Решение задач по теоретической механике. Ч.3. Динамика. Чеботарев А.С - 43 стр.

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Ɋɟɲɟɧɢɟ.
ɋɢɫɬɟɦɚ ɢɦɟɟɬ ɞɜɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ. ȼ ɤɚɱɟɫɬɜɟ ɨɛɨɛɳɟɧɧɵɯ
ɤɨɨɪɞɢɧɚɬ ɜɵɛɟɪɟɦ ɥɢɧɟɣɧɵɟ ɤɨɨɪɞɢɧɚɬɵ
s
1
ɢ s
2
, ɧɚɩɪɚɜɥɟɧɧɵɟ ɜɞɨɥɶ
ɧɚɤɥɨɧɧɵɯ ɩɥɨɫɤɨɫɬɟɣ ɜɧɢɡ.
Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɹ Ʌɚɝɪɚɧɠɚ ɞɥɹ ɨɛɨɛɳɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ
s
1
ɢ s
2
:
1
11
S
Q
s
T
s
T
dt
d
w
w
w
w
,
2
22
S
Q
s
T
s
T
dt
d
w
w
w
w
. (1)
Ⱥɤɬɢɜɧɵɦɢ ɫɢɥɚɦɢ ɹɜɥɹɸɬɫɹ:
Ɋ
1
– ɜɟɫ ɝɪɭɡɚ Ⱥ, Ɋ
2
– ɜɟɫ ɝɪɭɡɚ ȼ, Ɋ
3
–
ɜɟɫ ɛɥɨɤɚ
D, Ɋ
4
– ɜɟɫ ɛɥɨɤɚ ȿ, Ɋ
5
– ɜɟɫ ɛɥɨɤɚ Ʉ, Ɋ
6
– ɜɟɫ ɝɪɭɡɚ L. Ɋɟɚɤɰɢɢ
ɫɜɹɡɟɣ ɭɱɢɬɵɜɚɬɶ ɧɟ ɫɥɟɞɭɟɬ, ɬɚɤɤɚɤɜɫɟɫɜɹɡɢ, ɧɚɥɨɠɟɧɧɵɟ ɧɚ ɫɢɫɬɟɦɭ,
ɢɞɟɚɥɶɧɵ (ɧɚɤɥɨɧɧɵɟ ɩɥɨɫɤɨɫɬɢ ɢɞɟɚɥɶɧɨ ɝɥɚɞɤɢɟ, ɬɪɟɧɢɟ ɜ ɨɫɹɯ ɛɥɨɤɨɜ
ɨɬɫɭɬɫɬɜɭɟɬ, ɧɢɬɢ ɩɪɟɞɩɨɥɚɝɚɸɬɫɹ ɧɟɪɚɫɬɹɠɢɦɵɦɢ ɢ ɧɚɬɹɧɭɬɵɦɢ).
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɨɛɨɛɳɟɧɧɵɯ ɫɢɥ
1
S
Q
ɢ
2
S
Q
ɞɚɞɢɦ ɝɪɭɡɚɦ Ⱥ ɢ ȼ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɜɨɡɦɨɠɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ
G
s
1
ɢ
G
s
2
, ɧɚɩɪɚɜɥɟɧɧɵɟ
ɩɚɪɚɥɥɟɥɶɧɨ ɥɢɧɢɹɦ ɧɚɢɛɨɥɶɲɟɝɨ ɫɤɚɬɚ ɧɚɤɥɨɧɧɵɯ ɩɥɨɫɤɨɫɬɟɣ ɜ ɫɬɨɪɨɧɭ
ɜɨɡɪɚɫɬɚɧɢɹ ɤɨɨɪɞɢɧɚɬ
s
1
ɢ s
2
.
         Ɋɟɲɟɧɢɟ.
    ɋɢɫɬɟɦɚ ɢɦɟɟɬ ɞɜɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ. ȼ ɤɚɱɟɫɬɜɟ ɨɛɨɛɳɟɧɧɵɯ
ɤɨɨɪɞɢɧɚɬ ɜɵɛɟɪɟɦ ɥɢɧɟɣɧɵɟ ɤɨɨɪɞɢɧɚɬɵ s1 ɢ s2, ɧɚɩɪɚɜɥɟɧɧɵɟ ɜɞɨɥɶ
ɧɚɤɥɨɧɧɵɯ ɩɥɨɫɤɨɫɬɟɣ ɜɧɢɡ.
    Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɹ Ʌɚɝɪɚɧɠɚ ɞɥɹ ɨɛɨɛɳɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ s1 ɢ s2:
     d wT wT
                   QS 1 ,
     dt w s1 w s1
     d wT wT
                    QS 2 .                                           (1)
     dt w s2 w s2
    Ⱥɤɬɢɜɧɵɦɢ ɫɢɥɚɦɢ ɹɜɥɹɸɬɫɹ: Ɋ1 – ɜɟɫ ɝɪɭɡɚ Ⱥ, Ɋ2 – ɜɟɫ ɝɪɭɡɚ ȼ, Ɋ3 –
ɜɟɫ ɛɥɨɤɚ D, Ɋ4 – ɜɟɫ ɛɥɨɤɚ ȿ, Ɋ5 – ɜɟɫ ɛɥɨɤɚ Ʉ, Ɋ6 – ɜɟɫ ɝɪɭɡɚ L. Ɋɟɚɤɰɢɢ
ɫɜɹɡɟɣ ɭɱɢɬɵɜɚɬɶ ɧɟ ɫɥɟɞɭɟɬ, ɬɚɤ ɤɚɤ ɜɫɟ ɫɜɹɡɢ, ɧɚɥɨɠɟɧɧɵɟ ɧɚ ɫɢɫɬɟɦɭ,
ɢɞɟɚɥɶɧɵ (ɧɚɤɥɨɧɧɵɟ ɩɥɨɫɤɨɫɬɢ ɢɞɟɚɥɶɧɨ ɝɥɚɞɤɢɟ, ɬɪɟɧɢɟ ɜ ɨɫɹɯ ɛɥɨɤɨɜ
ɨɬɫɭɬɫɬɜɭɟɬ, ɧɢɬɢ ɩɪɟɞɩɨɥɚɝɚɸɬɫɹ ɧɟɪɚɫɬɹɠɢɦɵɦɢ ɢ ɧɚɬɹɧɭɬɵɦɢ).
    Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɨɛɨɛɳɟɧɧɵɯ ɫɢɥ QS1 ɢ QS2 ɞɚɞɢɦ ɝɪɭɡɚɦ Ⱥ ɢ ȼ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɜɨɡɦɨɠɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ Gs1 ɢ Gs2 , ɧɚɩɪɚɜɥɟɧɧɵɟ
ɩɚɪɚɥɥɟɥɶɧɨ ɥɢɧɢɹɦ ɧɚɢɛɨɥɶɲɟɝɨ ɫɤɚɬɚ ɧɚɤɥɨɧɧɵɯ ɩɥɨɫɤɨɫɬɟɣ ɜ ɫɬɨɪɨɧɭ
ɜɨɡɪɚɫɬɚɧɢɹ ɤɨɨɪɞɢɧɚɬ s1 ɢ s2.
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