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3. ɇԛɤɬɟɝɟ ԥɫɟɪ ɟɬɭɲɿ ɤԛɲɬɟɪ: ɞɟɧɟɧɿԙ ɫɚɥɦɚԑɵ P , ɬɿɤ (ɧɨɪɦɚɥɶ) ɪɟɚɤɰɢɹ

oo

N ɠԥɧɟ ԛɣɤɟɥɿɫ ɤԛɲɿ FǨ .
4. ɇԛɤɬɟ ԕɨɡԑɚɥɵɫɵɧɵԙ ɞɢɮɮɟɪɟɧɰɢɚɥɞɵԕ ɬɟԙɞɟɭɥɟɪɿɧ ԕԝɪɚɦɵɡ:
mx P sin D FxǨ ,

my N P cosD.

Ɍɟԙɞɟɭɥɟɪɞɿ ɬɚɥɞɚɣ ɨɬɵɪɵɩ, ɤɟɥɟɫɿ ԕɨɪɵɬɵɧɞɵԑɚ ɤɟɥɟɦɿɡ:

xx

- ɞɟɧɟ Ox ɨɫɿɧ ɛɨɣɵɦɟɧ ԕɨɡԑɚɥɚɬɵɧ ɛɨɥԑɚɧɞɵԕɬɚɧ, y 0 , ɹԑɧɢ
N P cosD ;

o

- Ʉɭɥɨɧ ɡɚԙɵ ɛɨɣɵɧɲɚ FǨ f ˜ N f ˜ P cosD ;

xx

- ɟɝɟɪ x 0 , ɹԑɧɢ P sinD FxǨ 0 ɧɟɦɟɫɟ P sin D f ˜ P cosD , ɨɧɞɚ ɞɟɧɟ
ɤԧɥɛɟɭ ɠɚɡɵԕɬɵԕɩɟɧ ԛɞɟɦɟɥɿ ԕɨɡԑɚɥɚɞɵ, ԧɣɬɤɟɧɿ tgD f .

Ⱦɟɦɟɤ, ɟɝɟɪ ɠɚɡɵԕɬɵԕɬɵԙ ɤԧɥɛɟɭɥɿɤ ɛԝɪɵɲɵ ԛɣɤɟɥɿɫ ɛԝɪɵɲɵɧɚɧ ԛɥɤɟɧ
ɛɨɥɫɚ, ɨɧɞɚ ɞɟɧɟ ԕɨɡԑɚɥɵɫԕɚ ɤɟɥɟɞɿ ɠԥɧɟ ɨɧɵԙ ԕɨɡԑɚɥɵɫɵ ԛɞɟɦɟɥɿ ɛɨɥɚɞɵ.

Ȼɿɪɿɧɲɿ ɬɟԙɞɟɭɝɟ ԛɣɤɟɥɿɫ ɤԛɲɿɧɿԙ ɲɚɦɚɫɵɧ ԕɨɣɵɩ, m -ɝɟ ԕɵɫԕɚɪɬԕɚɧɧɚɧ
ɤɟɣɿɧ – ɞɟɧɟ ԕɨɡԑɚɥɵɫɵɧɵԙ ɞɢɮɮɟɪɟɧɰɢɚɥɞɵԕ ɬɟԙɞɟɭɿɧ ɚɥɚɦɵɡ. əԑɧɢ:

xx

x g(sinD f ˜ cosD ) const .

x

5. Ԕɨɡԑɚɥɵɫɬɵԙ ɛɚɫɬɚɩԕɵ ɲɚɪɬɬɚɪɵ: t t0 ɛɨɥԑɚɧɞɚ x0 0 , x 0 .
6. Ⱦɢɮɮɟɪɟɧɰɢɚɥɞɵԕ ɬɟԙɞɟɭɥɟɪɞɿ ɢɧɬɟɝɪɚɥɞɚɣɦɵɡ. Ɉɥ ԛɲɿɧ ɬԝɪɚԕɬɵ

ɲɚɦɚɧɵ a ԥɪɩɿɦɟɧ ɛɟɥɝɿɥɟɣɦɿɡ, ɹԑɧɢ g(sinD f ˜ cosD ) a . ɋɨɧɞɚ:

x
dx
xx dt a ɧɟɦɟɫɟ x a ˜ dt . ɂɧɬɟɝɪɚɥɞɚԑɚɧɧɚɧ ɤɟɣɿɧ: x a ˜ t C1.

x dx x

ɂɧɬɟɝɪɚɥɞɚɭɞɵԙ ɬԝɪɚԕɬɵɫɵɧ – ɋ1 ɬɚɛɭ ԛɲɿɧ ɛɚɫɬɚɩԕɵ ɲɚɪɬɬɵ, ɹԑɧɢ t 0

x

ɠԥɧɟ x0 0 ɟɤɟɧɿɧ ɩɚɣɞɚɥɚɧɚɦɵɡ. ɋɨɧɞɚ ɋ1 0 ɟɤɟɧɿɧ ɤԧɪɟɦɿɡ. ɋɨɧɞɵԕɬɚɧ

x dx a ˜ t ɧɟɦɟɫɟ dx a ˜ t ˜ dt . Ɉɫɵ ɬɟԙɞɟɭɞɿ ɢɧɬɟɝɪɚɥɞɚԑɚɧɧɚɧ ɤɟɣɿɧ:
dt
x

x at 2 C2 . ɂɧɬɟɝɪɚɥɞɚɭɞɵԙ ɬԝɪɚԕɬɵɫɵɧ – ɋ2 ɬɚɛɭ ԛɲɿɧ ɛɚɫɬɚɩԕɵ
2

ɲɚɪɬɬɵ, ɹԑɧɢ t 0 ɠԥɧɟ x0 0 ɟɤɟɧɿɧ ɩɚɣɞɚɥɚɧɚɦɵɡ. ɋɨɧɞɚ ɋ2 0 ɟɤɟɧɿɧ

ɤԧɪɟɦɿɡ.
ɋɨɧɵɦɟɧ, ɞɢɮɮɟɪɟɧɰɢɚɥɞɵԕ ɬɟԙɞɟɭɞɿԙ ɲɟɲɿɦɿ:

x at 2 g (sin D f ˜ cosD ) ˜t2.
2 2

Ⱥɥɵɧԑɚɧ ɬɟԙɞɟɭ ɞɟɧɟɧɿԙ ԕɨɡԑɚɥɵɫ ɡɚԙɵ ɛɨɥɵɩ ɬɚɛɵɥɚɞɵ.

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