Page 552 - index

ɟɤɿ ɠɚɧɚɦɚ ɤɟɪɧɟɭɥɟɪ ɞɟ, ɬɿɤ ɤɟɪɧɟɭɥɟɪ ɞɟ J xz ɲɚɦɚɫɵɧɚ ԥɫɟɪɿɧ ɬɢɝɿɡɛɟɣɞɿ.
Ȼԝɥ ɬԝɠɵɪɵɦ, ԕɚɥԑɚɧ ɞɟɮɨɪɦɚɰɢɹɥɚɪ ɦɟɧ ɤɟɪɧɟɭɥɟɪ ԛɲɿɧ ɞɟ ɡɚԙɞɵ ɛɨɥɵɩ
ɬɚɛɵɥɚɞɵ. ɋɨɧɞɵԕɬɚɧ:

> @ H x1 Vx J xy W xy ,
E P Vy Vz G

> @H y 1 W yz , (8.40)
E V y PV z Vx J yz
G

> @ H z1 W xz .
E Vz P Vx V y J zx
G

Ȼԝɥ ɚɥɵɧԑɚɧ (8.39), (8.40) ԧɪɧɟɤɬɟɪ ɢɡɨɬɪɨɩ ɦɚɬɟɪɢɚɥɞɚɪ ԛɲɿɧ Ƚɭɤɬɵԙ
ԕɨɪɵɬɵɧɞɵ ɮɨɪɦɭɥɚɫɵ ɛɨɥɵɩ ɫɚɧɚɥɚɞɵ.

§9. ɉɨɬɟɧɰɢɚɥɞɵԕ ɷɧɟɪɝɢɹɧɵԙ ԕɨɪɵɬɵɧɞɵ ɬԛɪɿ

ɀɚɥɩɵ ɠɚԑɞɚɣɞɚ ɤɟɪɧɟɥɝɟɧ ɤԛɣɞɿԙ (V1 z 0 , V 2 z 0 , V 3 z 0 )
ɩɨɬɟɧɰɢɚɥɞɵԕ ɷɧɟɪɝɢɹɫɵɧ ԕɚɪɚɫɬɵɪɚɦɵɡ. Ɉɥ ԛɲɿɧ ɷɥɟɦɟɧɬɚɪ ɤԧɥɟɦɞɟ

ɠɢɧɚɥԑɚɧ ɩɨɬɟɧɰɢɚɥɞɵԕ ɷɧɟɪɝɢɹɧɵԙ ɨɫɵ ɤԧɥɟɦɧɿԙ ɛɟɬɿɧɟ ɬɚɪɚɥԑɚɧ ɤԛɲɬɟɪ

ԥɫɟɪɿ ɚɪԕɵɥɵ ɬɚɛɵɥɚɬɵɧɵɧ ɟɫɤɟɪɭɿɦɿɡ ɤɟɪɟɤ. Ɉɥɚɣ ɛɨɥɫɚ, V x ˜ dx ˜ dz ɤԛɲɿ

H x ˜ dx ɨɪɵɧ ɚɭɵɫɬɵɪɭɵɧɚ ɫԥɣɤɟɫ ɠԝɦɵɫ ɿɫɬɟɣɞɿ. Ȼԝɥ ɠԝɦɵɫɬɵԙ ɲɚɦɚɫɵ:

1 V x ˜ dy ˜ dz ˜H x dx .
2

Ԕɚɥԑɚɧ ɬɿɤ ɤɟɪɧɟɭɥɟɪ ɚɪԕɵɥɵ ԧɪɧɟɤɬɟɥɟɬɿɧ ɤԛɲɬɟɪɞɿԙ ɠԝɦɵɫɬɚɪɵ ɨɫɵ
ɫɟɤɿɥɞɿ ɬɚɛɵɥɚɞɵ.

Ⱥɥ, W xy ˜ dx ˜ dz ɤԛɲɿ J xy ˜ dy ɨɪɵɧ ɚɭɵɫɬɵɪɭɵɧɚ ɫԥɣɤɟɫ ɠԝɦɵɫ ɿɫɬɟɣɞɿ, ɹԑɧɢ

1 W xy ˜ dx ˜ dz ˜J xy dy .
2

Ȼɚɫԕɚ ɤԛɲɬɟɪɞɟɧ ɩɚɣɞɚ ɛɨɥɚɬɵɧ ɠԝɦɵɫɬɚɪɞɵ ɨɫɵɥɚɣɲɚ ɬɚɭɵɩ, ɷɥɟɦɟɧɬɚɪ
ɤԧɥɟɦɞɟɝɿ ɩɨɬɟɧɰɢɚɥɞɵԕ ɷɧɟɪɝɢɹɧɵ ɬԧɦɟɧɞɟɝɿɲɟ ɬɚɛɚɦɵɡ:

dU1
2 dx ˜ dy ˜ dz ˜ V xH x V yH y V zH z W xyJ xy W yzJ yz W zxJ zx . (8.41)

Ƚɭɤɬɵԙ ԕɨɪɵɬɵɧɞɵ ɮɨɪɦɭɥɚɫɵɧ ɟɫɤɟɪɟ ɨɬɵɪɵɩ, ɩɨɬɟɧɰɢɚɥɞɵԕ
ɷɧɟɪɝɢɹɧɵ ɤԧɥɟɦɝɟ ( dV dx ˜ dy ˜ dz ) ɛԧɥɟɦɿɡ.

dU> @ U 01 2 2 2 1 W2 2 2 .
dV 2E V x V Y V z 2P V xV y V yV z V zV x 2G xy W yz W zx

(8.42)

Ȼԝɥ ɮɨɪɦɭɥɚɧɵ ɛɚɫ ɤɟɪɧɟɭɥɟɪ ɚɪԕɵɥɵ ԧɪɧɟɤɬɟɫɟɤ

1> @ Uo2 2 2 1 W2 2 2 . (8.43)
2E V 1 V 2 V 3 2P V 1V 2 V 2V 3 V 3V 1 2G xy W yz W zc

Ɍɨɥɵԕ ɩɨɬɟɧɰɢɚɥɞɵԕ ɷɧɟɪɝɢɹɧɵ ɬɚɛɭ ԛɲɿɧ U0 ԧɪɧɟɝɿɧ ɷɥɟɦɟɧɬɚɪ ɤԧɥɟɦɝɟ
ɤԧɛɟɣɬɤɟɧɧɟɧ ɤɟɣɿɧ ɢɧɬɟɝɪɚɥɞɚɭ ɤɟɪɟɤ.

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