Page 85 - index

Ȼԝɥ ɬɟԙɞɟɭɥɟɪ ɞɟɤɚɪɬɬɵԕ ɤɨɨɪɞɢɧɚɬɬɚɪɞɚԑɵ ɧԛɤɬɟ ԕɨɡԑɚɥɵɫɵɧɵԙ
ɬɟԙɞɟɭɥɟɪɿ ɞɟɩ ɚɬɚɥɚɞɵ.

ȿɝɟɪ ɧԛɤɬɟ ɠɚɡɵԕ ɬɪɚɟɤɬɨɪɢɹ ɚɪԕɵɥɵ ԕɨɡԑɚɥɫɚ, ɨɧɞɚ Oxy ɤɨɨɪɞɢɧɚɬɚɥɚɪ

ɠԛɣɟɫɿɧɞɟ (3-ɫɭɪɟɬ) ɟɤɿ ɬɟԙɞɟɭ ɚɥɚɦɵɡ, ɞɟɦɟɤ:

x f1(t), y f2 (t) . (2ɚ)

3-ɫɭɪɟɬ

Ʉɨɨɪɞɢɧɚɬɬɵԕ ɬԥɫɿɥ ɤɟɡɿɧɞɟ, ɧԛɤɬɟɧɿԙ ɤɟԙɿɫɬɿɤɬɟɝɿ ɬɪɚɟɤɬɨɪɢɹɫɵ ɟɤɿ
ɬɟԙɞɟɭ ɚɪԕɵɥɵ (I1(x, y, z) 0 , I2 (x, y, z) 0 ) ԧɪɧɟɤɬɟɥɟɞɿ, ɚɥ ɠɚɡɵԕɬɵԕɬɚ –

ɛɿɪ ɬɟԙɞɟɭɦɟɧ (I(x, y) 0 ) ԧɪɧɟɤɬɟɥɟɞɿ.

3. ȼɟɤɬɨɪɥɵԕ ɬԥɫɿɥ. Ȼԝɥ ɬԥɫɿɥɞɟ Ɉɯɭz ɤɨɨɪɞɢɧɚɬɬɚɪ ɠԛɣɟɫɿɧɟ ԕɚɬɵɫɬɵ

oo

ɧԛɤɬɟɧɿԙ ɨɪɧɵ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɦɟɧ ( r OM ) ɚɧɵԕɬɚɥɚɞɵ. Ɋɚɞɢɭɫ-ɜɟɤɬɨɪ
ɞɟɝɟɧɿɦɿɡ – ɤɨɨɪɞɢɧɚɬɬɚɪ ɛɚɫ ɧԛɤɬɟɫɿɧ ɠԥɧɟ ɛɟɪɿɥɝɟɧ M (x, y, z) ɧԛɤɬɟɫɿɧ

ԕɨɫɚɬɵɧ ɜɟɤɬɨɪ. ɇԛɤɬɟɧɿԙ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɵ ɬԧɦɟɧɞɟɝɿ ɮɨɪɦɭɥɚɦɟɧ
ԧɪɧɟɤɬɟɥɟɞɿ (2-ɫɭɪɟɬ)
Ȼԝɥ ɠɟɪɞɟɝɿ: x, y, r& & ɧɟɦɟɫɟ r& xi& yi& zi' i&, &j , & (3)
– f (t) k –ɤɨɨɪɞɢɧɚɬ

z ɧԛɤɬɟɧɿԙ ɤɨɨɪɞɢɧɚɬɚɥɚɪɵ, ɚɥ

ɨɫɶɬɟɪɿɧɿԙ ɨɪɬɬɚɪɵ.
Ȼԝɥ ɬɟԙɞɟɭɥɟɪ (3) ɧԛɤɬɟ ԕɨɡԑɚɥɵɫɵɧɵԙ ɜɟɤɬɨɪɥɵԕ ɬɟԙɞɟɭɥɟɪɿ ɞɟɩ

ɚɬɚɥɚɞɵ. ɋɨɧɞɵԕɬɚɧ ɛԝɥ ɬɟԙɞɟɭɥɟɪ Ɇ (x, y, z) ɧԛɤɬɟɫɿɧɿԙ ɪɚɞɢɭɫ-

ɜɟɤɬɨɪɵɧɵԙ ɦɨɞɭɥɿ ɦɟɧ ɛɚԑɵɬɵɧɵԙ ԥɪɛɿɪ ɭɚԕɵɬ ɦɟɡɝɿɥɿɧɟ ɫԥɣɤɟɫ ɤɟɥɟɬɿɧ

ɦԥɧɞɟɪɿɧ ɬɚɛɭԑɚ ɦԛɦɤɿɧɞɿɤ ɛɟɪɟɞɿ. Ԕɨɡԑɚɥɵɫ ɤɟɡɿɧɞɟ r - ԧɡɿɧɿԙ ɦɨɞɭɥɿɧ ɞɟ,
ɛɚԑɵɬɵɧ ɞɚ ԧɡɝɟɪɬɟɞɿ. Ⱦɟɦɟɤ, ɨɥ t -ɧɵԙ ɛɿɪɦԥɧɞɿ, ԛɡɞɿɤɫɿɡ,

ɞɢɮɮɟɪɟɧɰɢɚɥɞɚɧɚɬɵɧ ɮɭɧɤɰɢɹɫɵ ɛɨɥɵɩ ɤɟɥɟɞɿ.
ȿɫɤɟɪɬɭ. Ԧɡɝɟɪɦɟɥɿ ɜɟɤɬɨɪɞɵԙ, ɛɟɪɿɥɝɟɧ ɧԛɤɬɟɞɟ ɬԝɪԑɵɡɵɥԑɚɧ

ɝɟɨɦɟɬɪɢɹɥɵԕ ɨɪɧɵ ɜɟɤɬɨɪɞɵΝ ɝɨɞɨɝɪɚɮɵ ɞɟɩ ɚɬɚɥɚɬɵɧɵ ɦɚɬɟɦɚɬɢɤɚɞɚɧ
ɛɟɥɝɿɥɿ. ɋɨɧɞɵԕɬɚɧ ɧԛɤɬɟɧɿԙ ɬɪɚɟɤɬɨɪɢɹɫɵ ɧԛɤɬɟɧɿԙ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɵɧɵԙ
ɝɨɞɨɝɪɚɮɵ ɛɨɥɵɩ ɬɚɛɵɥɚɞɵ.
4. ɇԛɤɬɟ ԕɨɡԑɚɥɵɫɵɧɵԙ ɬɪɚɟɤɬɨɪɢɹɫɵ. ɇԛɤɬɟ ԕɨɡԑɚɥɵɫɵɧɵԙ ɬɪɚɟɤɬɨ-
ɪɢɹɫɵɧɵԙ ɬɟԙɞɟɭɿɧ ԕԝɪɭ ԛɲɿɧ 2-ɬɟΝɞɟɭɥɟɪɞɟɧ, ɩɚɪɚɦɟɬɪ ɪɟɬɿɧɞɟ ɬԝɪԑɚɧ,

83