Page 76 - index

¦¦zC Fi ˜ zi .
Fi

Ⱥɥɵɧԑɚɧ ԛɲ ɬɟԙɞɿɤ, ɩɚɪɚɥɥɟɥɶ ɤԛɲɬɟɪ ɰɟɧɬɪɿɧɿԙ ɤɨɨɪɞɢɧɚɬɚɥɚɪɵɧɵԙ
ɮɨɪɦɭɥɚɥɚɪɵ ɛɨɥɵɩ ɬɚɛɵɥɚɞɵ. Ⱦɟɦɟɤ

¦¦ ¦¦ ¦¦xC Fi ˜ xi , yC Fi ˜ yi , zC Fi ˜ zi . (45ɚ)
Fi Fi Fi

ȿɝɟɪ ɩɚɪɚɥɥɟɥɶ ɤԛɲɬɟɪ ɰɟɧɬɪɿɧɿԙ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɵɧ rc ɫɢɦɜɨɥɵɦɟɧ, ɚɥ ɛԝɥ

ɤԛɲɬɟɪɞɿԙ ԥɫɟɪ ɟɬɭ ɧԛɤɬɟɥɟɪɿɧɿԙ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɥɚɪɵɧ r1 , r2 ,..., rn ɚɪԕɵɥɵ

ɛɟɥɝɿɥɟɫɟɤ, ɨɧɞɚ 45 ɚ-ɚɥɝɟɛɪɚɥɵΙ ɮɨɪɦɭɥɚɥɚɪɞɵ ɛɿɪ ɜɟɤɬɨɪɥɵԕ ɮɨɪɦɭɥɚ
ɚɪԕɵɥɵ ɠɚɡɭԑɚ ɛɨɥɚɞɵ, ɹԑɧɢ

¦¦rC Fi ˜ ri . (45ԥ)
Fi

Ԕɨɪɵɬɵɥԑɚɧ 45 ɚ- ɠΩɧɟ 45 Ω-ɮɨɪɦɭɥɚɥɚɪɵ ɛԥɪɿ ɛɿɪ ɠɚԕԕɚ ɛɚԑɵɬɬɚɥԑɚɧ
ɩɚɪɚɥɥɟɥɶ ɤԛɲɬɟɪ ԛɲɿɧ ɚɥɵɧԑɚɧ ɛɨɥɚɬɵɧ. ȿɝɟɪ ɦԝɧɞɚɣ ɩɚɪɚɥɥɟɥɶ ɤԛɲɬɟɪ ԥɪ
ɠɚԕԕɚ ɛɚԑɵɬɬɚɥɫɚ, ɨɧɞɚ ɛԝɥ ɮɨɪɦɭɥɚɥɚɪɞɵ ԕɨɥɞɚɧɭ ԛɲɿɧ ɤԛɲɬɟɪɞɿԙ ɛɿɪ
ɛɚԑɵɬɵɧ ɨԙ ɞɟɩ, ɚɥ ɟɤɿɧɲɿ ɛɚԑɵɬɬɵ ɫɨɥ ɛɚԑɵɬ ɪɟɬɿɧɞɟ ԕɚɛɵɥɞɚɩ,
ɦɨɦɟɧɬɬɟɪɞɿԙ ɬɚԙɛɚɥɚɪɵɧ ɟɫɤɟɪɫɟ ɠɟɬɤɿɥɿɤɬɿ.

§2. ɋɚɥɦɚԕ (ɚɭɵɪɥɵԕ) ɰɟɧɬɪɿ. ɋɚɥɦɚԕ ɰɟɧɬɪɿɧɿԙ ɮɨɪɦɭɥɚɥɚɪɵ
ɀɟɪ ɲɚɪɵɧɚ ɬɚɹɭ ɨɪɧɚɥɚɫԕɚɧ ԥɪɛɿɪ ɞɟɧɟɧɿ ɀɟɪ ԧɡɿɧɟ ɛɟɥɝɿɥɿ ɛɿɪ ɤԛɲɩɟɧ
ɬɚɪɬɚɞɵ. ɋɨɧɵɦɟɧ ԕɨɫɚ, ɞɟɧɟ ɀɟɪɦɟɧ ɛɿɪɝɟ, ɨɧɵԙ ɨɫɿɧ ɚɣɧɚɥɚ ԕɨɡԑɚɥɭɵɧɚ
ɛɚɣɥɚɧɵɫɬɵ ɬɚԑɵ ɛɿɪ ɤԛɲ ɩɚɣɞɚ ɛɨɥɚɞɵ. Ɉɫɵ ɟɤɿ ɤԛɲɬɿԙ ɬɟԙ ԥɫɟɪ ɤԛɲɿɧ
ɫɚɥɦɚԕ ɤԛɲɿ ɞɟɣɦɿɡ. ȿɤɿɧɲɿ ɤԛɲ ԧɬɟ ɚɡ ɛɨɥԑɚɧɞɵԕɬɚɧ ɨɧɵ ɟɥɟɦɟɭɝɟ ɛɨɥɚɞɵ,
ɫɨɧɞɵԕɬɚɧ ɫɚɥɦɚԕ ɤԛɲɿ ɪɟɬɿɧɞɟ ɬɟɤ ɀɟɪɞɿΝ ɬɚɪɬɭ ɤԛɲɿ ԑɚɧɚ ԕɚɛɵɥɞɚɧɚɞɵ.
Ⱦɟɧɟɧɿԙ ɫɚɥɦɚԕ ɤԛɲɿɧɿԙ ԥɫɟɪ ɟɬɭ ɧԛɤɬɟɫɿɧ ɚɧɵԕɬɚɭ ԛɲɿɧ ɞɟɧɟɧɿ ɤԧɩɬɟɝɟɧ
ԝɫɚԕ ɷɥɟɦɟɧɬɬɟɪɝɟ ɛԧɥɟɦɿɡ. Ɉɫɵ ɷɥɟɦɟɧɬɬɟɪɞɿԙ ɫɚɥɦɚԕ ɤԛɲɬɟɪɿɧɿԙ ԥɫɟɪ ɟɬɭ
ɫɵɡɵԕɬɚɪɵ, ɲɵɧɞɵԑɵɧɞɚ, ɀɟɪɞɿΝ ɰɟɧɬɪɿɧɿԙ ɦɚԙɵɧɞɚ ԕɢɵɥɵɫɚɞɵ, ɛɿɪɚԕ ɀɟɪ
ɛɟɬɿɧɞɟɝɿ ɟԙ ԛɥɤɟɧ ԑɢɦɚɪɚɬɬɵԙ ԧɥɲɟɦɞɟɪɿ ɀɟɪɞɿΝ ԧɥɲɟɦɞɟɪɿɦɟɧ
ɫɚɥɵɫɬɵɪɭԑɚ ɤɟɥɦɟɣɬɿɧɞɟɣ ɚɡ ɛɨɥԑɚɧɞɵԕɬɚɧ, ɷɥɟɦɟɧɬɬɟɪɞɿԙ ɫɚɥɦɚԕ ɤԛɲɿɧɿԙ
ԥɫɟɪ ɟɬɭ ɫɵɡɵԕɬɚɪɵ ɛɿɪ-ɛɿɪɿɧɟ ɩɚɪɚɥɥɟɥɶ ɞɟɩ ԕɚɪɚɫɬɵɪɭԑɚ ɛɨɥɚɬɵɧɵ ɫԧɡɫɿɡ.
ɋɨɧɵɦɟɧ, ɷɥɟɦɟɧɬɬɟɪɞɿԙ ԧɡɚɪɚ ɩɚɪɚɥɥɟɥɶ ɫɚɥɦɚԕ ɤԛɲɬɟɪɿɧɿԙ ɬɟԙ ԥɫɟɪ ɟɬɭ
ɤԛɲɿ ԕɚɪɚɫɬɵɪɵɥɵɩ ɨɬɵɪԑɚɧ ɞɟɧɟɧɿԙ ɫɚɥɦɚԕ ɤԛɲɿ ɛɨɥɵɩ ɟɫɟɩɬɟɥɟɞɿ.
ɋɨɧɞɵԕɬɚɧ ɩɚɪɚɥɥɟɥɶ ɤԛɲɬɟɪɞɿԙ ɰɟɧɬɪɿ ɨɫɵ ɞɟɧɟɧɿԙ ɫɚɥɦɚԕ ɰɟɧɬɪɿ ɛɨɥɵɩ
ɬɚɛɵɥɚɞɵ. Ⱦɟɧɟɧɿԙ ɫɚɥɦɚԕ ɰɟɧɬɪɿ ɝɟɨɦɟɬɪɢɹɥɵԕ ɧԛɤɬɟ, ɛɿɪɚԕ ɛԝɥ ɧԛɤɬɟ ɤɟɣ-
ɤɟɡɞɟ ɛԝɥ ɞɟɧɟɧɿԙ ɧԛɤɬɟɫɿ ɛɨɥɦɚɭɵ ɞɚ ɦԛɦɤɿɧ. Ɇɵɫɚɥɵ, ɫɚԕɢɧɚɧɵԙ ɫɚɥɦɚԕ
ɰɟɧɬɪɿ ɨɫɵ ɫɚԕɢɧɚɧɵԙ ɛɨɣɵɧɞɚ ɠɚɬɩɚɣɞɵ, ɬɟɤ ɨɧɵԙ ɝɟɨɦɟɬɪɢɹɥɵԕ ɰɟɧɬɪɿɧɞɟ
ɠɚɬɚɞɵ.
Ⱦɟɧɟɧɿԙ ɫɚɥɦɚԕ ɰɟɧɬɪɿɧɿԙ ɮɨɪɦɭɥɚɥɚɪɵɧ ԕɨɪɵɬɭ ԛɲɿɧ, ɞɟɧɟɧɿԙ i -ɲɿ
ɷɥɟɦɟɧɬɿɧɿԙ ɫɚɥɦɚԕ ɤԛɲɿɧ Pi ɞɟɩ, ɚɥ ɨɧɵԙ ɤɨɨɪɞɢɧɚɬɚɥɚɪɵɧ xi , yi ɠԥɧɟ zi

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