Краткий курс теоретической механики. Яковенко Г.Н. - 36 стр.

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B
C
O
W
B
îñ
W
A
âð
W
B
âð
A
W
A
= [ωωω
ωω
, V
A
] = [ωωω
ωω
, [ωωω
ωω
, OA]] = −OAω
2
e
2
tg
2
α,
W
A
= [ωωω
ωω
, V
A
] = [ωωω
ωω
, [ωωω
ωω
, OA]] = OAω
2
(−e
2
tg
2
α + e
3
tgα),
W
A
= 2[ωωω
ωω
, V
A
] = 2[ωωω
ωω
, [ωωω
ωω
, OA]] = 2O Aω
2
e
2
tg
2
α,
W
A
= W
A
+ W
A
+ W
A
= OAω
2
e
3
tgα.
W
B
= [ωωω
ωω
, V
B
] = [ωωω
ωω
, [ωωω
ωω
, OB]] = −OBω
2
e
2
tg
2
αcos2α,
W
B
= [ωωω
ωω
, V
B
] = [ωωω
ωω
, [ωωω
ωω
, OB]] = OBω
2
(e
2
tg
2
α − e
3
tgα),
W
B
= 2[ωωω
ωω
, V
B
] = 2[ωωω
ωω
, [ωωω
ωω
, OB]] = −2OBω
2
e
2
tg
2
α,
W
B
= W
B
+ W
B
+ W
B
= −OBω
2
(2e
2
sin
2
α + e
3
tgα).
W
A
= [εεε
εε
, OA] = OAω
2
e
3
tgα,
W
A
= [ωωω
ωω
, V
A
] = 0,
W
A
= W
A
+ W
A
= OAω
2
e
3
tgα.
W
B
= [εεε
εε
, OB] = OBω
2
(−2e
2
sin
2
α + e
3
tgαcos2α),
W
B
= [ωωω
ωω
, V
B
] = [ωωω
ωω
, [ωωω
ωω
, OB]] = −OBω
2
e
3
sin2α,
W
B
= W
B
+ W
B
= −OBω
2
(2e
2
sin
2
α + e
3
tgα).
                                                                  âð
                                                        WB
                                                                          B

                                                                          C
                                                                             îñ
                                                              âð          WB
O                                                    WA A
                                       Ðèñ. 10.4

            ïåð             ïåð
           WA      ω ïåð , VA
                = [ω                 ω ïåð , [ω
                                ] = [ω        ω ïåð , OA]] = −OAω 2 e2 tg2 α,
       îòí
      WA      ω îòí , VA
           = [ω        îòí
                                ω îòí , [ω
                           ] = [ω        ω îòí , OA]] = OAω 2 (−e2 tg2 α + e3 tgα),
           êîð
          WA       ω ïåð , VA
               = 2[ω        îòí
                                      ω ïåð , [ω
                                ] = 2[ω        ω îòí , OA]] = 2OAω 2 e2 tg2 α,
                          ïåð    îòí    êîð
                    WA = WA   + WA   + WA   = OAω 2 e3 tgα.

         ïåð             ïåð
        WB      ω ïåð , VB
             = [ω                 ω ïåð , [ω
                             ] = [ω        ω ïåð , OB]] = −OBω 2 e2 tg2 αcos2α,
        îòí
       WB      ω îòí , VB
            = [ω        îòí
                                 ω îòí , [ω
                            ] = [ω        ω îòí , OB]] = OBω 2 (e2 tg2 α − e3 tgα),
          êîð
         WB       ω ïåð , VB
              = 2[ω        îòí
                                     ω ïåð , [ω
                               ] = 2[ω        ω îòí , OB]] = −2OBω 2 e2 tg2 α,
                 ïåð    îòí    êîð
           WB = WB   + WB   + WB   = −OBω 2 (2e2 sin2 α + e3 tgα).
Ñ òî÷êè çðåíèÿ ïðèíàäëåæíîñòè ê òâ¼ðäîìó òåëó (òåîðåìà 5.1 è ñëåä-
ñòâèå èç íå¼, ðèñ 10.4).
                             âð
                            WA  = [εε, OA] = OAω 2 e3 tgα,
                                  îñ
                                 WA     ω , VA ] = 0,
                                     = [ω
                                 âð    îñ
                           WA = WA  + WA  = OAω 2 e3 tgα.

                 âð
                WB  = [εε, OB] = OBω 2 (−2e2 sin2 α + e3 tgαcos2α),
                  îñ
                 WB     ω , VB ] = [ω
                     = [ω                ω , OB]] = −OBω 2 e3 sin2α,
                                    ω , [ω
                       âð    îñ
                 WB = WB  + WB  = −OBω 2 (2e2 sin2 α + e3 tgα).
Ñðàâíåíèå äâóõ ñïîñîáîâ âû÷èñëåíèÿ óñêîðåíèé ïðèâîäèò ê âûâîäó î õîðîøåì
ñîâïàäåíèè ðåçóëüòàòîâ.

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