Page 385 - index

Ԕɚɪɚɫɬɵɪɵɥɵɩ ɨɬɵɪԑɚɧ ɦɵɫɚɥɞɚ, ԛɣɥɟɫɿɦɞɿɥɿɤ ɮɭɧɤɰɢɹɫɵɧ ɛԝɥԑɚԕ

ԕɢɫɵԑɵɧɵԙ Ɇ ɧԛɤɬɟɫɿɧɿԙ ɛɟɪɿɥɝɟɧ ԕɢɫɵԕɬɚɧ ɟԙ ԛɥɤɟɧ ɚɭɵɬԕɭɵ ɪɟɬɿɧɞɟ
ԕɚɛɵɥɞɚɭԑɚ ɛɨɥɚɞɵ, ɹԑɧɢ

' max yM y max , (*)

ɛԝɥ ɬɟԙɞɿɤɬɟɝɿ: yM – ɛɟɥɝɿɥɿ ɛɿɪ x ɚɛɫɰɢɫɫɚɫɵɧɚ ɫԥɣɤɟɫ, Ɇ ɧԛɤɬɟɫɿɧɿԙ
ɨɪɞɢɧɚɬɵ, y – ɛɟɪɿɥɝɟɧ ԕɢɫɵԕɬɵԙ ɚɬɚɥԑɚɧ x ɚɛɫɰɢɫɫɚɫɵɧɚ ɫԥɣɤɟɫ ɨɪɞɢɧɚɬɵ.

ɀɨԑɚɪɵɞɚԑɵ ԛɣɥɟɫɿɦɞɿɥɿɤ ɮɭɧɤɰɢɹɫɵɧ (*) ɚɲɵԕ ɬԛɪɞɟ ɫɢɧɬɟɡɞɿԙ
ɩɚɪɚɦɟɬɪɥɟɪɿ ɚɪԕɵɥɵ ԧɪɧɟɤɬɟɭ ɦԛɦɤɿɧ ɟɦɟɫ. Ȼɿɪɚԕ ɨɧɵ ɟɫɟɩɬɟɭɞɿԙ
ɠɨɥɞɚɪɵɧ, ɹԑɧɢ ɚɥɝɨɪɢɬɦɿɧ ɤԧɪɫɟɬɭɝɟ ɛɨɥɚɞɵ.
Ɇɵɫɚɥɵ, 'ABD ԛɲɛԝɪɵɲɵɧɚɧ BD ɞɢɚɝɨɧɚɥɿɧ ɠԥɧɟ ɨɫɵ ɞɢɚɝɨɧɚɥɶɞɿԙ
ɤԧɥɛɟɭ ɛԝɪɵɲɵɧ ɬɚɛɭԑɚ ɛɨɥɚɞɵ, ɨɥɚɪ:

e a 2 d 2 2ad cosM , G arcsin§¨ a sin M ¸· .
© e ¹

ȿɧɞɿ 'BCD ԛɲɛԝɪɵɲɵɧɚɧ - ɛԝɪɵɲɵɧ ɠԥɧɟ ɬɿɪɟɤ ɩɟɧ ɛԝɥԑɚԕɬɵԙ ( ȼɋ )
ɚɪɚɫɵɧɞɚԑɵ ɛԝɪɵɲɬɵ (D ) ɬɚɛɚɦɵɡ:

- arcsin b2 c 2 e2 ɠԥɧɟ D arcsin¨§ ɫ cos- ¸· G .
2bc © ɟ ¹

ɇԛɤɬɟɧɿԙ Ɇ ɿɡɞɟɥɿɩ ɨɬɵɪԑɚɧ ɤɨɨɪɞɢɧɚɬɬɚɪɵ:

xM xA a cosM J k cosD E J ,

yM yA a sinM J k sinD E J .

Ȼԝɥԑɚԕ ԕɢɫɵԑɵɧɵԙ ɤɨɨɪɞɢɧɚɬɬɚɪɵɧ ( xM ɠԥɧɟ yM ) ɬɚɩԕɚɧɧɚɧ ɤɟɣɿɧ,

ɛɟɪɿɥɝɟɧ ԕɢɫɵԕɬɵԙ ɬɟԙɞɟɭɿɧɟɧ y ɨɪɞɢɧɚɬɚɫɵɧ ɬɚɛɚɦɵɡ, ɨɥ ԛɲɿɧ x xM ɞɟɩ
ԕɚɛɵɥɞɚɣɦɵɡ, ɫɨɧɞɚ:

' yM y . (**)

Ⱥɥɵɧԑɚɧ ɬɟԙɞɿɤɬɟɝɿ ' ɲɚɦɚɫɵɧɵԙ, M ɛԝɪɵɲɵɧɵԙ ԥɪɬԛɪɥɿ ɲɚɦɚɥɚɪɵ

ɛɨɣɵɧɲɚ ɟɫɟɩɬɟɝɟɧɞɟɝɿ ɦԥɧɞɟɪɿɧɿԙ ɟԙ ԛɥɤɟɧɿ max – ɛɟɪɿɥɝɟɧ ԕɢɫɵԕɬɚɧ ɟԙ

ԛɥɤɟɧ ɚɭɵɬԕɭ, ɞɟɦɟɤ ԛɣɥɟɫɿɦɞɿɥɿɤ ɮɭɧɤɰɢɹɫɵ (*) ɛɨɥɵɩ ɬɚɛɵɥɚɞɵ.

Ԕɚɡɿɪɝɿ ɤɟɡɞɟ ɗȿɆ ԕɨɥɞɚɧɵɩ ɦɟɯɚɧɢɡɦɞɟɪɞɿ ɫɢɧɬɟɡɞɟɭɞɿԙ ɤɟɡ ɤɟɥɝɟɧ
ɟɫɟɩɬɟɪɿɧ ɲɟɲɭɝɟ ɛɨɥɚɞɵ, ɛɿɪɚԕ ɚɥɵɧɚɬɵɧ ɲɟɲɿɦɞɟɪɝɟ ɫɚɩɚɥɵ ɬɚɥɞɚɭ
(ɚɧɚɥɢɡ) ɠɚɫɚɭ ԥɪ ɭɚԕɵɬɬɚ ɦԛɦɤɿɧ ɛɨɥɚ ɛɟɪɦɟɣɞɿ. Ɇԝɧɞɚɣ ɬɚɥɞɚɭ ɠɚɫɚɭԑɚ,

ɦɟɯɚɧɢɡɦɞɟɪ ɫɢɧɬɟɡɿɧɿԙ ɮɭɧɤɰɢɹɥɚɪɞɵ ɠɭɵԕɬɚɭ ɬɟɨɪɢɹɫɵɧɚ ɧɟɝɿɡɞɟɥɝɟɧ
ɬԥɫɿɥɿ ɦԛɦɤɿɧɞɿɤ ɛɟɪɟɞɿ.

§2. Ɏɭɧɤɰɢɹɥɚɪɞɵ ɠɭɵԕɬɚɭ ɬԥɫɿɥɿɦɟɧ ɦɟɯɚɧɢɡɦɞɟɪɞɿ ɫɢɧɬɟɡɞɟɭ

Ɏɭɧɤɰɢɹɥɚɪɞɵ ɠɭɵԕɬɚɭ ɞɟɝɟɧɿɦɿɡ, ɛɟɪɿɥɝɟɧ ɮɭɧɤɰɢɹɧɵ y F x ɛɚɫԕɚ
ɛɿɪ ɮɭɧɤɰɢɹ y P x ɚɪԕɵɥɵ ɚɥɦɚɫɬɵɪɭ ɛɨɥɵɩ ɬɚɛɵɥɚɞɵ (69-ɫɭɪɟɬ).
Ɏɭɧɤɰɢɹ y P x ɠɭɵΙɬɚɭɲɵ ɮɭɧɤɰɢɹ ɞɟɩ ɚɬɚɥɚɞɵ, ɨɥ m ɬԝɪɚԕɬɵ

ɩɚɪɚɦɟɬɪɥɟɪɞɟɧ ɬԝɪɚɞɵ. r1, r2 , . . ., rm .

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