《理論力學(xué)》第十五章虛位移原理

1、0),(222lyxyxfx R0RxfABABAAyyxxyx)(,1,2,)(210,)(約束數(shù)；質(zhì)點(diǎn)數(shù)，snitfi ,r)(,1,2,)(210,)(約束數(shù)；質(zhì)點(diǎn)數(shù)snifi ,rvM2022)(vtlyx)(0 雙雙面面約約束束B(niǎo)y)(0 單面約束單面約束B(niǎo)y)(222雙雙面面約約束束lyx)(222單面約束單面約束lyx)(,1,2,)(210,)(約約束束數(shù)數(shù)；質(zhì)質(zhì)點(diǎn)點(diǎn)數(shù)數(shù)snifi ,r)(,1,2,)(210,)(約約束束數(shù)數(shù)；質(zhì)質(zhì)點(diǎn)點(diǎn)數(shù)數(shù)，snifii ,rrx RABABAAyyxxyx00RxRxCC可以積分為可以積分為cossinlylxcoscossinsincos

2、sin2211baybaxayax廣義坐標(biāo)廣義坐標(biāo)廣義坐標(biāo)廣義坐標(biāo),ab), 2 , 1(),(),(),(212121nitqqqzztqqqyytqqqxxkiikiikiixyOMBrArkjirkjirkjiFiiiiiiiiizyxzyxZYXiii0)(iiiiiizZyYxXBrAr0BFrFMWrrrrABA0)(ABFrFrMrFMWrMF/MCBAD 0CNFrFMWcos2AxAAxrrhrcos)290cos(CArrhrCtan0tanhFMWNFcothMFNxyCBAD 0sin2cos2aFhaMyFMWNCNF2hxAay axCAcos2sincothMFN

3、sin2cosayaxCAhahxAcos22OABCD0)90cos(ACFrQrPW31sin)902cos(OBOArrrrBABCcos32CArr0)cos32sin()90cos(CACFrQPrQrPWcot32QPsin5sin3sin21lxlxlxHOOcos5cos3cos21lxlxlxHOO0)sin(sin2)sin(sin2)sin(sin2)sin(sin20000221HHOOOxPxlkxlkxlkxlk0cos5cos5cos)sin(sin20lPlllk0)sin(sin2)sin(sin2)sin(sin2)sin(sin20000221HHOOOx

4、Pxlkxlkxlkxlk0cos5cos5cos)sin(sin20lPlllk0cos4)sin(sin2cos50lklPl)sin(sin580klPABCDABCD022lsMsFslqDDDE21DEssqllMFD2ABCD02lsMsqlsFsPEEBBBEBsslMqlPFB20)2(BBslMqlFPABCD02lsMsqlsFEEAAECAsss20)2(AAslMqlFqllMFA2), 2 , 1(),(),(),(212121nitqqqzztqqqyytqqqxxkiikiikii),2, 1(niqqzzqqyyqqxxkkiikkiikkii0)()()(11

5、1111knikiikiikiiNkNkNkkkiikkiiniNkkkiiiiiiiiFqqzZqyYqxXqqzZqqyYqqxXzZyYxXW0)()()(111111knikiikiikiiNkNkNkkkiikkiiniNkkkiiiiiiiiFqqzZqyYqxXqqzZqqyYqqxXzZyYxXW01nkkkFqQW), 2 , 1()(1NkqzZqyYqxXQnikiikiikiik), 2 , 1()(1NkqzZqyYqxXQnikiikiikiik等于零.等于零.而其它的廣義虛位移都而其它的廣義虛位移都: :令令0kqkkkqQW則則kkkqWQab21221211c

6、oscossinsincosbaybaxay22222121212111xFyFyFQxFyFyFQBABA22222221112112111cos,sin, 0cos,sin,sinbxbyyaxayay0cossin0cossin)(222111FbbFQFaaFFQBBAab21221211coscossinsincosbaybaxay22222221112112111cos,sin, 0cos,sin,sinbxbyyaxayay0cossin0cossin)(222111FbbFQFaaFFQBBABBAFFFFF21tantan21221211coscossinsincosbayb

7、axay112112111sincossinayaxay0cossin)(111221111FaaFFxFyFyFWQBABABAFFF1tan21221211coscossinsincosbaybaxay2222221sincos0bybxy0cossin222221112FbbFxFyFyFWQBBABFF2tan03111311111MMMMWQ13MM022231222MMWQAErEDrrrEBBE/30sin3223210221222312MMMMQ1221MM),(111nnniiizyxzyxzyxVV), 2 , 1()(nizVyVxViiiikjiF), 2 , 1()(

8、nizzVyyVxxViiiiiiFW), 2 , 1()(nizzVyyVxxViiiiiiFW0V),(21NqqqVV), 2 , 1()(NkqVqzzVqyyVqxxVQkkiikiikiik), 2 , 1(0NkqVQkk00qqdqdV穩(wěn)穩(wěn)定定平平衡衡狀狀態(tài)態(tài): :若若0022qqdqVd非非穩(wěn)穩(wěn)定定平平衡衡狀狀態(tài)態(tài): :若若0022qqdqVd數(shù)數(shù)需需進(jìn)進(jìn)一一步步分分析析其其高高階階導(dǎo)導(dǎo)0022qqdqVd: :若若隨隨遇遇平平衡衡狀狀態(tài)態(tài): :若若0022qqdqVdOABCxysin422lRmgymgVC0cos422lRmgddV為為其其平平衡衡位位置置.23,221

9、oo穩(wěn)穩(wěn)定定平平衡衡狀狀態(tài)態(tài)04222201lRmgdVd非非穩(wěn)穩(wěn)定定平平衡衡狀狀態(tài)態(tài)04222202lRmgdVd20)cos(cos2)coscoscos(22dlmgdlmgymgVC0)cos(sin2dlmgddV.,., 0221ooo舍舍棄棄2 2為為其其平平衡衡位位置置為為其其平平衡衡位位置置0o為為其其平平衡衡位位置置0o)cos(cos2dlmgV)cos(cos222dlmgdVd隨隨遇遇平平衡衡狀狀態(tài)態(tài)非非穩(wěn)穩(wěn)定定平平衡衡狀狀態(tài)態(tài)穩(wěn)穩(wěn)定定平平衡衡狀狀態(tài)態(tài)0cos0cos0cos)cos(2022dldldldlmgdVdcos2221lddll221)2(21lmT )cos(cos2dlmgVEdlmglm)cos(cos2)2(21221sin0)cos(21ldlg 0)cos(21ldlg 1)cos(ldlg), 2 , 1()(1NkqzZqyYqxXQnikiikiik