理论力学13_动力学_5.达朗贝尔原理2

1、000NNNzzzyyyxxxFFFFFFFFF0)cos(00)sin(sin0T2T111T2T1211FFgmFFFlmFyxT1T12T1T3T1cos2FFgmFFF,glmmm2121cos振动筛振动筛N0sin2NtmamgFagN0sin2NtmamgF0sin2NtmamgFniF,F,F,F21niNN2N1NF,F,F,FniFFFF,210)()()(0iONiOiOiNiiFMFMFMFFFABxACBmgdxxlmdFsin2sin21sin202mldxxlmFl0000mgFFFFFFAyyTAxx0sin2cos32cos0lmglFlFMTAABxACBmg

2、mgFmgmlFmgmlFAyAxTtan21sin61tan21sin3122sin21sin202mldxxlmFl0000mgFFFFFFAyyTAxx0sin2cos32cos0lmglFlFMTAOxydOR22RRdRmFi02sin0TiyFFF2sin221220mRdRmFTCiiiiimmaaFF)(RCmaF R0CMnCaCaRFnRFRFniaiai Fni F)(RnCCCiimmmaaaaFziiiiOJrrmMM)(OFRFRF)(RnCCCmmaaaFCJMCRFRFCmaFRCJMCBDCABADahmaF 0cos00sin0NAyyNAxxFmgFFFF

3、FF0sinsin2cos20)(hFlFlmgMNAFBDCAmaF )sincos(cossin2sin)sincos(2)sincos(sin22aghmlmgFaghmlmaFaghmlFAyAxN0cos00sin0NAyyNAxxFmgFFFFFF0sinsin2cos20)(hFlFlmgMNAFCDahbC020)(0000mgdhFMmgFFFFFDNyxFdgahdmgFmaFFN2,OrlAB，。ABCORFnRF223722mrJMmrmaFmrmaFOOnCnRCR00)(045cos)(0045cos)(0OAxAORnRAyyRnRAxxMmgrrFMMFFmgF

4、FFFFFF)43(3)()(2222mrmgrMmrmgFmrFAAyAxABCORFnRF223722mrJMmrmaFmrmaFOOnCnRCR00)(045cos)(0045cos)(0OAxAORnRAyyRnRAxxMmgrrFMMFFmgFFFFFFFABC223122mrJMmrmaFmrmaFCCnCnRCR045cos)(0)(045cos)(0045cos)(0CRnRAARnRAyyRnRAxxMrFFmgrMMFFmgFFFFFFF)43(3)()(2222mrmgrMmrmgFmrFAAyAxRFnRFABClAC00RFmgRMMMACCmRmgRMaA3)(2A

5、ACCCAAmRaRamRJMmaF21212AC00)(RFmgRMMMACCFmRmgRMaA3)(20000ACyyCxxFmgmgFFFFRmgRMFFCyCx3)2(2,0AACCCAAmRaRamRJMmaF21212BC020)(000011lFlgmMMFgmFFFFFCyBBCyByyCxBxxFRlmgRMglmMRmgRMgmFFBByBx3)2(223)2(2011ABOmgmgBAO0232320)(221lFlmglmgMMMOF12111312mlMlmF222212121)2(mlMllmFlg1251121mgBA0232320)(221lFlmglmgMMM

6、OF222212121)2(mlMllmFlg12511210220)(22lFlmgMMAFlg32321lglg73,7921mgBA222212121)2(mlMllmF0220)(22lFlmgMMAFlg32321lglg73,792100002FmgFFFFAyyAxxmgFFAyAx1410mgmgBAO000021FFmgmgFFFFOyyOxxmgFFOyOx720ABO2220)(2213121222lmglmglmmllg792030sin30cos)2(30cos2002000CxyNBAAyyNByxAxxMlFlmgFlFMmgFFFFFFFOAABC2mglFml

7、Ax1231222CCCyyCxxJMmaFmaFABCOAAanAanAaAaCAaABnAaAaBAa1279laglaAnACAAnACaaaa060sinBAnAByaaalg7332BAAnABaaaa14960sin143360cos1gaaaglaaaCAnACyCAACxOAABC2mglFmlAx1231030sin30cos)2(30cos20)(02000CxyNBAAyyNByxAxxMlFlmgFlFMmgFFFFFFFF14960sin143360cos1gaaaglaaaCAnACyCAACx222CCCyyCxxJMmaFmaFOAABC2mgmgFmgFmgF

8、lglglgNBAyAx49654996493373349397921Orimiri)(iOOiFMMaaFFCiimmiiiivrarvi)()()(iOOiiiiiiiiimmmvrrrarFMM)()()()(iiiiijkjikrvijkjikrkjiryxzyxyxzyxzyx)()(2ijiijkvyxyxOrimiri)()()()()()()()(2222OijjikjikjiijkjivrkrrMyzxzmyzxzyxmyxmzyxyxmzyxmmiiiiiiiiii)()()()(iiiiijkjikrvijkjikrkjiryxzyxyxzyxzyx)()(2ijiijk

9、vyxyxOrimiri)()()()()()()()(2222OijjikjikjiijkjivrkrrMyzxzmyzxzyxmyxmzyxyxmzyxmmiiiiiiiiii222)(iiizrmyxmJ刚刚体体对对z z轴轴的的惯惯性性积积yzmJxzmJiyzixzkjiMzxzyzyzxzJJJJJ)()(22OkjiMzxzyzyzxzJJJJJ)()(22OzzxzyzyyzxzxJMJJMJJM22ABO主主动动力力系系的的主主矩矩主主动动力力系系的的主主矢矢惯惯性性力力系系的的主主矩矩惯惯性性力力系系的的主主矢矢ORORMFMFABO000000zzyyAxBxxxAyByRzBzyRyByAyxRxBxAxMMMMOAFOBFMMOAFOBFFFFFFFFFFFRzBzyxRyxByxyRxyBxyxRyxAyxyRxyAxFFOAFMOAFMABFOAFMOAFMABFOBFMOBFMABFOBFMOBFMABF)()(1)()(1)()(1)()(1