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P. 200
2. ɀԛɣɟɝɟ ԥɫɟɪ ɟɬɭɲɿ ɫɵɪɬԕɵ ɤԛɲɬɟɪɞɿԙ ɛɚɫ ɜɟɤɬɨɪɵɧɵԙ ɤɨɨɪɞɢɧɚɬ
ɨɫɶɬɟɪɿɧɿԙ ɛɿɪɟɭɿɧɞɟɝɿ ԑɚɧɚ, ɦɵɫɚɥɵ, Ox ɨɫɿɧɞɟɝɿ ɩɪɨɟɤɰɢɹɫɵ ɠԛɣɟ
ԕɨɡԑɚɥɵɫɵɧɵԙ ɛɚɪɥɵԕ ɭɚԕɵɬɵɧɞɚ ɧԧɥɝɟ ɬɟԙ ɛɨɥɫɵɧ. Ȼԝɥ ɠɚԑɞɚɣɞɚ, 86-
xx x
ɬɟΝɞɟɭɞɟɧ xC 0 ɧɟɦɟɫɟ xC const ɟɤɟɧɿɧ ɤԧɪɟɦɿɡ. Ⱦɟɦɟɤ, ɠԛɣɟɝɟ ԥɫɟɪ
ɟɬɭɲɿ ɫɵɪɬԕɵ ɤԛɲɬɟɪɞɿԙ ɛɚɫ ɜɟɤɬɨɪɵɧɵԙ ɤɨɨɪɞɢɧɚɬ ɨɫɶɬɟɪɿɧɿԙ ɛɿɪɟɭɿɧɞɟɝɿ
ɩɪɨɟɤɰɢɹɫɵ ɠԛɣɟ ԕɨɡԑɚɥɵɫɵɧɵԙ ɛɚɪɥɵԕ ɭɚԕɵɬɵɧɞɚ ɧԧɥɝɟ ɬɟԙ ɛɨɥɫɚ, ɨɧɞɚ:
- ɟɝɟɪ ɠԛɣɟ ɦɚɫɫɚɫɵɧɵԙ ɰɟɧɬɪɿ ɛɚɫɬɚɩԕɵ ɫԥɬɬɟ ԕɨɡԑɚɥɵɫɬɚ ɛɨɥɦɚɫɚ, ɨɧɞɚ
ɨɥ ɨɫɶ ɛɨɣɵɦɟɧ ԕɨɡԑɚɥɦɚɣɞɵ, ɹԑɧɢ ԧɡɿɧɿԙ ɛԝɪɵɧԑɵ ɬɵɧɵɲɬɵԕ ɤԛɣɿɧ
ɫɚԕɬɚɣɞɵ;
- ɟɝɟɪ ɛɚɫɬɚɩԕɵ ɫԥɬɬɟ ԕɨɡԑɚɥɵɫɬɚ ɛɨɥɫɚ, ɨɧɞɚ ɨɥ ɨɫɶ ɛɨɣɵɦɟɧ ԕɨɡԑɚɥɵɩ,
ԧɡɿɧɿԙ ɠɵɥɞɚɦɞɵԑɵɧ ԧɡɝɟɪɬɩɟɣɞɿ.
Ȼԝɥ ɬԝɠɵɪɵɦɞɚɦɚɥɚɪ ɠΟɣɟ ɦɚɫɫɚɫɵɧɵΝ ɰɟɧɬɪɿ ΙɨɡΕɚɥɵɫɵɧɵΝ ɫɚΙɬɚɥɭ
ɡɚΝɵɧ ԕԝɪɚɣɞɵ.
Ɇɵɫɚɥ. Ɇɚɫɫɚɫɵ m1 ɚɪɛɚ ɪɟɥɶɫɩɟɧ ԕɨɡԑɚɥɵɫɬɚ ɛɨɥɫɵɧ, ɚɥ ɨɧɵԙ ԛɫɬɿɧɞɟ
ɦɚɫɫɚɫɵ m2 ɠԝɦɵɫɲɵ ɬԝɪɫɵɧ (20-ɫɭɪɟɬ).
Ⱥɥԑɚɲԕɵ ɫԥɬɬɟ ɠԝɦɵɫɲɵ ɠԥɧɟ ɚɪɛɚ ɬɵɧɵɲɬɵԕ ɤԛɣɞɟ (ԕɨɡԑɚɥɵɫɫɵɡ)
ɛɨɥɫɵɧ. Ⱥɪɛɚɧɵԙ ɞԧԙɝɟɥɟɝɿ ɦɟɧ ɪɟɥɶɫɬɿԙ ɚɪɚɫɵɧɞɚԑɵ ԛɣɤɟɥɿɫɬɿ ɟɫɤɟɪɦɟɭɝɟ
ɛɨɥɚɞɵ. ȿɝɟɪ ɠԝɦɵɫɲɵ ɚɪɛɚɧɵԙ ԛɫɬɿɦɟɧ l ԕɚɲɵԕɬɵԕԕɚ ɠԛɪɫɟ (ԕɨɡԑɚɥɫɚ),
ɨɧɞɚ ɚɪɛɚ ԕɚɧɲɚԑɚ ɠɵɥɠɢɞɵ (ɚɪɛɚɧɵԙ ɨɪɵɧ ɚɭɵɫɬɵɪɭɵ ԕɚɧɲɚ ɛɨɥɚɪ ɟɞɿ)?
Ȼԝɥ ɟɫɟɩɬɿ ɟɤɿ ɞɟɧɟɞɟɧ (ɚɪɛɚ ɠԥɧɟ ɠԝɦɵɫɲɵ) ɬԝɪɚɬɵɧ ɠԛɣɟ ɪɟɬɿɧɞɟ
o
ԕɚɪɚɫɬɵɪɚɦɵɡ. ɀԛɣɟɝɟ ԥɫɟɪ ɟɬɟɬɿɧ ɫɵɪɬԕɵ ɤԛɲɬɟɪ: ɚɪɛɚɧɵԙ ɫɚɥɦɚԑɵ ( P1 ),
oo
ɠԝɦɵɫɲɵɧɵԙ ɫɚɥɦɚԑɵ ( P2 ) ɠԥɧɟ ɪɟɥɶɫɬɿԙ ɬɿɤ (ɧɨɪɦɚɥɶ) ɪɟɚɤɰɢɹɥɚɪɵ ( N1
o
ɠԥɧɟ N2 ). Ȼɚɪɥɵԕ ɫɵɪɬԕɵ ɤԛɲɬɟɪ Ox ɨɫɿɧɟ ɩɟɪɩɟɧɞɢɤɭɥɹɪ ɛɨɥԑɚɧɞɵԕɬɚɧ,
ɨɥɚɪɞɵԙ Ox ɨɫɿɧɟ ɩɪɨɟɤɰɢɹɥɚɪɵ ɧԧɥɝɟ ɬɟԙ ɛɨɥɚɞɵ. ɋɨɧɞɵԕɬɚɧ ɠԛɣɟ
ɦɚɫɫɚɫɵɧɵԙ ɰɟɧɬɪɿ ɠԝɦɵɫɲɵ ɚɪɛɚɧɵԙ ԛɫɬɿɦɟɧ ԕɨɡԑɚɥԑɚɧɞɚ – ɫɨɥ ɛԝɪɵɧԑɵ,
ɬɵɧɵɲɬɵԕ ɤԛɣɿɧɞɟɝɿ ɨɪɧɵɧɚɧ ɟɲԕɚɣɞɚ ɠɵɥɠɵɦɚɣɞɵ.
Ʉɨɨɪɞɢɧɚɬɚ ɛɚɫɵɧ O ɧԛɤɬɟɫɿɧɟ ɛɟɤɿɬɿɩ, ɠԛɣɟ ɦɚɫɫɚ ɰɟɧɬɪɿɧɿԙ
ɚɛɫɰɢɫɫɚɫɵɧ ɚɧɵԕɬɚɣɦɵɡ. Ɉɥ ԛɲɿɧ 83-ɮɨɪɦɭɥɚɧɵ ɩɚɣɞɚɥɚɧɚɦɵɡ, ɫɨɧɞɚ:
xCo m1 x01 m2 x02 ,
m1 m2
ɛԝɥ ɬɟԙɞɿɤɬɟɝɿ x01 ɠԥɧɟ x02 – ɚɪɛɚ ɦɟɧ ɠԝɦɵɫɲɵɧɵԙ ɫɚɥɦɚԕ ɰɟɧɬɪɥɟɪɿɧɿԙ
ɚɛɫɰɢɫɫɚɥɚɪɵ (ɛɚɫɬɚɩԕɵ ɤԛɣɞɟɝɿ).
ɀԝɦɵɫɲɵ ɨԙ ɠɚԕԕɚ ԕɚɪɚɣ l ԕɚɲɵԕɬɵԕԕɚ ɠԛɪɝɟɧɞɟ, ɚɪɛɚ ɫɨɥ ɠɚԕԕɚ ԕɚɪɚɣ
O ɲɚɦɚɫɵɧɚ ɠɵɥɠɢɞɵ. ɀԝɦɵɫɲɵɧɵԙ ɠԥɧɟ ɚɪɛɚɧɵԙ ɫɚɥɦɚԕ ɰɟɧɬɪɥɟɪɿɧɿԙ
ɠɚԙɚ ɤɨɨɪɞɢɧɚɬɬɚɪɵ: x1 x01 O , x2 x02 l O . Ȼԝɥ ɤɟɡɞɟ ɠԛɣɟ
ɦɚɫɫɚɫɵɧɵԙ ɰɟɧɬɪɿɧɿԙ ɚɛɫɰɢɫɫɚɫɵ:
xC m1 (x01 O) m2 (x02 l O) .
m1 m2
198
