Решение задач по теоретической механике. Ч.3. Динамика. Чеботарев А.С - 52 стр.

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52
x ɭɫɬɚɧɨɜɢɬɶ ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɢ ɜɵɛɪɚɬɶ ɨɛɨɛɳɟɧɧɵɟ
ɤɨɨɪɞɢɧɚɬɵ;
x
ɩɪɟɞɩɨɥɨɠɢɜ, ɱɬɨ ɫɢɫɬɟɦɚ ɞɜɢɠɟɬɫɹ ɬɚɤ, ɱɬɨ ɜɫɟ ɨɛɨɛɳɟɧɧɵɟ
ɤɨɨɪɞɢɧɚɬɵ ɭɜɟɥɢɱɢɜɚɸɬɫɹ, ɫɨɫɬɚɜɢɬɶ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɤɢɧɟɬɢɱɟɫɤɨɣ
ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ, ɩɪɢ ɷɬɨɦ ɜɫɟ ɩɟɪɟɦɟɧɧɵɟ ɜɟɥɢɱɢɧɵ, ɜɯɨɞɹɳɢɟ ɜ
Ɍ,
ɞɨɥɠɧɵ ɛɵɬɶ ɜɵɪɚɠɟɧɵ ɱɟɪɟɡ ɨɛɨɛɳɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɢ ɨɛɨɛɳɟɧɧɵɟ
ɫɤɨɪɨɫɬɢ, ɬ. ɟ.
);,...,,;,...,,(
2121
tqqqqqqTT
SS
(ɜ ɫɥɭɱɚɟ ɫɬɚɰɢɨɧɚɪɧɵɯ
ɫɜɹɡɟɣ ɜɪɟɦɹ
t ɧɟ ɜɯɨɞɢɬ ɜ ɜɵɪɚɠɟɧɢɟ T);
x
ɨɩɪɟɞɟɥɢɬɶ ɱɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ
j
q
T
w
w
; ɨɩɪɟɞɟɥɢɬɶ ɩɪɨɢɡɜɨɞɧɵɟ
¸
¸
¹
·
¨
¨
©
§
w
w
j
q
T
dt
d
, ɫɱɢɬɚɹ ɜɫɟ ɩɟɪɟɦɟɧɧɵɟ, ɜɯɨɞɹɳɢɟ ɜ
j
q
T
w
w
, ɮɭɧɤɰɢɹɦɢ
ɜɪɟɦɟɧɢ
t;
x
ɧɚɣɬɢ ɨɛɨɛɳɟɧɧɵɟ ɫɢɥɵ; ɩɨɞɫɬɚɜɢɬɶ ɜɫɟ ɧɚɣɞɟɧɧɵɟ ɜɟɥɢɱɢɧɵ ɜ
ɢɫɯɨɞɧɨɟ ɭɪɚɜɧɟɧɢɟ.
x ɭɫɬɚɧɨɜɢɬɶ ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɢ ɜɵɛɪɚɬɶ ɨɛɨɛɳɟɧɧɵɟ
  ɤɨɨɪɞɢɧɚɬɵ;
x ɩɪɟɞɩɨɥɨɠɢɜ, ɱɬɨ ɫɢɫɬɟɦɚ ɞɜɢɠɟɬɫɹ ɬɚɤ, ɱɬɨ ɜɫɟ ɨɛɨɛɳɟɧɧɵɟ
  ɤɨɨɪɞɢɧɚɬɵ ɭɜɟɥɢɱɢɜɚɸɬɫɹ, ɫɨɫɬɚɜɢɬɶ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɤɢɧɟɬɢɱɟɫɤɨɣ
  ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ, ɩɪɢ ɷɬɨɦ ɜɫɟ ɩɟɪɟɦɟɧɧɵɟ ɜɟɥɢɱɢɧɵ, ɜɯɨɞɹɳɢɟ ɜ Ɍ,
  ɞɨɥɠɧɵ ɛɵɬɶ ɜɵɪɚɠɟɧɵ ɱɟɪɟɡ ɨɛɨɛɳɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɢ ɨɛɨɛɳɟɧɧɵɟ
  ɫɤɨɪɨɫɬɢ, ɬ. ɟ. T T ( q1 , q2 ,..., q S ; q1 , q 2 ,..., q S ; t ) (ɜ ɫɥɭɱɚɟ ɫɬɚɰɢɨɧɚɪɧɵɯ
  ɫɜɹɡɟɣ ɜɪɟɦɹ t ɧɟ ɜɯɨɞɢɬ ɜ ɜɵɪɚɠɟɧɢɟ T);
                                                         wT
x ɨɩɪɟɞɟɥɢɬɶ ɱɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ                                 ; ɨɩɪɟɞɟɥɢɬɶ ɩɪɨɢɡɜɨɞɧɵɟ
                                                        wq j
    d §¨ wT
         ·
         ¸ , ɫɱɢɬɚɹ ɜɫɟ ɩɟɪɟɦɟɧɧɵɟ, ɜɯɨɞɹɳɢɟ ɜ wT , ɮɭɧɤɰɢɹɦɢ
    dt ¨© wq j
         ¸
         ¹                                     wq j
  ɜɪɟɦɟɧɢ t;
x ɧɚɣɬɢ ɨɛɨɛɳɟɧɧɵɟ ɫɢɥɵ; ɩɨɞɫɬɚɜɢɬɶ ɜɫɟ ɧɚɣɞɟɧɧɵɟ ɜɟɥɢɱɢɧɵ ɜ
  ɢɫɯɨɞɧɨɟ ɭɪɚɜɧɟɧɢɟ.




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