Уравнения Максвелла (55
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ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɡɚɩɢɫɶ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɡɚɪɹɞɚ ɜ ɥɨɤɚɥɶɧɨɣ ɮɨɪɦɭɥɢɪɨɜɤɟ: ɫɤɨɪɨɫɬɶ ɭɜɟɥɢɱɟɧɢɹ ɡɚɪɹɞɚ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ (wU
wt) ɪɚɜɧɚ ɡɚɪɹɞɭ, ɜɬɟ-
ɤɚɸɳɟɦɭ ɜ ɷɬɨɬ ɟɞɢɧɢɱɧɵɣ ɨɛɴɟɦ ɱɟɪɟɡ ɨɝɪɚɧɢɱɢɜɚɸɳɭɸ ɟɝɨ ɩɨɜɟɪɯɧɨɫɬɶ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ( div &j) . Ɂɞɟɫɶ ɭɦɟɫɬɧɨ ɜɫɩɨɦ-
ɧɢɬɶ, ɱɬɨ (ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ ɞɢɜɟɪɝɟɧɰɢɢ) |
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ɉɪɢɧɢɦɚɹ ɜɨ ɜɧɢɦɚɧɢɟ, ɱɬɨ &j |
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ɢ icU ɹɜɥɹɸɬɫɹ ɤɨɦɩɨɧɟɧɬɚɦɢ |
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4-ɜɟɤɬɨɪɚ jk , ɚ ɢ w
w(ict) – ɤɨɦɩɨɧɟɧɬɚɦɢ 4-ɜɟɤɬɨɪɚ w
wxk ,
ɡɚɩɢɲɟɦ ɥɟɜɭɸ ɱɚɫɬɶ ɪɚɜɟɧɫɬɜɚ (4.3) ɜ ɜɢɞɟ 4-ɞɢɜɟɪɝɟɧɰɢɢ ɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɢɦ:
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ȼɜɟɞɟɦ 4-ɜɟɤɬɨɪ «ɬɨɤɚ ɦɚɫɫ» |
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,icU |
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(4.6) |
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ɚɧɚɥɨɝɢɱɧɵɣ 4-ɜɟɤɬɨɪɭ ɬɨɤɚ ɡɚɪɹɞɨɜ (3.1). Ɂɞɟɫɶ U(0m) – «ɩɥɨɬ-
ɧɨɫɬɶ ɦɚɫɫɵ» ɜ ɦɝɧɨɜɟɧɧɨ ɫɨɩɭɬɫɬɜɭɸɳɟɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ. ȿɫɥɢ ɜ ɫɢɫɬɟɦɟ ɩɪɨɬɟɤɚɸɬ ɬɨɥɶɤɨ ɭɩɪɭɝɢɟ ɩɪɨɰɟɫɫɵ, ɬɨ ɦɚɫɫɵ ɱɚɫɬɢɰ ɩɨɫɬɨɹɧɧɵ ɢ ɢɦɟɟɬ ɦɟɫɬɨ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɫɭɦɦɵ ɦɚɫɫ ɱɚɫɬɢɰ ɫɢɫɬɟɦɵ. ȼ ɥɨɤɚɥɶɧɨɣ ɮɨɪɦɭɥɢɪɨɜɤɟ ɷɬɨɬ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ, ɚɧɚɥɨɝɢɱɧɨɦ (4.3) ɢɥɢ (4.5):
wU(m) |
div &j (m) |
wjk(m) |
0 . |
(4.7) |
wt |
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11
5. ɉɨɥɟɜɚɹ ɮɨɪɦɚ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ
Ɋɟɥɹɬɢɜɢɫɬɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ a -ɣ ɱɚɫɬɢɰɵ ɜ ɡɚɞɚɧɧɨɦ ɜɧɟɲɧɟɦ ɩɨɥɟ ɢɦɟɟɬ ɜɢɞ:
dU (a)
ma k (5.1)
dt0(a)
ɝɞɟ m |
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– ɦɚɫɫɚ ɱɚɫɬɢɰɵ, U (a) – ɟɟ 4-ɫɤɨɪɨɫɬɶ, dt(a) |
– ɩɪɨɦɟɠɭ- |
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ɬɨɤ |
ɫɨɛɫɬɜɟɧɧɨɝɨ |
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ɜɪɟɦɟɧɢ, |
fk(a) ( f&a , f4(a) ) |
– 4-ɫɢɥɚ, |
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– 3-ɫɢɥɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɱɚɫɬɢɰɭ ɫɨ |
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ɫɬɨɪɨɧɵ ɜɧɟɲɧɟɝɨ ɩɨɥɹ.
ɉɟɪɟɣɞɟɦ ɤ ɩɨɥɟɜɨɣ ɮɨɪɦɟ ɡɚɩɢɫɢ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ. Ⱦɨɦɧɨɠɢɦ ɥɟɜɭɸ ɢ ɩɪɚɜɭɸ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (5.1) ɧɚ ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɦɧɨɠɢɬɟɥɶ G(r& r&a )
Ja ɢ ɩɪɨɫɭɦɦɢɪɭɟɦ ɩɨ ɜɫɟɦ ɱɚɫɬɢɰɚɦ ɫɢɫɬɟɦɵ:
¦ |
G(r& r& ) |
ma |
dU (a) |
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k |
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Ja |
(a) |
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dt0 |
¦G(r& r&a ) fk(a) . |
(5.2) |
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ȼɜɟɞɟɦ ɩɨɥɟ ɫɤɨɪɨɫɬɟɣ ɢ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫɨɨɬɧɨɲɟɧɢɟɦ (2.3) ɞɥɹ 4-ɭɫɤɨɪɟɧɢɹ, ɫɜɨɣɫɬɜɨɦ (2.7) ɞɟɥɶɬɚɮɭɧɤɰɢɢ, ɜɵɪɚɠɟɧɢɟɦ (2.13) ɞɥɹ «ɩɥɨɬɧɨɫɬɢ ɦɚɫɫɵ», ɪɚɜɟɧɫɬ-
ɜɨɦ U(m) JU(0m) , ɜɵɪɚɠɟɧɢɟɦ (4.6) ɞɥɹ 4-ɜɟɤɬɨɪɚ «ɬɨɤɚ ɦɚɫɫ» ɢ
ɡɚɤɨɧɨɦ ɫɨɯɪɚɧɟɧɢɹ (4.7) ɞɥɹ ɫɭɦɦɵ ɦɚɫɫ ɱɚɫɬɢɰ ɫɢɫɬɟɦɵ. ɉɪɢ ɷɬɨɦ ɥɟɜɚɹ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ (5.2) ɩɨɞɜɟɪɝɧɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɦ:
¦ |
G(r& r& ) |
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dU |
(a) |
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m G(r& |
r& ) |
& |
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ma |
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aJ(r& |
,t) a |
Ul (ra |
,t) |
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Uk |
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dt(a) |
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m G(r& r& ) |
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U(m) (r&,t) |
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aJ(r&,t) |
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Ul (r ,t) |
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Uk (r ,t) |
J(r&,t) |
Ul (r,t) |
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U(m) (r&,t)U |
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j(m) (r&,t) |
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^jl(m)Uk `. |
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(5.3) |
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ȼ ɩɪɚɜɨɣ ɱɚɫɬɢ ɪɚɜɟɧɫɬɜɚ (5.2) ɫɬɨɢɬ 4-ɜɟɤɬɨɪ |
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F (V ) |
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(F&(V ) , F (V ) ) , |
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(5.4) |
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(V ) |
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ɝɞɟ |
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ȼɟɥɢɱɢɧɚ F |
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ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɭɦ- |
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ɦɚɪɧɭɸ ɜɧɟɲɧɸɸ ɫɢɥɭ, ɞɟɣɫɬɜɭɸɳɭɸ ɧɚ ɱɚɫɬɢɰɵ, ɧɚɯɨɞɹɳɢɟɫɹ ɜ ɟɞɢɧɢɱɧɨɦ ɨɛɴɟɦɟ:
F&(V ) |
¦G(r& r&a ) f&(a) |
Ja |
¦G(r& r&a )F&a . |
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ȼ ɪɟɡɭɥɶɬɚɬɟ (5.2) ɡɚɩɢɲɟɬɫɹ ɜ ɜɢɞɟ: |
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wT (m) |
F (V ) . |
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Ɂɞɟɫɶ |
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T (m) |
j(m)U |
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U(m)U U |
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U(m) 1 v2 c2 U U |
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(5.7) |
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Ɋɚɜɟɧɫɬɜɨ (5.6) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɨɥɟɜɭɸ ɮɨɪɦɭ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɜ ɡɚɞɚɧɧɨɦ ɜɧɟɲɧɟɦ ɩɨɥɟ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɷɬɢɦɢ ɱɚɫɬɢɰɚɦɢ.
6. Ɍɟɧɡɨɪ ɷɧɟɪɝɢɢ-ɢɦɩɭɥɶɫɚ
ɫɢɫɬɟɦɵ ɱɚɫɬɢɰ
4-ɬɟɧɡɨɪ Tkl(m) ɧɚɡɵɜɚɸɬ ɬɟɧɡɨɪɨɦ ɷɧɟɪɝɢɢ-ɢɦɩɭɥɶɫɚ ɫɢɫɬɟɦɵ ɱɚɫɬɢɰ. ɗɬɨɬ ɬɟɧɡɨɪ ɫɢɦɦɟɬɪɢɱɟɧ:
Tkl(m) Tlk(m) . (6.1)
ɉɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɬɟɧɡɨɪɚ TDE(m) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ E-ɸ ɩɪɨɟɤɰɢɸ ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ D-ɣ ɩɪɨɟɤɰɢɢ ɢɦɩɭɥɶɫɚ ɱɚɫɬɢɰ, ɬɨ ɟɫɬɶ ɤɨɥɢɱɟɫɬɜɨ D-ɣ ɩɪɨɟɤɰɢɢ ɢɦɩɭɥɶɫɚ, ɩɟɪɟɧɨɫɢ-
13
ɦɨɟ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɜ ɧɚɩɪɚɜɥɟɧɢɢ E-ɣ ɞɟɤɚɪɬɨɜɨɣ ɨɫɢ ɱɟ-
ɪɟɡ ɨɪɬɨɝɨɧɚɥɶɧɭɸ ɷɬɨɣ ɨɫɢ ɟɞɢɧɢɱɧɭɸ ɩɥɨɳɚɞɤɭ:
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TDE(m) |
D |
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1 v2 |
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ȼɪɟɦɟɧɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɬɟɧɡɨɪɚ ɪɚɜɧɚ ɜɡɹɬɨɣ ɫ ɨɛɪɚɬɧɵɦ
ɡɧɚɤɨɦ ɩɥɨɬɧɨɫɬɢ ɷɧɟɪɝɢɢ: |
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T (m) |
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1 v2 c2 |
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ɋɦɟɲɚɧɧɚɹ ɤɨɦɩɨɧɟɧɬɚ |
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U(m)vD |
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T (m) |
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D4 |
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ɪɚɜɧɚ D-ɣ ɩɪɨɟɤɰɢɢ ɩɥɨɬɧɨɫɬɢ ɢɦɩɭɥɶɫɚ, ɭɦɧɨɠɟɧɧɨɣ ɧɚ ic , ɢɥɢ ɠɟ D-ɣ ɩɪɨɟɤɰɢɢ ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ ɷɧɟɪɝɢɢ, ɭɦɧɨɠɟɧɧɨɣ ɧɚ i
c .
Ɂɚɩɢɫɚɧɧɵɟ ɜ ɬɪɟɯɦɟɪɧɨɣ ɮɨɪɦɟ ɭɪɚɜɧɟɧɢɹ (5.6) ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɥɨɤɚɥɶɧɵɟ ɮɨɪɦɭɥɢɪɨɜɤɢ ɬɟɨɪɟɦ ɨɛ ɢɡɦɟɧɟɧɢɢ ɢɦɩɭɥɶɫɚ ɢ ɨɛ ɢɡɦɟɧɟɧɢɢ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ ɱɚɫɬɢɰ:
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w U(m)v& |
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U(m)v& |
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(V ) |
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( v) |
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, |
(6.5) |
|
|
wt |
|
1 v2 |
c2 |
1 v2 c2 |
|
|||||||||
w U(m)ɫ2 |
& |
|
U(m)ɫ2 |
&& |
(V ) |
|
|
||||||||
|
|
|
|
( v) |
|
|
|
(vF |
|
) . |
(6.6) |
||||
wt |
|
|
1 v2 c2 |
|
1 v2 c2 |
|
|||||||||
ɂɡ ɪɚɜɟɧɫɬɜɚ (6.5) ɫɥɟɞɭɟɬ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɢɦɩɭɥɶɫɚ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ ɪɚɜɧɚ ɫɭɦɦɟ ɢɦɩɭɥɶɫɚ, ɜɬɟɤɚɸɳɟɝɨ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɜ ɷɬɨɬ ɟɞɢɧɢɱɧɵɣ ɨɛɴɟɦ ɱɟɪɟɡ ɨɝɪɚɧɢɱɢɜɚɸɳɭɸ ɟɝɨ ɩɨɜɟɪɯɧɨɫɬɶ, ɢ ɫɢɥɵ F&(V ) , ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɱɚɫɬɢɰɵ ɜ ɷɬɨɦ ɨɛɴɟɦɟ. Ɋɚɜɟɧɫɬɜɨ (6.6) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɷɧɟɪɝɢɢ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ ɪɚɜɧɚ ɫɭɦɦɟ ɷɧɟɪɝɢɢ, ɜɬɟɤɚɸɳɟɣ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɜ ɷɬɨɬ ɟɞɢɧɢɱɧɵɣ ɨɛɴɟɦ ɱɟɪɟɡ ɨɝɪɚɧɢɱɢɜɚɸɳɭɸ
14
ɟɝɨ ɩɨɜɟɪɯɧɨɫɬɶ, ɢ ɪɚɛɨɬɵ, ɤɨɬɨɪɭɸ ɫɨɜɟɪɲɚɟɬ ɜ ɟɞɢɧɢɰɭ ɜɪɟ-
ɦɟɧɢ ɫɢɥɚ F&(V ) ɧɚɞ ɱɚɫɬɢɰɚɦɢ ɜ ɷɬɨɦ ɨɛɴɟɦɟ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɜɟɧɫɬɜɨ (5.6) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɥɨɤɚɥɶɧɭɸ ɮɨɪɦɭɥɢɪɨɜɤɭ ɬɟɨɪɟɦɵ ɨɛ ɢɡɦɟɧɟɧɢɢ 4-ɢɦɩɭɥɶɫɚ ɫɢɫɬɟɦɵ ɱɚɫɬɢɰ. ȼ ɨɬɫɭɬɫɬɜɢɟ ɫɢɥ (5.6) ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɥɨɤɚɥɶɧɭɸ ɮɨɪɦɭɥɢɪɨɜɤɭ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ 4-ɢɦɩɭɥɶɫɚ ɫɢɫɬɟɦɵ ɧɟɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɱɚɫɬɢɰ:
wT (m)
kl 0 . (6.7) wxl
7. ɉɟɪɟɦɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɩɪɢɧɰɢɩ ɤɚɥɢɛɪɨɜɨɱɧɨɣ ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ
ȼɡɚɢɦɨɞɟɣɫɬɜɢɟ ɦɟɠɞɭ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɱɟɪɟɡ ɩɨɫɪɟɞɫɬɜɨ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɉɨɷɬɨɦɭ ɩɪɢ ɨɩɢɫɚɧɢɢ ɷɜɨɥɸɰɢɢ ɫɢɫɬɟɦɵ ɧɚɪɹɞɭ ɫ ɩɟɪɟɦɟɧɧɵɦɢ ɫɨɫɬɨɹɧɢɹ ɱɚɫɬɢɰ (ɢɯ ɤɨɨɪɞɢɧɚɬɚɦɢ ɢ ɫɤɨɪɨɫɬɹɦɢ) ɧɟɨɛɯɨɞɢɦɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɢ ɩɟɪɟɦɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɩɨɥɹ. Ɉɩɵɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɫɨɫɬɨɹɧɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɦɨɠɧɨ ɨɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɬɚɤ ɧɚɡɵɜɚɟɦɵɦ 4-ɩɨɬɟɧɰɢɚɥɨɦ Ak ɢ ɩɪɨɢɡɜɨɞɧɵɦɢ wAk 
wxl («ɤɨ-
ɨɪɞɢɧɚɬɚɦɢ» ɢ «ɫɤɨɪɨɫɬɹɦɢ»), ɩɨɬɪɟɛɨɜɚɜ ɩɪɢ ɷɬɨɦ, ɱɬɨɛɵ ɜɵɩɨɥɧɹɥɫɹ ɩɪɢɧɰɢɩ ɤɚɥɢɛɪɨɜɨɱɧɨɣ ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ, ɬɨ ɟɫɬɶ ɱɬɨɛɵ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɞɥɹ ɱɚɫɬɢɰ ɢ ɞɥɹ ɩɨɥɹ ɛɵɥɢ ɢɧɜɚɪɢɚɧɬɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ
c |
|
wf |
|
|
Ak o Ak |
Ak wx |
, |
(7.1) |
|
|
|
k |
|
|
ɝɞɟ f – ɩɪɨɢɡɜɨɥɶɧɚɹ ɮɭɧɤɰɢɹ ɤɨɨɪɞɢɧɚɬ ɢ ɜɪɟɦɟɧɢ. ɉɪɟɨɛɪɚ-
ɡɨɜɚɧɢɟ (7.1) ɧɚɡɵɜɚɸɬ ɤɚɥɢɛɪɨɜɨɱɧɵɦ, ɢɥɢ ɝɪɚɞɢɟɧɬɧɵɦ. Ɉɬɦɟɬɢɦ, ɱɬɨ ɜ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɤɚɥɢɛɪɨɜɨɱɧɨɣ
ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ (7.1) ɧɟ-
15
ɨɛɯɨɞɢɦɨ ɩɪɨɢɡɜɨɞɢɬɶ ɜɦɟɫɬɟ ɫ ɧɚɞɥɟɠɚɳɢɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟɦ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ ɱɚɫɬɢɰ. ȼ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɡɞɟɫɶ ɤɥɚɫɫɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɩɟɪɟɦɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɱɚɫɬɢɰ ɤɚɥɢɛɪɨɜɨɱɧɨɦɭ ɩɪɟɨɛɪɚɡɨɜɚɧɢɸ ɧɟ ɩɨɞɜɟɪɝɚɸɬɫɹ. ɉɨɷɬɨɦɭ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɤɚɥɢɛɪɨɜɨɱɧɨɣ ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ ɞɨɫɬɚɬɨɱɧɨ ɩɨɬɪɟɛɨɜɚɬɶ, ɱɬɨɛɵ ɩɟɪɟɦɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɯɨɞɢɥɢ ɜ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɜ ɜɢɞɟ ɤɚɥɢɛɪɨɜɨɱɧɨ-ɢɧɜɚɪɢɚɧɬɧɵɯ ɤɨɦɛɢɧɚɰɢɣ. ɇɟɡɚɜɢɫɢɦɵɦɢ ɤɨɦɛɢɧɚɰɢɹɦɢ ɬɚɤɨɝɨ ɪɨɞɚ, ɤɚɤ ɥɟɝɤɨ ɜɢɞɟɬɶ, ɹɜɥɹɸɬɫɹ ɬɨɥɶɤɨ ɤɨɦɩɨɧɟɧɬɵ ɚɧɬɢɫɢɦɦɟɬɪɢɱɧɨɝɨ 4- ɬɟɧɡɨɪɚ wAl 
wxk wAk 
wxl , ɞɥɹ ɤɨɬɨɪɨɝɨ ɦɵ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɨɛɨɡɧɚɱɟɧɢɟ Fkl :
F |
{ |
§ wAl |
wAk |
·. |
(7.2) |
|
kl |
|
¨ |
wx |
wx |
¸ |
|
|
|
© |
¹ |
|
||
|
|
k |
l |
|
||
Ɍɟɧɡɨɪ Fkl ɧɚɡɵɜɚɸɬ ɬɟɧɡɨɪɨɦ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɂɫ-
ɩɨɥɶɡɭɹ (7.2), ɧɟɬɪɭɞɧɨ ɩɪɨɜɟɪɢɬɶ ɬɨɠɞɟɫɬɜɨ |
|
|||||
|
wFml |
|
wFkm |
wFlk |
0 . |
(7.3) |
|
wx |
wx |
||||
|
|
wx |
|
|
||
|
k |
|
l |
m |
|
|
ɗɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɩɨɬɪɟɛɭɟɬɫɹ ɧɚɦ ɜ ɞɚɥɶɧɟɣɲɟɦ.
8. ɍɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ
ɱɚɫɬɢɰ ɜ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɦ ɩɨɥɟ
ɉɪɢɧɰɢɩ ɩɪɢɱɢɧɧɨɫɬɢ ɭɬɜɟɪɠɞɚɟɬ, ɱɬɨ ɧɚɱɚɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ ɡɚɦɤɧɭɬɨɣ ɮɢɡɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɩɪɟɞɨɩɪɟɞɟɥɹɟɬ ɜɫɟ ɟɟ ɩɨɫɥɟɞɭɸɳɢɟ ɫɨɫɬɨɹɧɢɹ. ɂɡ ɷɬɨɝɨ ɜɵɬɟɤɚɟɬ, ɱɬɨ ɩɪɢ ɡɚɞɚɧɧɵɯ ɩɚɪɚɦɟɬɪɚɯ ɫɢɫɬɟɦɵ ɡɧɚɱɟɧɢɹ ɩɟɪɜɵɯ ɩɪɨɢɡɜɨɞɧɵɯ ɩɨ ɜɪɟɦɟɧɢ ɨɬ ɩɟɪɟɦɟɧɧɵɯ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ ɜ ɧɟɤɨɬɨɪɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɡɚɜɢɫɹɬ ɨɬ ɡɧɚɱɟɧɢɣ ɫɚɦɢɯ ɩɟɪɟɦɟɧɧɵɯ ɫɨɫɬɨɹɧɢɹ ɜ ɬɨɬ ɠɟ ɦɨɦɟɧɬ. Ɋɚɜɟɧɫɬɜɚ, ɜɵɪɚɠɚɸɳɢɟ ɷɬɢ ɡɚɜɢɫɢɦɨɫɬɢ, ɧɚɡɵɜɚɸɬɫɹ ɭɪɚɜɧɟɧɢɹɦɢ ɞɜɢɠɟɧɢɹ.
16
Ɋɚɫɫɦɨɬɪɢɦ ɫɢɫɬɟɦɭ, ɫɨɫɬɨɹɳɭɸ ɢɡ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɜɯɨɞɹɳɚɹ ɜ ɭɪɚɜɧɟ-
ɧɢɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ (5.6) 4-ɫɢɥɚ Fk(V ) ɞɨɥɠɧɚ ɛɵɬɶ ɜɵɪɚɠɟɧɚ ɱɟɪɟɡ 4-ɬɟɧɡɨɪ Fkl , ɤɨɬɨɪɵɣ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɫɨɫɬɨɹɧɢɟ ɷɥɟɤɬɪɨ-
ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɞɟɣɫɬɜɭɸɳɟɝɨ ɧɚ ɱɚɫɬɢɰɵ, ɢ ɱɟɪɟɡ 4-ɜɟɤɬɨɪ jk , ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣ ɪɚɫɩɨɥɨɠɟɧɢɟ ɢ ɞɜɢɠɟɧɢɟ ɡɚɪɹɞɨɜ, ɢɫ-
ɩɵɬɵɜɚɸɳɢɯ ɞɟɣɫɬɜɢɟ ɩɨɥɹ. 4-ɬɨɤ jk ɞɨɥɠɟɧ ɜɯɨɞɢɬɶ ɜ ɜɵɪɚ-
ɠɟɧɢɟ ɞɥɹ Fk(V ) ɥɢɧɟɣɧɨ, ɱɬɨɛɵ ɨɛɟɫɩɟɱɢɬɶ ɩɪɨɩɨɪɰɢɨɧɚɥɶ-
ɧɨɫɬɶ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɡɚɪɹɞ, ɜɟɥɢɱɢɧɟ ɷɬɨɝɨ ɡɚɪɹɞɚ. Ʌɢ-
ɧɟɣɧɨɣ ɞɨɥɠɧɚ ɛɵɬɶ ɢ ɡɚɜɢɫɢɦɨɫɬɶ Fk(V ) ɨɬ ɬɟɧɡɨɪɚ ɩɨɥɹ Fkl ,
ɱɬɨɛɵ ɨɛɟɫɩɟɱɢɬɶ ɜɵɩɨɥɧɟɧɢɟ ɩɪɢɧɰɢɩɚ ɫɭɩɟɪɩɨɡɢɰɢɢ, ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɦɭ ɩɨɥɟ, ɫɨɡɞɚɜɚɟɦɨɟ ɫɢɫɬɟɦɨɣ ɢɫɬɨɱɧɢɤɨɜ, ɪɚɜɧɨ ɫɭɦɦɟ ɩɨɥɟɣ, ɫɨɡɞɚɜɚɟɦɵɯ ɤɚɠɞɵɦ ɢɡ ɢɫɬɨɱɧɢɤɨɜ ɜ ɨɬɞɟɥɶɧɨɫɬɢ. ɇɨ ɢɡ 4-ɬɟɧɡɨɪɚ Fkl ɢ 4-ɜɟɤɬɨɪɚ jk ɦɨɠɧɨ ɫɤɨɧɫɬɪɭɢɪɨɜɚɬɶ ɬɨɥɶɤɨ ɨɞɢɧ 4-ɜɟɤɬɨɪ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɣ ɭɤɚɡɚɧɧɵɦ ɬɪɟɛɨɜɚɧɢ-
ɹɦ, ɚ ɢɦɟɧɧɨ Fkl jl . ɗɬɢɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ 4-ɫɢɥɵ Fk(V ) ɮɢɤɫɢɪɭ-
ɟɬɫɹ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɦɧɨɠɢɬɟɥɹ, ɤɨɬɨɪɵɣ ɜ ɫɢɥɭ ɨɞɧɨɪɨɞɧɨɫɬɢ ɩɪɨɫɬɪɚɧɫɬɜɚ ɢ ɜɪɟɦɟɧɢ ɞɨɥɠɟɧ ɛɵɬɶ ɩɨɫɬɨɹɧɧɵɦ. Ʉɨɧɤɪɟɬɧɨɟ ɡɧɚɱɟɧɢɟ ɷɬɨɝɨ ɦɧɨɠɢɬɟɥɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɜɵɛɨɪɨɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ. Ɇɵ ɛɭɞɟɦ ɩɨɥɶɡɨɜɚɬɶɫɹ ɝɚɭɫɫɨɜɨɣ ɫɢɫɬɟɦɨɣ ɟɞɢɧɢɰ, ɜ ɤɨɬɨɪɨɣ ɩɨɥɚɝɚɸɬ
F (V ) |
1 F |
j . |
(8.1) |
k |
c kl |
l |
|
ɉɪɢ ɷɬɨɦ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɞɥɹ ɱɚɫɬɢɰ ɜ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɛɭɞɟɬ ɢɦɟɬɶ ɜɢɞ:
wT (m) |
1 |
|
kl |
c Fkl jl . |
(8.2) |
wx |
||
l |
|
|
ȼɵɪɚɡɢɜ Fkl ɱɟɪɟɡ ɩɪɨɢɡɜɨɞɧɵɟ 4-ɩɨɬɟɧɰɢɚɥɚ, ɩɨɥɭɱɢɦ:
17
wTkl(m) |
1 |
§ wAl |
wAk |
· j . |
(8.3) |
||
wx |
c |
¨ |
wx |
wx |
¸ |
l |
|
© |
¹ |
|
|
||||
l |
|
k |
l |
|
|
||
ɂɡ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɢ ɜɵɪɚɠɟɧɢɣ (5.7) ɞɥɹ Tkl(m) ɢ (3.1) ɞɥɹ jk
ɜɵɬɟɤɚɟɬ, ɱɬɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɟ ɤɨɦɩɨɧɟɧɬɵ 4-ɩɨɬɟɧɰɢɚɥɚ ɞɨɥɠɧɵ ɛɵɬɶ ɤɨɦɩɨɧɟɧɬɚɦɢ ɩɨɥɹɪɧɨɝɨ 3-ɜɟɤɬɨɪɚ A&, ɚ ɜɪɟɦɟɧɧɚɹ ɤɨɦɩɨɧɟɧɬɚ A4 ɞɨɥɠɧɚ ɛɵɬɶ ɢɫɬɢɧɧɵɦ 3-ɫɤɚɥɹɪɨɦ, ɩɨ-
ɫɤɨɥɶɤɭ ɨɩɵɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɡɚɦɤɧɭɬɨɣ ɮɢɡɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɧɟ ɪɚɡɪɭɲɚɸɬ ɟɟ ɡɟɪɤɚɥɶɧɭɸ ɫɢɦɦɟɬɪɢɸ, ɟɫɥɢ ɬɚɤɨɜɚɹ ɢɦɟɥɚɫɶ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ, ɚ ɷɬɨ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɩɪɢ ɭɫɥɨɜɢɢ ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ ɡɚɤɨɧɨɜ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɢɧɜɟɪɫɢɢ.
9. ɍɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ
ɞɥɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
Ɍɟɩɟɪɶ ɫɤɨɧɫɬɪɭɢɪɭɟɦ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɞɥɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɟɥɹɬɢɜɢɫɬɫɤɨɣ ɤɨɜɚɪɢɚɧɬɧɨɫɬɢ ɭɪɚɜɧɟɧɢɣ ɢɯ ɧɭɠɧɨ ɫɬɪɨɢɬɶ ɢɡ 4-ɬɟɧɡɨɪɨɜ. «Ʉɨɧɫɬɪɭɤɰɢɨɧɧɵɣ ɧɚɛɨɪ» ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɫɨɞɟɪɠɢɬ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: 1) 4- ɬɨɤ jk , ɨɩɢɫɵɜɚɸɳɢɣ ɪɚɫɩɨɥɨɠɟɧɢɟ ɢ ɞɜɢɠɟɧɢɟ ɡɚɪɹɞɨɜ, ɫɨɡ-
ɞɚɸɳɢɯ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɟ ɩɨɥɟ; 2) 4-ɬɟɧɡɨɪ Fkl , ɯɚɪɚɤɬɟɪɢ-
ɡɭɸɳɢɣ ɫɨɫɬɨɹɧɢɟ ɷɬɨɝɨ ɩɨɥɹ; 3) 4-ɜɟɤɬɨɪ w
wxk , ɜ ɫɨɫɬɚɜ ɤɨɬɨ-
ɪɨɝɨ ɜɯɨɞɢɬ ɨɩɟɪɚɬɨɪ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɹ ɩɨ ɜɪɟɦɟɧɢ. ɋɨɝɥɚɫɧɨ ɩɪɢɧɰɢɩɭ ɩɪɢɱɢɧɧɨɫɬɢ ɢɫɤɨɦɵɟ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɞɥɹ ɩɨɥɹ ɞɨɥɠɧɵ ɫɜɹɡɵɜɚɬɶ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ ɜɪɟɦɟɧɢ ɨɬ ɤɨɦɩɨɧɟɧɬ ɬɟɧɡɨɪɚ Fkl ɜ ɧɟɤɨɬɨɪɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɫ ɩɟɪɟɦɟɧɧɵɦɢ ɫɨ-
ɫɬɨɹɧɢɹ ɩɨɥɹ ɢ ɱɚɫɬɢɰ ɜ ɬɨɬ ɠɟ ɦɨɦɟɧɬ. ȼ ɪɚɜɟɧɫɬɜɟ (7.3) ɫɨɞɟɪɠɚɬɫɹ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ ɜɪɟɦɟɧɢ ɨɬ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɤɨɦɩɨɧɟɧɬ ɬɟɧɡɨɪɚ ɩɨɥɹ ( FDE, ɝɞɟ D ɢ E ɩɪɨɛɟɝɚɸɬ ɡɧɚɱɟɧɢɹ 1, 2, 3) ɢ ɧɟ ɫɨɞɟɪɠɚɬɫɹ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ ɜɪɟɦɟɧɢ ɨɬ ɫɦɟɲɚɧɧɵɯ
18
ɤɨɦɩɨɧɟɧɬ ( FD4 ). ɉɪɨɢɡɜɨɞɧɵɟ wFD4 
wt ɜɯɨɞɹɬ ɜ ɫɨɫɬɚɜ 4-
ɜɟɤɬɨɪɚ wFkl 
wxl . ɍɱɟɬ ɩɪɢɧɰɢɩɚ ɫɭɩɟɪɩɨɡɢɰɢɢ ɢ ɬɪɟɛɨɜɚɧɢɣ ɪɟɥɹɬɢɜɢɫɬɫɤɨɣ ɤɨɜɚɪɢɚɧɬɧɨɫɬɢ ɩɪɢɜɨɞɢɬ ɤ ɜɵɜɨɞɭ ɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ 4-ɜɟɤɬɨɪɨɜ wFkl 
wxl ɢ jk . ɉɪɢ ɷɬɨɦ ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɜ ɫɢɥɭ ɨɞɧɨɪɨɞɧɨɫɬɢ ɩɪɨɫɬɪɚɧɫɬɜɚ ɢ ɜɪɟɦɟɧɢ ɞɨɥɠɟɧ ɛɵɬɶ ɩɨɫɬɨɹɧɧɵɦ, ɚ ɤɨɧɤɪɟɬɧɨɟ ɡɧɚɱɟɧɢɟ ɷɬɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɶɤɨ ɜɵɛɨɪɨɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ. ȼ ɝɚɭɫɫɨɜɨɣ ɫɢɫɬɟɦɟ ɟɞɢɧɢɰ ɩɢɲɭɬ
|
wFkl |
4S |
jk . |
(9.1) |
|
wx |
c |
||
|
l |
|
|
|
4-ɞɢɜɟɪɝɟɧɰɢɹ ɥɟɜɨɣ ɱɚɫɬɢ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ( w2 F |
wx wx ) |
|||
|
|
|
kl |
k l |
ɪɚɜɧɚ ɧɭɥɸ ɤɚɤ ɫɜɟɪɬɤɚ ɫɢɦɦɟɬɪɢɱɧɨɝɨ ( w2
wxkwxl ) ɢ ɚɧɬɢɫɢɦ-
ɦɟɬɪɢɱɧɨɝɨ ( Fkl ) ɬɟɧɡɨɪɨɜ. ɉɨɷɬɨɦɭ ɢɡ (9.1) ɜɵɬɟɤɚɟɬ ɡɚɤɨɧ ɫɨ-
ɯɪɚɧɟɧɢɹ ɡɚɪɹɞɚ:
wjk |
0 . |
(9.2) |
|
wxk |
|||
|
|
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɪɚɦɤɚɯ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɢ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɡɚɪɹɞɚ ɨɤɚɡɵɜɚɟɬɫɹ ɫɥɟɞɫɬɜɢɟɦ ɟɟ ɨɫɧɨɜɧɵɯ ɭɪɚɜɧɟɧɢɣ – ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ ɞɥɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ.
ȿɫɥɢ, ɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɫɨɨɬɧɨɲɟɧɢɟɦ (7.2), ɜɵɪɚɡɢɬɶ Fkl
ɱɟɪɟɡ ɩɪɨɢɡɜɨɞɧɵɟ 4-ɩɨɬɟɧɰɢɚɥɚ, ɬɨ ɪɚɜɟɧɫɬɜɨ (7.3) ɨɛɪɚɳɚɟɬɫɹ ɜ ɬɨɠɞɟɫɬɜɨ, ɚ ɪɚɜɟɧɫɬɜɨ (9.1) ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ:
w |
§wAk wAl |
· |
|
4S j . |
(9.3) |
|||
|
¸ |
|||||||
wx |
¨ |
wx |
wx |
|
c |
k |
|
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l © |
l |
k ¹ |
|
|
|
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||
Ʉɚɥɢɛɪɨɜɨɱɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ (7.1) ɫɨɞɟɪɠɢɬ ɨɞɧɭ ɩɪɨɢɡɜɨɥɶɧɭɸ ɫɤɚɥɹɪɧɭɸ ɮɭɧɤɰɢɸ. ɗɬɨɬ ɩɪɨɢɡɜɨɥ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɜɵɛɪɚɬɶ 4-ɩɨɬɟɧɰɢɚɥ ɬɚɤ, ɱɬɨɛɵ ɨɧ ɭɞɨɜɥɟɬɜɨɪɹɥ ɤɚɤɨɦɭɧɢɛɭɞɶ ɨɞɧɨɦɭ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦɭ ɭɫɥɨɜɢɸ. Ɉ ɜɵɛɨɪɟ ɤɨɧɤɪɟɬɧɨɝɨ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɭɫɥɨɜɢɹ ɝɨɜɨɪɹɬ ɤɚɤ ɨ ɤɚɥɢɛɪɨɜɤɟ 4-
19
ɩɨɬɟɧɰɢɚɥɚ. ȼ ɱɚɫɬɧɨɫɬɢ, ɦɨɠɧɨ ɩɨɬɪɟɛɨɜɚɬɶ, ɱɬɨɛɵ ɜɵɩɨɥɧɹɥɨɫɶ ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɭɫɥɨɜɢɟ Ʌɨɪɟɧɰɚ:
wAk |
0 . |
(9.4) |
|
wxk |
|||
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ɉɪɢ ɬɚɤɨɣ (ɥɨɪɟɧɰɟɜɨɣ) ɤɚɥɢɛɪɨɜɤɟ ɭɪɚɜɧɟɧɢɟ (9.3) – ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɞɥɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ – ɩɪɢɦɟɬ ɜɢɞ:
w2 A |
|
4S |
j . |
(9.5) |
k |
c |
|||
wx2 |
|
k |
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l |
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10. Ɍɟɧɡɨɪ ɷɧɟɪɝɢɢ-ɢɦɩɭɥɶɫɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
Ɋɚɜɟɧɫɬɜɨ (6.7) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɥɨɤɚɥɶɧɭɸ ɮɨɪɦɭɥɢɪɨɜɤɭ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ 4-ɢɦɩɭɥɶɫɚ ɫɢɫɬɟɦɵ ɧɟɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɱɚɫɬɢɰ. Ɂɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ 4-ɢɦɩɭɥɶɫɚ ɡɚɦɤɧɭɬɨɣ ɫɢɫɬɟɦɵ, ɫɨɫɬɨɹɳɟɣ ɢɡ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɫ ɧɢɦ ɱɚɫɬɢɰ, ɞɨɥɠɟɧ ɡɚɩɢɫɵɜɚɬɶɫɹ ɜ ɚɧɚɥɨɝɢɱɧɨɦ ɜɢɞɟ:
w |
Tkl(m) Tkl 0 , |
(10.1) |
wx |
||
l |
|
|
ɝɞɟ Tkl – ɬɟɧɡɨɪ ɷɧɟɪɝɢɢ-ɢɦɩɭɥɶɫɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɤɨ-
ɬɨɪɵɣ ɧɚɦ ɩɪɟɞɫɬɨɢɬ ɧɚɣɬɢ.
ɂɡ (10.1) ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ (9.1) ɢ (8.2) ɢɦɟɟɦ:
w |
T |
|
|
w |
|
T (m) |
|
|
1 F j |
|
1 |
F |
wFml |
|||||
wx |
|
wx |
|
4S |
||||||||||||||
kl |
|
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kl |
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ɫ |
km m |
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km wx |
||||||||
l |
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l |
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l |
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1 |
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§ |
|
w |
(F |
F |
) F |
wFkm |
·. |
(10.2) |
||||
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¨ |
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|||||||||||
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4S |
|
wx |
km |
ml |
ml |
wx |
¸ |
|
|||||||
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© |
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¹ |
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||||||||
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l |
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l |
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ɉɪɟɨɛɪɚɡɭɟɦ ɩɨɫɥɟɞɧɟɟ ɫɥɚɝɚɟɦɨɟ ɜ ɫɤɨɛɤɚɯ, ɭɱɢɬɵɜɚɹ ɫɨɨɬɧɨɲɟɧɢɟ (7.3) ɢ ɢɫɩɨɥɶɡɭɹ ɩɪɢɟɦ ɩɟɪɟɨɛɨɡɧɚɱɟɧɢɹ ɢɧɞɟɤɫɨɜ ɫɭɦɦɢɪɨɜɚɧɢɹ:
F |
wFkm |
1 F |
wFkm |
1 F |
§ wFml wFlk |
· |
||||
ml |
2 |
ml |
2 |
ml ¨ |
wx |
wx |
¸ |
|||
|
wx |
|
wx |
|
© |
¹ |
||||
|
l |
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l |
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k |
m |
||
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20 |
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