Page 84 - index

1. Ɍɚɛɢԑɢ ɬԥɫɿɥ. ɇԛɤɬɟ ԕɨɡԑɚɥɵɫɵ ɛɟɪɿɥɭɿɧɿԙ ɛԝɥ ɬԥɫɿɥɿɧɞɟ, ɧԛɤɬɟɧɿԙ ɤɟɡ

ɤɟɥɝɟɧ ɛɿɪ ɫɚɧɚԕ ɠԛɣɟɫɿɧɟ ԕɚɬɵɫɬɵ ɬɪɚɟɤɬɨɪɢɹɫɵ ɠԥɧɟ ɧԛɤɬɟ ԕɨɡԑɚɥɵɫɵɧɵԙ
ɡɚԙɵ ɛɟɪɿɥɟɞɿ. Ɇɵɫɚɥɵ, Ɇ ɧԛɤɬɟɫɿ Ⱥȼ ɬɪɚɟɤɬɨɪɢɹɫɵɦɟɧ ԕɨɡԑɚɥɫɵɧ.
Ɍɪɚɟɤɬɨɪɢɹ ɛɨɣɵɧɚɧ, ɞɨԑɚ ԝɡɵɧɞɵԑɵɧ ɟɫɟɩɬɟɭɞɿԙ ɛɚɫɬɚɩԕɵ ɧԛɤɬɟɫɿ ɪɟɬɿɧɞɟ
Ɉ ɧԛɤɬɟɫɿɧ ԕɚɛɵɥɞɚɣɦɵɡ. Ԕɚɲɵԕɬɵԕɬɵ ɫɚɧɚɭɞɵԙ ɨԙ ɛɚԑɵɬɵ ɪɟɬɿɧɞɟ ɦԛɦɤɿɧ
ɟɤɿ ɛɚԑɵɬɬɵԙ ɤɟɡ ɤɟɥɝɟɧ ɛɿɪɿɧ ɚɥɚɦɵɡ. Ɇɵɫɚɥɵ, ɫɚԑɚɬ ɬɿɥɿɧɿԙ ɛɚԑɵɬɵɧ ɚɥɫɚԕ,
ɨɧɞɚ Ɇ ɧԛɤɬɟɫɿɧɿԙ ɨɪɧɵ S OM ɲɚɦɚɫɵɦɟɧ ɚɧɵԕɬɚɥɚɞɵ (1-ɫɭɪɟɬ).

1-ɫɭɪɟɬ
Ȼԝɥ ɤɟɡɞɟ, ɧԛɤɬɟɧɿԙ ɬɪɚɟɤɬɨɪɢɹ ɛɨɣɵɧɞɚԑɵ ɨɪɧɵ ԝɡɵɧɞɵԑɵ S OM

ɞɨԑɚɧɵԙ ԝɡɵɧɞɵԑɵɦɟɧ ɚɧɵԕɬɚɥɚɞɵ ɠԥɧɟ ɛԝɥ ɞɨԑɚ ɧԛɤɬɟɧɿԙ ɞɨΕɚɥɵΙ
ɤɨɨɪɞɢɧɚɬɚɫɵ ɞɟɩ ɚɬɚɥɚɞɵ. Ԕɨɡԑɚɥɵɫ ɤɟɡɿɧɞɟ ɞɨԑɚɥɵԕ ɤɨɨɪɞɢɧɚɬɚ ɛɟɥɝɿɥɿ
ɛɿɪ ɡɚԙɞɵɥɵԕɩɟɧ ɭɚԕɵɬԕɚ ɛɚɣɥɚɧɵɫɬɵ ԧɡɝɟɪɿɩ ɨɬɵɪɚɞɵ:

s f t . (1)

Ⱦɨԑɚ ԝɡɵɧɞɵԑɵ ɦɟɧ ɭɚԕɵɬ ɚɪɚɫɵɧɞɚԑɵ ɮɭɧɤɰɢɹɥɵԕ ɛԝɥ ɬԥɭɟɥɞɿɥɿɤ (1)

ɧԛɤɬɟ ԕɨɡԑɚɥɵɫɵɧɵԙ ɬɟԙɞɟɭɿ ɧɟɦɟɫɟ ɧԛɤɬɟɧɿԙ ɬɪɚɟɤɬɨɪɢɹ ɛɨɣɵɦɟɧ
ԕɨɡԑɚɥɭɵɧɵԙ ɡɚԙɵ ɞɟɩ ɚɬɚɥɚɞɵ.

ȿɫɤɟɪɬɭ. Ⱦɨԑɚɥɵԕ ɤɨɨɪɞɢɧɚɬɚ s -ɬɿ t ɭɚԕɵɬɬɚ ɠԛɪɿɥɝɟɧ ɠɨɥ S ɩɟɧ
ɲɚɬɚɫɬɵɪɵɩ ɚɥɦɚɭ ɤɟɪɟɤ. ȿɝɟɪ ɧԛɤɬɟ ԛɧɟɦɿ ɛɿɪ ɛɚԑɵɬɬɚ ɚɲɵԕ ɬɪɚɟɤɬɨɪɢɹ ɚɪԕɵɥɵ

ԕɨɡԑɚɥɵɩ ɠԥɧɟ ɨɫɵ ɧԛɤɬɟɧɿԙ ɚɥԑɚɲԕɵ ɨɪɧɵ ɞɨԑɚɧɵԙ ɫɚɧɚԕ ɛɚɫɵɧɚ ɞԥɥ ɤɟɥɝɟɧ
ɤԛɧɞɟ ԑɚɧɚ, ɞɨԑɚɥɵԕ ɤɨɨɪɞɢɧɚɬɚ s ɩɟɧ ɠԛɪɿɥɝɟɧ ɠɨɥ S ɛɿɪ-ɛɿɪɿɧɟ ɫԥɣɤɟɫ ɤɟɥɟɞɿ.

2. Ʉɨɨɪɞɢɧɚɬɬɵԕ ɬԥɫɿɥ. Ȼԝɥ ɬԥɫɿɥɞɟ, M (x, y, z) ɧԛɤɬɟɫɿɧɿԙ ԕɨɡԑɚɥɵɫɵ

ɚɛɫɨɥɸɬ ԕɨɡԑɚɥɦɚɣɬɵɧ ɨɫɶɬɟɪ ɠԛɣɟɫɿɧɞɟ, ɭɚԕɵɬ ɮɭɧɤɰɢɹɫɵ ɪɟɬɿɧɞɟ ɛɟɪɿɥɟɞɿ
(2-ɫɭɪɟɬ).
ɋɨɧɵɦɟɧ, ɟɝɟɪ ɨɫɵ ɧԛɤɬɟɧɿԙ ɤɨɨɪɞɢɧɚɬɚɥɚɪɵ ɯ, ɭ, z ɭɚԕɵɬɬɵԙ (t)
ԛɡɞɿɤɫɿɡ ɛɿɪɦԥɧɞɿ ɮɭɧɤɰɢɹɥɚɪɵ ɛɨɥɵɩ ɤɟɥɫɟ, ɨɧɞɚ:

x f1(t), y f2 (t), z f3 (t) . (2)

2-ɫɭɪɟɬ

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