理论力学十一动量矩定理

1、理论力学十一动量矩定理理论力学十一动量矩定理理论力学十一动量矩定理理论力学十一动量矩定理理论力学十一动量矩定理vrvMmmO)()()(vvMmMmzzO ()OMm vvv q O x y z A A ()zMm vv rv Q Q j m vv ()xym vv理论力学十一动量矩定理ii)(vrvMLmmiiOO)(iizzmMLvzzOLL理论力学十一动量矩定理22)(iiiiiiiiizzrmrmrvmmMLvz2iiJrmzzJL 理论力学十一动量矩定理)()()()(FMFrvvvrvrvrvMOOmmdtdmdtdmdtdmdtd)()(FMvMOOmdtd ()OMm vvv

2、O x y z A rv Q m vv Fv ( )OMFvv理论力学十一动量矩定理)()(FMvMOOmdtd)()()()()()(FvFvFvzzyyxxMmMdtdMmMdtdMmMdtd0)(.FzM若若2 2恒矢量恒矢量)( vMmO量量 恒恒)( vmMz0)(.FMO若若1 1理论力学十一动量矩定理0)(OFM恒矢量恒矢量vrvMmmO)(constmvhmO)( vM理论力学十一动量矩定理)()()()()(iiOeiOiiOmdtdFMFMvM)(eiOdtdFMLO0)()(iiOFM)()()()()(iiOeiOiiOmdtdFMFMvM)()()(e)izz(e)i

3、yy(e)ixxMLdtdMLdtdMLdtdFFF理论力学十一动量矩定理eeeddddddOzOzOyOyOxOxMtLMtLMtL000eeeOzOyOxMMM321CLCLCLOzOyOxeddOOtMLCLO，0eOM理论力学十一动量矩定理vRgWJLOOWRMe)(RvvRgWRJLOO)()(eOMtdLdWRdtdvRgWRJO)()(22RgWJWRaO理论力学十一动量矩定理理论力学十一动量矩定理ABabCDcdABCDabcdzLLLLdL111222coscosrvdtqLrvdtqLVABabVCDcd)(ddezzMtL)coscos(111222rvrvqMVz)co

4、scos(111222rvrvqMnMVzzVqn理论力学十一动量矩定理 0)(ezM恒恒量量zL020122maamaLz22)sin(2lamLz022)sin(laa12zzLL=理论力学十一动量矩定理0)(e)izMF: :解解0 0量量 恒恒zL0rvmrvmBaBAaAuvvuvvBrBaArAaBaAavv2BrArvvu2BrArBaAavvvv理论力学十一动量矩定理ziiiiiiiiOzJr )rm(r )m(LviiizrmJ2)()(izzMJdtdF)(22FzzzzMdtdJdtdJJ理论力学十一动量矩定理)(FzzMJFa mconstM(e)iz0)(.F若若1

5、1constconstM(e)iz)(.F若若2 2理论力学十一动量矩定理sin22mgadtdJOsin022OJmgadtd)sin(0tJmgaOmgaJTO2理论力学十一动量矩定理RfFFRdtdJNOdtRfFdJtNO000RFfJtNO0理论力学十一动量矩定理11112222JMF RJF RMaa=-=-1111122222211RRRRRRawaawa=?)()(2122112211iJJiMMFF=理论力学十一动量矩定理2iizrmJ)(FzzMJ理论力学十一动量矩定理222201212C zi ilJm rmdx xm ll=?231mlJAz22mRrmJiiCz x

6、dx l z A B C理论力学十一动量矩定理22022212mRdRmrmJRiiCz2zzmJ惯性半径(回转半径)惯性半径(回转半径)mJzz理论力学十一动量矩定理)(212121yxmrmJiizCiiiiiizmdymdyxmdyxmyxmrmJ21212121212222)()()(01iiCmymy2mdJJzCz理论力学十一动量矩定理)83(3122221ldldmlmJO2231)2(mllmJJCzz盘杆OOOJJJ2131lmJO杆)83()2(22222ldldmdlmJJCO盘理论力学十一动量矩定理mgRJO2222321mRmRmRJORg32CyOyeyCxOxex

7、maFmgFmaFF)()(gRaaCyCx23, 0mgFFOyOx210理论力学十一动量矩定理xFyFABi)(tdd)(eiOOFML理论力学十一动量矩定理)(GQPgrLz)(tdd)(eizzFMLQrPrtGQPgrdd)(rGQPgQPraGQPgQPdtda)()(,)(OBAzJrgQrgPLxFyFABirrgGmrJO22理论力学十一动量矩定理BFNBFAFNAF)()(eizzFMJ理论力学十一动量矩定理)3(0)2(0mgFFFFFymFxmFmaANBBNAycxcc BFNBFAFNAF)5()4(fFFfFFNBBNAA) 1 (dd212rFrFtmrBANB

8、NABAFFFF,理论力学十一动量矩定理)1(2)1(d)1()1(2d020200fgfrfttfrffgtNBNABAFFFF,2221,1ffmgFfmgfFBA)1 ()1 (2dd2frfgftBFNBFAFNAF理论力学十一动量矩定理xFyF理论力学十一动量矩定理xFyF)(tdd)(eizzFML理论力学十一动量矩定理cos2332lgQPQPcos2332ddlgQPQPt2220333lgQPlgQlgPLcos22coscos2332lQPQllPlgQP理论力学十一动量矩定理cos2332ddddddcos2332ddlgQPQPtlgQPQPtdcos2332dlgQP

9、QPdcos2332d00lgQPQPsin332lgQPQP理论力学十一动量矩定理CririrCCCOLrL miiCiiCCCOFrrFrLrL)()(dddd mttiiiCCCCCCFrFrLrrtmtmtdddddd 理论力学十一动量矩定理()CCi iii iLMm vrm v=?邋vvvvv0 (0)i ii CCm rm rr?=邋vvvQCLv()CCi irii irLMm vrm v=?邋vvvvv()CCi iii ii iCi iirLMm vrm vm rvm rv=?=?邋邋vvvvvvvvvCii iii irLrm vrm v=?邋vvvvvCririr理论力

10、学十一动量矩定理CririrOCCCLrm vL=?vvvv()()OOi iii iCii iCi iii iLMm vrm vrrm vrm vrm v=?=+?=?邋邋vvvvvvvvvvvvi iCm vm v=vv理论力学十一动量矩定理Cii iii iCi iLrm vrm vrm v=?邋?vvvvvvvddddddCiiii iiiCi iCiLvvvm vrmvm vrmttt=?邋邋vvvvvvvvv(i )0iirF ?vvdd,ddiiiiiiCiCivvrmrFrmrFtt?创=?邋邋vvvvvvvv0,0ii iCi ivm vvm v?邋vvvv(i )(e)dd

11、CiiCiiiiiiiLrFrFrFtrFrF=?=?邋?邋vvvvvvvvvvv(e)(e)d()dCiiCiLrFMFt=?邋vvvvv理论力学十一动量矩定理)()(dd)(CCC)(CeieiFJJtFmaM)(dddd)(C22C)(2C2eieiMtJtmFFr理论力学十一动量矩定理AaCAanCAaAamgTC)3(25. 0)2() 1 (0TJTmgmamaccycx理论力学十一动量矩定理)3(25. 0)2() 1 (0TJTmgmamaccycxAaCAanCAaAamgTC0ncAa25. 0coscosACaaacAcyc2m/s92. 61712,25. 01712gagc理论力学十一动量矩定理mgT21mgT9 . 42gaacyc)3(25. 0)2() 1 (0TJTmgmamaccycx理论力学十一动量矩定理00cossin)()()(eCCCyNeyCCxexMJmaFmgFmamamgFco