DA ûh ihgbfZxl ij_\ur_gb_ ihegh]h gZihjZ `b^dhklb gZ

\oh^_ \ gZkhk gZ^ gZihjhf, dhlhjuc khhl\_lkl\m_l ^Z\e_gbx gZkus_ggh]h iZjZ

jg.i i_j_dZqb\Z_fhc `b^dhklb ijb jZ[hq_c l_fi_jZlmj_

� �gpgVgph k/// g.i2\\o �� ' UU . (27.2)

< ijZdlbd_ wdkiemZlZpbb ehiZklguo ]b^jhfZrbg gZjy^m k ûh

bkihevam_lky b lZdhc iZjZf_lj dZd djblbq_kdbc dZ\blZpbhgguc aZiZk ûhdj,

khhl\_lkl\mxsbc fhf_glm gZqZeZ dZ\blZpbb \ ihlhd_ `b^dhklb. >ey

hij_^_e_gby dZ\blZpbhgguo dZq_kl\ gZkhkZ ijh\h^yl _]h bkiulZgby, ih

j_amevlZlZf dhlhjuo ihemqZxl dZ\blZpbhggmx oZjZdl_jbklbdm (jbk.27.1).

280

Jbk. 27.1

HgZ ij_^klZ\ey_l kh[hc aZ\bkbfhklb gZihjZ G, fhsghklb N, DI> � hl

>DA ûh ijb ihklhygguo agZq_gbyo ih^Zqb gZkhkZ Q b qZklhlu \jZs_gby n

jZ[hq_]h dhe_kZ. Ijb ^hklZlhqgh [hevrbo agZq_gbyo >DA ûh ihdZaZl_eb

gZkhkZ (G, N, �) khojZgyxlky ihklhyggufb. H^gZdh ijb ^hklb`_gbb

djblbq_kdh]h agZq_gby >DA (ûhdj) wlb ihdZaZl_eb mf_gvrZxlky. GZ

dZ\blZpbhgghc oZjZdl_jbklbd_ h[uqgh jZaebqZxl ^\Z djblbq_kdbo j_`bfZ

dZ\blZpbb - i_j\uc b \lhjhc ijb agZq_gbyo ûhdj1 b ûhdj2 khhl\_lkl\_ggh.

I_j\uc djblbq_kdbc j_`bf khhl\_lkl\m_l fhf_glm gZqZeZ dZ\blZpbb \ gZkhk_

b hij_^_ey_lky ih gZqZem kgb`_gby gZihjZ, fhsghklb b DI>. <lhjhc j_`bf

(ijb ûhdj2) khhl\_lkl\m_l fhf_glm kju\Z jZ[hlu gZkhkZ b oZjZdl_jbam_lky

gZqZehf j_adh]h iZ^_gby gZihjZ, fhsghklb, DI> b ih^Zqb. ?keb ijb

wdkiemZlZpbb gZkhkZ g_h[oh^bfh bkdexqblv dZ\blZpbhgguc j_`bf, lh \ wlhf

kemqZ_ aZ gZbf_gvrbc dZ\blZpbhgguc aZiZk ijbgbfZ_lky agZq_gb_ ûhdj1.

281

Djblbq_kdbc dZ\blZpbhgguc aZiZk fh`_l [ulv jZkkqblZg ih nhjfme_

K.K.Jm^g_\Z

� 3/4

dj /10 CQnh ' � , (27.3)

]^_ n - qZklhlZ \jZs_gby jZ[hq_]h dhe_kZ, fbg-1

; Q – ih^ZqZ gZkhkZ, f3/k;

K - dZ\blZpbhgguc dhwnnbpb_gl [ukljhoh^ghklb (K = 800 – 1000 ^ey ûhdj1 b K

= 1300 –1500 ^ey ûhdj2).

GZ ijZdlbd_, \\b^m keh`ghklb mq_lZ \k_o nZdlhjh\, gZagZqZxl g_[hevrh_

ij_\ur_gb_ ^himklbfh]h dZ\blZpbhggh]h aZiZkZ gZ^ djblbq_kdbf. H[uqgh wlh

ij_\ur_gb_ ijbgbfZ_lky jZ\guf

� � dj^hi 3,11,1 hh '� ' . (27.4)

LZdbf h[jZahf, ^ey h[_ki_q_gby ghjfZevghc jZ[hlu gZkhkZ g_h[oh^bfh,

qlh[u

ûh � ûh^hi . (27.5)

IjbgbfZy \h \gbfZgb_ mkeh\b_ (27.5) ba \ujZ`_gby (27.2) ke_^m_l

� � � � � � hgpgVgj '�t� k/2/k/ g.i2\\o . (27.6)

Ijh\_^y ij_h[jZah\Zgb_ aZ\bkbfhklb (27.1) k mq_lhf \ujZ`_gby (27.6)

ihemqbf nhjfmem ^ey jZkq_lZ ^himklbfhc \ukhlu \kZku\Zgby , ijb

dhlhjhc h[_ki_qb\Z_lky mkeh\b_ [_kdZ\blZpbhgghc jZ[hlu gZkhkZ. >ey kemqZy

aZ[hjZ `b^dhklb ba hldjulh]h j_a_j\mZjZ

^hi\H

282

� � � � ^hilj.\kg.iZ^hi\ k/ hhgjjG '��� . (27.7)

Ba aZ\bkbfhklb (27.7) \b^gh, qlh \ukhlZ aZ\bkbl hl ^Z\e_gby \

iblZl_evghf j_a_j\mZj_, l_fi_jZlmju `b^dhklb (l_fi_jZlmjZ `b^dhklb

h^ghagZqgh \eby_l gZ ^Z\e_gb_ gZkus_gguo iZjh\ jg.i (kf. lZ[e.

27.1),^himklbfh]h dZ\blZpbhggh]h aZiZkZ b ihl_jv gZihjZ \h \kZku\Zxs_f

ljm[hijh\h^_.

^hi\H

<ebygb_ l_fi_jZlmju gZ ^Z\e_gb_ jg.i gZkus_ggh]h iZjZ \h^u

LZ[ebpZ 27.1

t, 0C jg.i, IZ t,

0C jg.i, IZ t,

0C jg.i, IZ

0 600 30 4300 80 48200

5 900 40 7500 90 71400

10 1208 50 12600 100 100330

20 2337 60 20200 125 237000

25 3200 70 31700 150 48500

HIBK:GB? HIULGHC MKL:GH<DB

Hiulu ijh\h^ylky gZ wdki_jbf_glZevghc mklZgh\d_ (kf. jbk. 26.3),

hibkZgb_ dhlhjhc ijb\_^_gh \ jZ[hl_ 26. :[khexlgh_ ^Z\e_gb_ gZ \oh^_ \

gZkhk baf_gy_lky k ihfhsvx j_]mebjmxs_c aZ^\b`db 5, mklZgh\e_gghc gZ

\kZku\Zxs_c ebgbb.

IHJY>HD <UIHEG?GBY J:;HLU

1.Ih^]hlh\dZ, imkd b ijh\_jdZ jZ[hlu eZ[hjZlhjgh]h kl_g^Z (kf. jbk.

26.3) \uihegyxlky ijb iheghklvx hldjulhc aZ^\b`d_ 5 \ khhl\_lkl\bb k

ijZ\beZfb, ijb\_^_ggufb \ jZ[hl_ 27.

283

2. Ih jZkoh^hf_jm <_glmjb 8 b ^bnn_j_gpbZevghfm fZghf_ljm 16

hij_^_ey_lky ih^ZqZ Q , ijb dhlhjhc ijh\h^ylky dZ\blZpbhggu_ bkiulZgby

gZkhkZ. Ijb wlhf kgbfZxlky ihdZaZgby \Zdmmf_ljZ 14, fZghf_ljZ 15, lZohf_ljZ

17, \Zllf_ljZ 18.

3. Ijb ihfhsb aZ^\b`db 5 mklZgZ\eb\Z_lky \Zdmmf_ljbq_kdh_ ^Z\e_gb_

gZ \oh^_ \ gZkhk, gZijbf_j, jZ\gh_ 35 dIZ. Iml_f ijbdjulby (hldjulby)

aZ^\b`db 7 \hkklZgZ\eb\Z_lky bkoh^gZy ih^ZqZ gZkhkZ (dZ\blZpbhggZy

oZjZdl_jbklbdZ kljhblky ijb Q = const) b ijhba\h^blky ih\lhjguc hlkq_l

ihdZaZgbc ijb[hjh\, mdZaZgguo \ i.2.

4. MklZgZ\eb\Zy \hajZklZxsb_ agZq_gby \Zdmf_ljbq_kdh]h ^Z\e_gby

(40, 50, 65, 70, 75 dIZ), ZgZeh]bqguf h[jZahf ijh\h^ylky ihke_^mxsb_ hiulu.

Ijb ijb[eb`_gbb d dZ\blZpbhgghfm j_`bfm b ijb gZqZ\r_cky dZ\blZpbb

ke_^m_l ^hihegbl_evgh kgylv g_kdhevdh lhq_d k f_gvrbfb bgl_j\ZeZfb.

5. Baf_jyxlky l_fi_jZlmjZ `b^dhklb b \_ebqbgZ Zlfhkn_jgh]h ^Z\e_gby.

H;J:;HLD: HIULGUO >:GGUO

1. GZihj G, ih^ZqZ Q, fhsghklb N b Ni, DI> gZkhkZ � hij_^_eyxlky

lZdbf `_ h[jZahf, dZd wlh ^_eZehkv \ jZ[hl_ � 27.

2. Ih nhjfme_ (27.2) ^ey dZ`^h]h hiulZ \uqbkey_lky dZ\blZpbhgguc

aZiZk

ûh. G_h[oh^bfu_ ^ey jZkq_lZ ûh agZq_gby ^Z\e_gby jg.i [_jmlky ba lZ[ebpu 27.

<k_ j_amevlZlu baf_j_gbc b \uqbke_gbc aZghkylky \ lZ[ebpm 27.1 (kf. jZ[hlm

27).

3. Ih ihemq_gguf j_amevlZlZf \uqbke_gbc kljhblky dZ\blZpbhggZy

oZjZdl_jbklbdZ gZkhkZ G = f(ûh); N = f(ûh); � = f(ûh). Ijb ihkljh_gbb

dZ\blZpbhgghc oZjZdl_jbklbdb aZ h[jZa_p ijbgbfZxlky ]jZnbdb, ijb\_^_ggu_

gZ jbk. 27.

284

4. Ih dZ\blZpbhgghc oZjZdl_jbklbd_ hij_^_eyxlky i_j\uc (ûhdj1) b

\lhjhc (ûhdj2) djblbq_kdb_ dZ\blZpbhggu_ aZiZku k ihke_^mxsbf kjZ\g_gb_f

bo agZq_gbc k \_ebqbghc, \uqbke_gghc ih nhjfme_ (27.3).

5. Ih nhjfmeZf (27.4) b (27.7) jZkkqblu\Zxlky khhl\_lkl\_ggh

^himklbfu_ dZ\blZpbhgguc aZiZk ûh^hi b \ukhlZ \kZku\Zgby . ^hi\H

J:;HL: 28

BAMQ?GB? Y<E?GBY D:<BL:PBB < =B>JHKBKL?F:O

P_ev jZ[hlu. 1. <bamZevgh_ gZ[ex^_gb_ y\e_gby dZ\blZpbb \ f_klghf

khijhlb\e_gbb.

2. Hij_^_e_gb_ lbiZ, nhjfu b klZ^bb dZ\blZpbb.

3. <bamZevgh_ gZ[ex^_gb_ Zdmklbq_kdhc dZ\blZpbb.

4. Hij_^_e_gb_ qbkeZ dZ\blZpbb b kjZ\g_gb_ _]h agZq_gby k djblbq_kdbf.

H;SB? K<?>?GBY

DZ\blZpby fh`_l \hagbdgmlv \ `b^dhklyo, gZoh^ysboky dZd \ khklhygbb

ihdhy, lZd b \ ^\b`_gbb. JZaebqZxl dZ\blZpbx ^bgZfbq_kdh]h b Zdmklbq_kdh]h

ijhbkoh`^_gby. ?keb ihgb`_gb_ ^Z\e_gby, \uau\Zxs__ dZ\blZpbx,

ijhbkoh^bl \ j_amevlZl_ [hevrbo f_klguo kdhjhkl_c \ ihlhd_ ^\b`ms_cky

dZi_evghc `b^dhklb, lh dZ\blZpby – ]b^jh^bgZfbq_kdZy, Z ijb Zdmklbq_kdbo

\hegZo – Zdmklbq_kdZy. < wlhf kemqZ_ __ \uau\Zxl mevljZa\mdh\u_ dhe_[Zgby.

Djblbq_kdh_, k lhqdb aj_gby \hagbdgh\_gby dZ\blZpbb, ^Z\e_gb_

hij_^_ey_lky nbabq_kdbfb k\hckl\Zfb `b^dhklb b, \ aZ\bkbfhklb hl __

khklhygby, fh`_l baf_gylvky \ ^h\hevgh agZqbl_evguo ij_^_eZo. <

ijZdlbq_kdbo jZkq_lZo, k\yaZgguo k dZ\blZpbhggufb j_`bfZfb jZ[hlu

285

]b^jZ\ebq_kdbo fZrbg b kbkl_f, \ dZq_kl\_ djblbq_kdh]h ^Z\e_gby h[uqgh

ijbgbfZxl ^Z\e_gb_ jg.i. gZkus_gguo iZjh\ `b^dhklb ijb ^Zgghc

l_fi_jZlmj_.

DZ\blZpby khijh\h`^Z_lky jZajmr_gb_f ih\_joghklb, gZ dhlhjhc

\hagbdZxl b g_dhlhjh_ \j_fy kms_kl\mxl dZ\blZpbhggu_ imaujb. Wlh

jZajmr_gb_ y\ey_lky h^gbf ba kZfuo hiZkguo ihke_^kl\bc dZ\blZpbb b

gZau\Z_lky dZ\blZpbhgghc wjhab_c, \uau\Z_fhc koehiu\Zgb_f dZ\blZpbhgguo

dZ\_jg k h[jZah\Zgb_f dmfmeylb\guo fbdjhkljmc.

Y\e_gb_ dZ\blZpbb \ ]b^jZ\ebq_kdbo kbkl_fZo b mkljhckl\Zo \hagbdZ_l,

ij_`^_ \k_]h, \ l_o f_klZo, ]^_ ihlhd ij_l_ji_\Z_l f_klgh_ km`_gb_ k

ihke_^mxsbf jZkrbj_gb_f, gZijbf_j, \ j_]mebjmxsbo hj]ZgZo, ^bZnjZ]fZo,

dhe_gZo, jZ[hqbo dhe_kZo p_gljh[_`guo gZkhkh\ b ^j.

< keh`guo ]b^jZ\ebq_kdbo kbkl_fZo [hevrhc ijhly`_gghklb ijhp_kk

h[jZah\Zgby b jZajmr_gby dZ\blZpbhgguo ahg ijb\h^bl d \hagbdgh\_gbx

]b^jZ\ebq_kdh]h m^ZjZ. DZ\blZpby g_[eZ]hijbylgh hljZ`Z_lky gZ jZ[hl_

h[hjm^h\Zgby, ijb\h^bl d \b[jZpbb b rmfZf, wjhabhgghfm jZajmr_gbx,

m\_ebq_gbx ]b^jZ\ebq_kdbo khijhlb\e_gbc, mf_gvr_gbx ih^Zqb, gZihjZ,

fhsghklb b d.i.^. ehiZklguo gZkhkh\.

Lbiu dZ\blZpbb:

IjhnbevgZy dZ\blZpby gZ[ex^Z_lky gZ ohjhrh h[l_dZ_fuo

ih\_joghklyo, \hagbdZ_l ba y^_j dZ\blZpbb, gZoh^ysboky gZ l\_j^uo kl_gdZo.

<hagbdZ_l h[uqgh \ ljm[Zo, \h^hf_jguo mkljhckl\Zo lbiZ ljm[u <_glmjb,

dZgZeZo ]b^jZ\ebq_kdbo fZrbg.

Kju\gZy dZ\blZpby \hagbdZ_l \ \bojyo aZ iehoh h[l_dZ_fufb

we_f_glZfb ]b^jZ\ebq_kdbo mkljhckl\, fh`_l bf_lv f_klh gZ ]jZgbp_

aZlhie_gghc kljmb, \ul_dZxs_c ba hl\_jklby k [hevrhc kdhjhklvx.

286

Nhjfu dZ\blZpbb:

Imaujvdh\Zy nhjfZ oZjZdl_jbam_lky jhklhf, khdjZs_gb_f b

koehiu\Zgb_f ihqlb kn_jbq_kdbo dZ\_jg, ijhghkysboky ih jZaebqguf

ljZ_dlhjbyf q_j_a ahgm ihgb`_ggh]h ^Z\e_gby.

Ie_ghqgZy nhjfZ ij_^klZ\ey_l kh[hc klZpbhgZjgmx dZ\_jgm, dZd [u

ijbebirmx \ \b^_ lhgdh]h kehy ih i_jbf_ljm k`Zlh]h k_q_gby \ dZdhf-eb[h

we_f_gl_ f_klgh]h khijhlb\e_gby, gZijbf_j, ljm[u <_glmjb. Ih\_joghklv

dZ\_jgu ijhajZqgZ, o\hklh\Zy qZklv imevkbjm_l, i_jbh^bq_kdb hlju\Z_lky b

mghkblky ihlhdhf.

Wr_ehggZy nhjfZ oZjZdl_jbam_lky l_f, qlh [ebadh b^msb_ ^jm] aZ

^jm]hf \aju\Zxsb_ky b koehiu\Zxsb_ky ihqlb kn_jbq_kdb_ dZ\_jgu

jZkiheh`_gu gZ h^ghc ljZ_dlhjbb, gZqbgZxs_cky \ g_dhlhjhc g_ih^\b`ghc

lhqd_.

<boj_\Zy nhjfZ ij_^klZ\ey_l kh[hc ^bkdj_lgh ke_^mxsb_ k ihlhdhf

\bojb, gZ hkyo dhlhjuo \hagbdZxl b jZa\b\Zxlky dZ\blZpbhggu_ dZ\_jgu, g_

ijbe_]Zxsb_ d ih\_joghklb h[l_dZ_fh]h we_f_glZ.

KlZ^bb jZa\blby dZ\blZpbb:

I – khhl\_lkl\m_l gZqZem ihy\e_gby hl^_evguo imaujvdh\, dhlhju_

h[jZamxl g_mklhcqb\mx dZ\blZpbhggmx ahgm. OZjZdl_jbam_lky keZ[uf

m\_ebq_gb_f rmfZ.

II – oZjZdl_jbam_lky baf_g_gb_f ]b^jZ\ebq_kdbo oZjZdl_jbklbd ihlhdZ,

h[jZah\Zgb_f mklhcqb\uo dZ\blZpbhgguo ahg hij_^_e_gguo jZaf_jh\, dhlhju_

kl_kgyxl `b\h_ k_q_gb_ ihlhdZ, m\_ebqb\Zxlky ihl_jb wg_j]bb, mom^rZxlky

oZjZdl_jbklbdb fZrbg, mkbeb\Z_lky rmf.

III – hij_^_ey_lky ij_djZs_gb_f ijbjhklZ jZkoh^Z ijb m\_ebq_gbb

i_j_iZ^Z ^Z\e_gbc, ijhbkoh^bl «kju\» jZ[hlu ]b^jZ\ebq_kdhc fZrbgu beb

kbkl_fu. <g_rgb_ oZjZdl_jbklbdb klZgh\ylky kh\_jr_ggh g_ijb_fe_fufb.

287

>ey oZjZdl_jbklbdb f_klguo ]b^jZ\ebq_kdbo khijhlb\e_gbc \

hlghr_gbb dZ\blZpbb ijbf_gy_lky [_ajZaf_jguc djbl_jbc, gZau\Z_fuc

qbkehf dZ\blZpbb:

æ 2/2

g.i.1

V

jj

U

� , (28.1)

]^_ j1 b V – khhl\_lkl\_ggh ^Z\e_gb_ b kdhjhklv \ oZjZdl_jghf k_q_gbb

(gZijbf_j, \ k_q_gbb aZ f_klguf khijhlb\e_gb_f);

jg.i. – ^Z\e_gb_ gZkus_gguo iZjh\ `b^dhklb.

AgZq_gb_ 1, ijb dhlhjhf \ f_klghf khijhlb\e_gbb gZqbgZ_lky dZ\blZpby,

gZau\Z_lky djblbq_kdbf qbkehf dZ\blZpbb ædj. Ih k\h_fm kfukem qbkeh

dZ\blZpbb ZgZeh]bqgh qbkem Wce_jZ 2ff

f

V

pWu

U , hgh bkihevam_lky ijb

]b^jh^bgZfbq_kdhf fh^_ebjh\Zgbb, dZd djbl_jbc ih^h[by l_q_gby k

dZ\blZpb_c.

HIBK:GB? HIULGHC MKL:GH<DB

DZ\blZpbhggZy mklZgh\dZ (jbk. 28.1) khklhbl ba ihjrg_\h]h gZkhkZ 1 k

j_]mebjm_fhc ih^Zq_c, f_klgh]h khijhlb\e_gby 2, ^jhkk_e_c 3 b 4, [ZdZ 5,

ij_^hojZgbl_evgh]h deZiZgZ 6, ]b^jhZddmfmeylhjZ 7, fZghf_ljh\ 8 b 9,

\Zdmmf_ljZ 10, jZkoh^hf_jZ 11 b kh_^bgbl_evguo ljm[hijh\h^h\.

F_klgh_ khijhlb\e_gb_ 2 ij_^klZ\ey_l kh[hc kf_gguc ijhajZqguc

we_f_gl, ba]hlh\e_gguc ba hj]Zgbq_kdh]h kl_deZ, \gmlj_ggyy ihehklv dhlhjh]h

\uiheg_gZ \ \b^_ ljm[u <_glmjb beb dZgZeZ dZdh]h-eb[h bgh]h k_q_gby

(\g_aZigh_ jZkrbj_gb_, \g_aZigh_ km`_gb_ b l.^.). >jhkk_eb 3 b 4 iha\heyxl

baf_gylv i_j_iZ^ ^Z\e_gbc gZ f_klghf khijhlb\e_gbb, ]b^jhZddmfmeylhj 7

h[_ki_qb\Z_l k]eZ`b\Zgb_ imevkZpbc ih^Zqb gZkhkZ, Z deZiZg 6 ij_^hojZgy_l

_]h hl i_j_]jmadb.

288

Jbk. 28.1

:dmklbq_kdZy dZ\blZpby hkms_kl\ey_lky \ ijhajZqghf khkm^_ k \h^hc

ijb ihfhsb mevljZa\mdh\h]h ^bki_j]ZlhjZ.

IHJY>HD IJH<?>?GBY J:;HLU

1. <dexqZxl gZkhk.

2. Nbdkbjmxl ihdZaZgby fZghf_ljh\, \Zdmmf_ljZ b jZkoh^hf_jZ ijb

fbgbfZevghc ih^Zq_ gZkhkZ.

3. M\_ebqb\Zxl ih^Zqm gZkhkZ ^h ihy\e_gby dZ\blZpbhgguo imaujvdh\,

\bamZevgh hij_^_eyxl lbi, nhjfm b klZ^bx dZ\blZpbb, nbdkbjmxl ihdZaZgby

ijb[hjh\.

289

4. Ijb ihfhsb ^jhkk_e_c baf_gyxl i_j_iZ^ ^Z\e_gby gZ f_klghf

khijhlb\e_gbb b nbdkbjmxl ihdZaZgby ijb[hjh\ ijb 3…4 jZaebqguo jZkoh^Zo

b i_j_iZ^Zo ^Z\e_gby.

5. <bamZevgh gZ[ex^Zxl Zdmklbq_kdmx dZ\blZpbx \ khkm^_ ^bki_j]ZlhjZ

gZ jZaebqguo qZklhlZo b fhsghklb.

H;J:;HLD: HIULGUO >:GGUO

1. Ih ihdZaZgbyf fZghf_ljZ \uqbkeyxl i_j_iZ^ ^Z\e_gby gZ f_klghf

khijhlb\e_gbb.

2. Ih ihdZaZgbyf jZkoh^hf_jZ \uqbkeyxl kdhjhklv `b^dhklb \

]hjeh\bg_ ljm[u <_glmjb.

3. <uqbkeyxl qbkeh dZ\blZpbb ih nhjfme_

æ2/2

k`1

V

jj

U

� , (28.2)

]^_ ! – iehlghklv \h^u; j1– ^Z\e_gb_ gZ \oh^_ \ ljm[m <_glmjb; jk` –

^Z\e_gb_ \ madhf k_q_gbb ljm[u <_glmjb; V – kdhjhklv gZ \oh^_ \ ljm[m

<_glmjb beb gZ \uoh^_.

4. <uqbkeyxl djblbq_kdh_ qbkeh dZ\blZpbb ædj

æ 2/2

g.i1dj

V

jj

U

� , (28.3)

]^_ jg.i - ^Z\e_gb_ gZkus_gguo iZjh\.

>ey ljm[u <_glmjb

290

æ 1

2

2

1

21

21

22

dj �¸̧¹

·¨̈©

§

�

S

S

V

VV, (28.4)

]^_ S1 – iehsZ^v k_q_gby i_j_^ \oh^hf \ ljm[m <_glmjb; S2 – iehsZ^v

k_q_gby \ madhc qZklb ljm[u <_glmjb.

Hiulgu_ ^Zggu_ b j_amevlZlu \uqbke_gbc k\h^yl \ lZ[ebpm.

LZ[ebpZ 28.1

IhdZaZgby ijb[hjh\

<uqbke_ggu_ \_ebqbgu �

i/i

>Z\e_gb_ gZ \u

-

oh^_ j

1, FIZ

>Z\e_gb_ gZ \u

-

oh^_ j

2, FIZ

>Z\e_gb_ \ k`b

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fZ_fhf

k_q_gbb

jk`

, FIZ

JZkoh^

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3/k

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^Z\e_gbc

j1-j

2, FIZ

Kdhjhklv

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Qbkeh

dZ\blZpbb

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Djblbq_kdh_ qbk-

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dj

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gZ[ex^_gby

1 2 3 4 5 6 7 8 9 10

J:;HL: 29

HIJ?>?E?GB? DHWNNBPB?GL: IHE?AGH=H >?CKL<BY

<H>HKLJMCGH=H G:KHK:

P_ev jZ[hlu. HagZdhfe_gb_ k jZ[hlhc \h^hkljmcgh]h gZkhkZ b

hij_^_e_gb_ _]h dhwnnbpb_glZ ihe_agh]h ^_ckl\by.

H;SB? K<?>?GBY

Kljmcguc gZkhk – gZkhk lj_gby, \ dhlhjhf `b^dhklv (]Za) i_j_f_sZxlky,

m\e_dZ_fu_ ihlhdhf (kljmzc) `b^dhc beb ]Zahh[jZaghc kj_^u. < aZ\bkbfhklb

291

hl \b^Z kj_^u jZaebqZxl `b^dhkljmcgu_ (gZijbf_j, \h^hkljmcgu_), ]Zah- b

iZjhkljmcgu_ gZkhku.

Kljmcgu_ gZkhku ^ey gZ]g_lZgby ]ZaZ beb `b^dhklb \ j_a_j\mZju bgh]^Z

gZau\Zxl bg`_dlhjZfb, ^ey hlkZku\Zgby - w`_dlhjZfb, ^ey ljZgkihjlbjh\Zgby

g_dhlhjuo ]b^jhkf_k_c - ]b^jhwe_\ZlhjZfb. Kljmcgu_ gZkhku g_ kh^_j`Zl

^\b`msboky qZkl_c b ijhklu \ ba]hlh\e_gbb, bf_xl ohjhrb_ dZ\blZpbhggu_

dZq_kl\Z, d.i.^. ^hklb]Z_l 40 %.

< kljmcguo gZkhkZo wg_j]by ihlhdZ jZ[hq_c `b^dhklb i_j_^Zzlky ihlhdm

i_j_dZqb\Z_fhc `b^dhklb [_a dZdbo- eb[h ijhf_`mlhqguo f_oZgbafh\, \ k\yab

k q_f wlb gZkhku ih oZjZdl_jm jZ[hq_]h ijhp_kkZ ijbgpbibZevgh hlebqZxlky

hl gZkhkh\ \k_o ^jm]bo \b^h\. Ohly ih h[sbf dhgkljmdlb\guf ijbagZdZf bo

g_h[oh^bfh hlg_klb d ^bgZfbq_kdbf gZkhkZf, lZd dZd \ ijhp_kk_ jZ[hlu h[tzf

jZ[hq_c dZf_ju gZkhkZ g_ baf_gy_lky b hgZ ihklhyggh khh[sZ_lky k

\kZku\Zxsbf b gZ]g_lZl_evguf iZljm[dZfb gZkhkZ.

>hklhbgkl\Zfb kljmcguo gZkhkh\ y\ey_lky ijhklhlZ dhgkljmdpbb

gZ^z`ghklv \ jZ[hl_, g_[hevrb_ jZaf_ju b g_\ukhdZy klhbfhklv. ;eZ]h^Zjy

wlhfm kljmcgu_ gZkhku rbjhdh ijbf_gyxlky \h fgh]bo hljZkeyo gZjh^gh]h

ohayckl\Z, \ qZklghklb, \ kbkl_fZo l_ieh]ZahkgZ[`_gby, \_glbeypbb b

dhg^bpbhgbjh\Zgby \ha^moZ, kbkl_fZo ih^Zqb lhieb\Z \ e_lZl_evguo

ZiiZjZlh\, \ k\Zjhqguo ]hj_edZo b l.^.

< l_iehnbdZpbhgguo mklZgh\dZo kljmcgu_ ZiiZjZlu bkihevamxl \

dZq_kl\_ kf_kbl_e_c gZ hlhibl_evguo Z[hg_glkdbo \\h^Zo (\h^hkljmcgu_

we_\Zlhju); \ \_glbeypbhgguo mklZgh\dZo – ^ey kha^Zgby g_ij_ju\gh]h

ihlhdZ \ha^moZ q_j_a dZgZeu b ihf_s_gby (w`_dlhju); \ oheh^bevghc l_ogbd_-

\ dZq_kl\_ Z]j_]Zlh\ oheh^bevguo mklZgh\hd. Kljmcgu_ ZiiZjZlu ijbf_gyxl

lZd`_ \ \h^hijh\h^guo mklZgh\dZo ^ey ih^tzfZ \h^u ba ]em[hdbo dheh^p_\ b

kd\Z`bg, \ dZgZebaZpbhgguo mklZgh\dZo k bo ihfhsvx m^Zeyxl hkZ^hd ba

i_kdheh\hd.

292

JZ[hqbc ijhp_kk \ kljmcghf gZkhk_ hkms_kl\ey_lky ke_^mxsbf h[jZahf.

JZ[hqZy `b^dhklv ih ljm[hijh\h^m ih^Zqb jZ[hq_c `b^dhklb 1 ih^ ^Z\e_gb_f

ih^Zzlky \ khieh 2 kljmcgh]h gZkhkZ (jbk 29.1), hldm^Z k [hevrhc kdhjhklvx

ihklmiZ_l \ dZf_jm kf_r_gby 4. <ke_^kl\b_ agZqbl_evgh]h m\_ebq_gby

kdhjhklb gZ \uoh^_ ba khieZ 2 ^Z\e_gb_ \ dZf_j_ kf_r_gby 4 fh`_l klZlv

f_gvr_ Zlfhkn_jgh]h, l._. ijb hij_^_ezgghc kdhjhklb bkl_q_gby `b^dhklb ba

khieZ 2 \h \kZku\Zxs_c dZf_j_ 3 kljmcgh]h gZkhkZ \hagbdZ_l \Zdmmf.

1 – ljm[hijh\h^ ih^Zqb jZ[hq_c `b^dhklb; 2 – khieh; 3 – \kZku\ZxsZy

dZf_jZ; 4 – dZf_jZ kf_r_gby; 5 – ^bnnmahj; 6 – gZihjguc ljm[hijh\h^; 7 –

\kZku\Zxsbc ljm[hijh\h^.

Jbk. 29.1 Ko_fZ \h^hkljmcgh]h gZkhkZ

Ih^ ^_ckl\b_f \ZdmmfZ `b^dhklv ba \kZku\Zxs_]h ljm[hijh\h^Z 7

ihklmiZ_l \h \kZku\Zxsmx dZf_jm 3 b ^Ze__ \ dZf_jm kf_r_gby 4. < dZf_j_

kf_rb\Zgby 4 jZ[hqZy b i_j_dZqb\Z_fZy `b^dhklb kf_rb\Zxlky b

h[f_gb\Zxlky wg_j]byfb, ijb wlhf jZ[hqZy `b^dhklv, ihklmiZxsZy ih

ljm[hijh\h^m 1, hl^Zzl qZklv k\h_c wg_j]bb `b^dhklb, ihklmiZxs_c ba

\kZku\Zxs_]h ljm[hijh\h^Z 7.

Ijhp_kk kf_r_gby fh`gh mkeh\gh jZa^_eblv gZ ^\Z wlZiZ - gZqZevguc

b hkgh\ghc. L_q_gb_ gZ gZqZevghf mqZkld_ dZf_ju kf_r_gby fh`gh

293

jZkkfZljb\Zlv dZd lmj[me_glgmx kljmx, ^\b`msmxky \ kimlghf ihlhd_. Ih^

^_ckl\b_f ihi_j_qguo imevkZpbc kdhjhklb, k\hckl\_gguo lmj[me_glghfm

^\b`_gbx, ihlhdb \g_^jyxlky ^jm] \ ^jm]Z, h[jZamy ihkl_i_ggh

jZkrbjyxsmxky ahgm kf_r_gby – ih]jZgbqguc kehc kljmb.

D dhgpm gZqZevgh]h mqZkldZ ih]jZgbqguc kehc kljmb aZihegy_l \kz

k_q_gb_ dZf_ju kf_r_gby, b ^Ze__ gZ hkgh\ghf mqZkld_ kf_r_gby

ijh^he`Z_lky \ujZ\gb\Zgb_ kdhjhkl_c ih k_q_gbx ihlhdZ. < dhg_qghf k_q_gbb

dZf_ju kf_r_gby, hlklhys_f gZ 4 - 6 _z ^bZf_ljh\ hl gZqZevgh]h k_q_gby,

h[jZam_lky ^hklZlhqgh h^ghjh^gZy kf_kv kf_rb\Z_fuo `b^dhkl_c.

Ijb ijhoh`^_gbb h[jZah\Z\r_cky kf_kb ^\mo `b^dhkl_c q_j_a ^bnnmahj

5 \ gZihjguc ljm[hijh\h^ 6 ijhbkoh^bl ij_h[jZah\Zgb_ dbg_lbq_kdhc wg_j]bb

\ ihl_gpbZevgmx, ijbqzf kdhjhklv ihlhdZ ihkl_i_ggh mf_gvrZ_lky, Z

klZlbq_kdbc gZihj m\_ebqb\Z_lky. LZdbf h[jZahf, ^Z\e_gb_ kf_r_ggh]h ihlhdZ

gZ \uoh^_ ba ^bnnmahjZ hdZau\Z_lky \ur_ ^Z\e_gby w`_dlbjm_fh]h ihlhdZ,

ihklmiZxs_]h ih \kZku\Zxs_fm ljm[hijh\h^m.

JZ[hlZ kljmcguo gZkhkh\ hkgh\ZgZ gZ i_j_^Zq_ wg_j]bb hl h^ghc kj_^u

(jZ[hq_c), ^\b`ms_cky k [hevrhc kdhjhklvx, d ^jm]hc kj_^_ (ih^kZku\Z_fhc),

h[eZ^Zxs_c agZqbl_evgh f_gvrbf aZiZkhf wg_j]bb. I_j_^ZqZ wg_j]bb

ijhbkoh^bl \ ijhp_kk_ kf_r_gby h[_bo kj_^, ijbq_f dbg_lbq_kdZy wg_j]by

jZ[hq_c kj_^u qZklbqgh khh[sZ_lky ih^kZku\Z_fhc kj_^_, qZklv `_ l_jy_lky

\ke_^kl\b_ agZqbl_evgh]h \boj_h[jZah\Zgby. Wg_j]by h[jZah\Z\r_cky kf_kb

bkihevam_lky ^ey __ ih^t_fZ beb ljZgkihjlbjh\Zgby ih ljm[Zf.

?keb h[hagZqblv Q1 – jZkoh^ jZ[hq_c `b^dhklb, ih^Z\Z_fhc \ khieh

kljmcgh]h gZkhkZ, Q2 – jZkoh^ ih^kZku\Z_fhc `b^dhklb, lh hq_\b^gh, qlh

h[sbc jZkoh^ `b^dhklb, ijhoh^ys_c q_j_a dZf_jm kf_r_gby, beb ih^ZqZ

kljmcgh]h gZkhk

Q = Q1 + Q2 (29.1)

294

Hlghr_gb_ ih^Zqb kljmcgh]h gZkhkZ d jZkoh^m jZ[hq_c `b^dhklb

gZau\Z_lky dhwnnbpb_glhf w`_dpbb

D = Q / Q1 (29.2)

Hlghr_gb_ \ukhlu ih^tzfZ i_j_dZqb\Z_fhc `b^dhklb H0 d jZ[hq_fm

gZihjm H1 gZau\Z_lky dhwnnbpb_glhf gZihjZ kljmcgh]h gZkhkZ E ,l._.

E = H0 / H1 , (29.3)

]^_ H0 = H2 + h\ (29.4)

Dhwnnbpb_gl ihe_agh]h ^_ckl\by kljmcgh]h gZkhkZ hij_^_ey_lky

hlghr_gb_f ihe_aghc fhsghklb N i d ihlj_[ey_fhc N , l._

� = N i / N (29.5)

Ihe_agZy fhsghklv gZkhkZ ijb jZ\_gkl\_ kdhjhkl_c \h \kZku\Zxs_f ( V\ )

b gZihjghf ( Vg ) ljm[hijh\h^Zo hij_^_ey_lky \ujZ`_gb_f

N i = Ug Q2 (H2 + h\) (29.6)

?keb ij_g_[j_qv \_ebqbghc V12/ 2g ( V1 - kdhjhklv jZ[hq_c `b^dhklb \

ljm[hijh\h^_ 1), lh ihlj_[ey_fZy gZkhkhf fhsghklv hij_^_ey_lky \ujZ`_gb_f

N = UjgQ1 H1 (29.7)

< nhjfmeZo (29.6) b (29.7) ijbgylu h[hagZq_gby: Up b U – iehlghklb

jZ[hq_c b \kZku\Z_fhc ih ljm[hijh\h^m 7 `b^dhklyfb; Q1 b H1 -

295

khhl\_lkl\_ggh jZkoh^ b gZihj jZ[hq_c `b^dhklb \ ljm[hijh\h^_ 1 i_j_^

gZkhkhf; Q2 b h\ - jZkoh^ `b^dhklb b \ukhlZ \kZku\Zgby \h \kZku\Zxs_f

ljm[hijh\h^_ 7; G2 - gZihj `b^dhklb gZ \uoh^_ ba gZkhkZ.

?keb iehlghklb jZ[hq_c b \kZku\Z_fhc `b^dhkl_c h^bgZdh\u, lh d.i.^.

gZkhkZ hij_^_ey_lky \ujZ`_gb_f

� = >Q2 (H2 + h\)@ / (Q1 H1 ) (29.8)

HIBK:GB? HIULGHC MKL:GH<DB

Wdki_jbf_glZevgZy mklZgh\dZ (jbk. 29.2) \dexqZ_l ke_^mxsb_ hkgh\gu_

we_f_glu: \h^hkljmcguc gZkhk 6, jZ[hqbc 1, gZihjguc 8 b \kZku\Zxsbc 9

ljm[hijh\h^u, j_a_j\mZj 10, j_]mebjmxsmx b baf_jbl_evgmx ZiiZjZlmjm.

<h^Z ba gZihjgh]h [ZdZ (gZ jbkmgd_ g_ ihdZaZg) ijb hldjulbb \_glbey 2

ihklmiZ_l \ \h^hkljmcguc gZkhk 6 ih ljm[hijh\h^m 1; jZkoh^ \h^u \ g_f

hij_^_ey_lky k ihfhsvx jZkoh^hf_jZ <_glmjb 4 (kf. jZ[hlm 6) ih ihdZaZgbyf

^bnn_j_gpbZevgh]h fZghf_ljZ 3; gZihj \h^u \ ljm[hijh\h^_ i_j_^ gZkhkhf

hij_^_ey_lky ih iv_ahf_ljm 5 . <h^Z \kZku\Z_lky \ gZkhk ih ljm[hijh\h^m 9 ba

j_a_j\mZjZ 10, \ dhlhjuc ih ljm[hijh\h^m 12 ihklmiZ_l ba gZihjgh]h [ZdZ ijb

hldjulbb \_glbey 13. < j_a_j\mZj_ 10 bf__lky ohehklhc keb\ 11,

h[_ki_qb\Zxsbc \ l_q_gb_ hiulZ ihklhygguc mjh\_gv \h^u \ g_f. NbdkZpby

mjh\gy \ j_a_j\mZj_ ijhba\h^blky k ihfhsvx iv_ahf_ljZ 14, gme_\h_ ^_e_gb_

rdZeu dhlhjh]h kh\iZ^Z_l k hk_\hc ebgb_c ljm[hijh\h^Z 1. Ihkdhevdm

jZaf_ldZ rdZeu iv_ahf_ljZ 14 b^_l k\_jom \gba, hlkq_l ih rdZe_ iv_ahf_ljZ

g_ihkj_^kl\_ggh hij_^_ey_l \ukhlm \kZku\Zgby h\. <ukhlgh_ iheh`_gb_

ohehklh]h keb\Z fh`gh baf_gylv, lZd `_ fh`gh baf_gylv hl hiulZ d hiulm b

\ukhlm \kZku\Zgby.

<h^Z ba ^bnnmahjZ gZkhkZ 6 ihklmiZ_l \ gZihjguc ljm[hijh\h^ 8, \

gZqZe_ dhlhjh]h mklZgh\e_g iv_ahf_lj 7, iha\heyxsbc hij_^_eylv gZihj G2