Page 248 - index
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ɞɟɩ ɚɬɚɥɚɞɵ. Ⱦɢɮɮɟɪɟɧɰɢɚɥɞɚɭɞɵԙ ɟɪɟɠɟɫɿɧ ɛɿɥɟɬɿɧɞɿɤɬɟɧ, ɜɚɪɢɚɰɢɹɥɚɭɞɵ
ɨɪɵɧɞɚɭ ɤԧɩ ԕɢɵɧɞɵԕ ɬɭɞɵɪɦɚɣɞɵ. Ⱥɥɞɵɧ ɚɥɚ, ɫɵɡɛɚɧɵԙ ɤԧɦɟɝɿɦɟɧ,
ɠԛɣɟɧɿԙ ɩɚɪɚɦɟɬɪɥɟɪɿɧ ɛɚɣɥɚɧɵɫɬɵɪɚɬɵɧ ɬɟԙɞɟɭɞɿ ԕԝɪɵɩ ɚɥɵɩ, ɫɨɞɚɧ ɤɟɣɿɧ
ɬɟԙɞɟɭɞɿ ɜɚɪɢɚɰɢɹɥɚɭ ɤɟɪɟɤ. Ɉɫɵɧɵԙ ɧԥɬɢɠɟɫɿɧɞɟ, ɜɢɪɬɭɚɥɞɵ ɨɪɵɧ
ɚɭɵɫɬɵɪɭɥɚɪɞɵԙ ɚɪɚɫɵɧɞɚԑɵ ɿɡɞɟɥɿɩ ɨɬɵɪԑɚɧ ɛɚɣɥɚɧɵɫ ɚɧɵԕɬɚɥɚɞɵ.
ȿɝɟɪ ɛɚɣɥɚɧɵɫ ɫɬɚɰɢɨɧɚɪ ɛɨɥɫɚ, ɨɧɞɚ ɧɚԕɬɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭ ɜɢɪɬɭɚɥɞɵ
ɨɪɵɧ ɚɭɵɫɬɵɪɭɥɚɪɞɵԙ ɛɿɪɟɭɿɧɟ ɞԥɥ ɤɟɥɟɞɿ, ɚɥ ɛɚɣɥɚɧɵɫ ɫɬɚɰɢɨɧɚɪ ɛɨɥɦɚɫɚ,
ɨɧɞɚ ɧɚԕɬɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭ ɜɢɪɬɭɚɥɞɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭɥɚɪɞɵԙ
ɟɲԕɚɣɫɵɫɵɦɟɧ ɞɟ ɞԥɥ ɤɟɥɦɟɣɞɿ.
1. ɋɬɚɰɢɨɧɚɪ ɛɚɣɥɚɧɵɫɬɵԙ ɬɟԙɞɟɭɿ f (x, y, z) 0 ɛɨɥɫɵɧ. Ɍɟԙɞɟɭɞɿ
ɞɢɮɮɟɪɟɧɰɢɚɥɞɚɩ, ɫɨɞɚɧ ɤɟɣɿɧ ɜɚɪɢɚɰɢɹɥɚɫɚԕ:
wf dx wf dy wf dz 0,
wx wy wz
wf Gx wf Gy wf Gz 0.
wx wy wz
Ȼԝɥ ɬɟԙɞɟɭɥɟɪɞɟɧ, ɧɚԕɬɵ ɠԥɧɟ ɜɢɪɬɭɚɥɞɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭɥɚɪɞɵԙ ɟɤɟɭɿ ɞɟ
ɛɿɪ ɬɟԙɞɟɭɞɿ ԕɚɧɚԑɚɬɬɚɧɞɵɪɚɬɵɧɵɧ ɤԧɪɟɦɿɡ.
2. ɋɬɚɰɢɨɧɚɪ ɟɦɟɫ ɛɚɣɥɚɧɵɫɬɵԙ ɬɟԙɞɟɭɿ f (x, y, z,t) 0 ɛɨɥɫɵɧ. Ɍɟԙɞɟɭɞɿ
ɞɢɮɮɟɪɟɧɰɢɚɥɞɚɩ, ɫɨɞɚɧ ɤɟɣɿɧ ɜɚɪɢɚɰɢɹɥɚɫɚԕ:
wf dx wf dy wf dz wf dt 0,
wx wy wz dt
wf G x wf G y wf G z 0.
wx wy wz
o
Ȼԝɥ ɬɟԙɞɟɭɥɟɪɞɟɧ, ɧɚԕɬɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭ dr(dx, dy, dz) ɠԥɧɟ ɜɢɪɬɭɚɥɞɵ
o
ɨɪɵɧ ɚɭɵɫɬɵɪɭ G r(G x,G y,G z) ԥɪɬԛɪɥɿ ɬɟԙɞɟɭɥɟɪɞɿ ԕɚɧɚԑɚɬɬɚɧɞɵɪɚɬɵɧɵɧ
ɤԧɪɟɦɿɡ, ɫɨɧɞɵԕɬɚɧ ɧɚԕɬɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭ ɜɢɪɬɭɚɥɞɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭɥɚɪɞɵԙ
ɟɲԕɚɣɫɵɫɵɦɟɧ ɞɟ ɞԥɥ ɤɟɥɦɟɣɞɿ.
ɀԛɣɟɧɿԙ ɜɢɪɬɭɚɥɞɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭɵ ɞɟɩ, ɨɫɵ ɠԛɣɟɧɿԙ ɛɚɪɥɵԕ
ɧԛɤɬɟɥɟɪɿɧɿԙ ɜɢɪɬɭɚɥɞɵ ɨɪɵɧ ɚɭɵɫɬɵɪɭɥɚɪɵɧɵԙ ɠɢɵɧɬɵԑɵ ɚɬɚɥɚɬɵɧɵ ɟɫɬɟ
ɛɨɥɭ ɤɟɪɟɤ.
Ɍԛɫɿɧɿɤɬɿ ɛɨɥɭ ԛɲɿɧ ɦɵɧɚ ɛɿɪ ɦɵɫɚɥɞɵ ɤɟɥɬɿɪɟɣɿɤ. ȿɪɤɿɧ ɟɦɟɫ ɧԛɤɬɟ
ԕɨɡԑɚɥɦɚɣɬɵɧ S ɛɟɬɿɧɞɟ ɬԝɪɚԕɬɵ ɬԛɪɞɟ ɠɚɬɚɬɵɧ ɛɨɥɫɵɧ (53-ɫɭɪɟɬ).
53-ɫɭɪɟɬ
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