Page 178 - index

b 2n, c k 2 (21)
mm

ɞɟɩ ɛɟɥɝɿɥɟɣɿɤ.
Ɉɫɵ ɬԝɪɚԕɬɵɥɚɪɞɵ ɬɟԙɞɟɭɝɟ ԕɨɣɵɩ, ɤɨɷɮɮɢɰɢɟɧɬɬɟɪɿ ɬԝɪɚԕɬɵ ɛɨɥɚɬɵɧ

ɛɿɪɬɟɤɬɿ, ɫɵɡɵԕɬɵԕ ɞɢɮɮɟɪɟɧɰɢɚɥɞɵԕ ɬɟԙɞɟɭ ɚɥɚɦɵɡ:

xx 2n x k 2 0. (22)

x x

Ɇԝɧɵ ɲɟɲɭ ԛɲɿɧ ɨɧɵԙ ɫɢɩɚɬɬɚɦɚɥɵԕ ɬɟԙɞɟɭɿɧ ԕԝɪɵɩ, ɬԛɛɿɪɥɟɪɿɧ
ɬɚɛɚɦɵɡ:

r 2 2nr k 2 0 Ÿ r1,2 n r n2 k 2 . (23)

Ⱥɥɵɧԑɚɧ ɲɟɲɿɦɝɟ ɛɚɣɥɚɧɵɫɬɵ, ԛɲ ɬԛɪɥɿ ɠɚԑɞɚɣ ɛɨɥɭ ɦԛɦɤɿɧ: 1) n % k ,
2) n k , 3) n k . Ʉɨɷɮɢɰɢɟɧɬ n (ɛԝɥ ɤɨɷɮɮɢɰɢɟɧɬ ɞɟɦɮɢɪɥɿɤ ɤɨɷɮɮɢɰɢɟɧɬ

xx

ɞɟɩ ɚɬɚɥɚɞɵ – ɧɟɦɿɫɲɟ D ɚmpfung , ɹԑɧɢ «ԧɲɭ») ɬɟɪɛɟɥɿɫ ɛɨɥɚɬɵɧ ɨɪɬɚɧɵԙ

ɤɟɞɟɪɝɿɫɿɧɿԙ ɞԥɪɟɠɟɫɿɧ ɤԧɪɫɟɬɟɬɿɧ ɛɨɥԑɚɧɞɵԕɬɚɧ, ɛɿɪɿɧɲɿ ɠɚԑɞɚɣɞɵ – ɚɡ
ɤɟɞɟɪɝɿɥɿ ɠɚԑɞɚɣ, ɟɤɿɧɲɿɧɿ – ɤԧɩ ɤɟɞɟɪɝɿɥɿ ɠɚԑɞɚɣ, ɚɥ ԛɲɿɧɲɿ – ɞɚԑɞɚɪɵɫ
ɤɟɞɟɪɝɿɥɿ ɠɚԑɞɚɣɵ ɞɟɩ ɚɬɚɣɦɵɡ.

Ɍԥɠɿɪɢɛɟɞɟ ɠɢɿ ɤɟɡɞɟɫɟɬɿɧ ɛɿɪɿɧɲɿ ɠɚԑɞɚɣɞɵ ԕɚɪɚɫɬɵɪɚɣɵԕ. Ȼԝɥ ɠɚԑɞɚɣɞɚ
n % k ɛɨɥԑɚɧɞɵԕɬɚɧ, ɫɢɩɚɬɬɚɦɚɥɵԕ ɬɟԙɞɟɭɞɿԙ ɬԛɛɿɪɥɟɪɿ ɤɨɦɩɥɟɤɫɬɿ ɛɨɥɚɞɵ.

Ɉɥɚɪɞɵ

r1,2 n r k1 ˜ i , (24)

k1 k 2 n2 (25)

ɬԛɪɿɧɞɟ ɠɚɡɚɣɵԕ

24-ɮɨɪɦɭɥɚɞɚΕɵ i 1 .
Ⱦɢɮɮɟɪɟɧɰɢɚɥɞɵԕ ɬɟԙɞɟɭɞɿԙ (22) ԕɚɪɚɫɬɵɪɵɥɵɩ ɨɬɵɪԑɚɧ ɠɚԑɞɚɣ ԛɲɿɧ
ɲɟɲɿɦɿ:

x ent (C1 cos k1t C2 sin k1t) . (26)
Ɍԝɪɚԕɬɵɥɚɪɞɵ ɛɚɫԕɚɲɚ ԧɪɧɟɤɬɟɣɿɤ:

LJ1 Asin D1, (27)
LJ2 AcosD1.

Ⱥɥɵɧԑɚɧ ԧɪɧɟɤɬɟɪɞɿ ɬɟԙɞɟɭɝɟ ԕɨɣɵɩ, ɚɦɩɥɢɬɭɞɚ ɬԛɪɿɧɞɟɝɿ ɲɟɲɿɦ ɚɥɚɦɵɡ:

x A ˜ ent sin(k1t D1 ) (28)

ɂɧɬɟɝɪɚɥɞɚɭɞɵԙ ɬԝɪɚԕɬɵɥɚɪɵ ɛɚɫɬɚɩԕɵ ɲɚɪɬɬɚɪɞɚɧ ɚɧɵԕɬɚɥɚɞɵ.

xx

Ɇɵɫɚɥɵ, t 0 ɛɨɥԑɚɧɞɚ, x x0 ɠԥɧɟ x x0 ɛɨɥɫɵɧ. ɋɨԙԑɵ ɲɚɪɬɬɵ ԕɨɸ
ԛɲɿɧ 26-ɬɟΝɞɟɭɞɟɧ ɬɭɵɧɞɵ ɚɥɚɦɵɡ, ɹԑɧɢ:

x nent (C1 cos k1t C2 sin k1t) k1ent (C1 sin k1t C2 cos k1t) . (29)

x

Ȼɚɫɬɚɩԕɵ ɲɚɪɬɬɚɪɞɵ ɚɬɚɥԑɚɧ ɟɤɿ ɬɟԙɞɟɭɥɟɪɝɟ (26, 29) ԕɨɣԑɚɧɧɚɧ ɤɟɣɿɧ:

176