18Ùµ1ì^$ÄAugust27,2010SNÄþVg^=$Äî.§¥(Ä^$Ä—g^Vg^¥(^$Ä^ÄåƯKÄþ?ØfN1ì^ÄåƯK§Äþ(½¡ÄþÝ!ÄþÝ)´agdnØåƧ?ÛfNé,:=ħdfN3XÄþ1ì^Cz´7Ù%u)=ħ1ì7fN%o=ÄÝω1ìþ:mi:§ÙܤÝ˙Ri,T:éu%oÄþ½Â§Hi=ri×mi˙Ri(1)du˙Ri=˙R0+˙ri,þª¤§Hi=ri×mi˙ri+ri×mi˙R0(2)ªm1´ÄIXoxyz¥Äþ¶1´Ï%$Ä)Vë^ÄåƯKÄþFigure:6.11ìþ:^ÄåƯKÄþ^3miþåFi'uo:åÝMi½Â§Mi=ri×Fi=ri×mi¨Ri=ri×mi¨Ri(3)Ï˙ri×˙ri=0§ª(3)¤§Mi=ddt(ri×mi˙ri)+¨R0×miri(4)ÄÄþHiCzÇUª(2)u§dHidt=ddt(ri×mi˙ri)+¨R0×miri+˙R0×mi˙ri(5)âª(4)ª(5)1ìþ?:éu%Äþ½n§Mi=dHidt+˙R0×mi˙ri(6)^ÄåƯK^=$Äî.§cdª(1)L«:é%oÄþݧ*ÐþëY©ÙfN§1ìéuÙ%ÄþÝH=XiHi=Xiri×mi˙Ri(7)â˙Ri=˙R0+ω×ri(8)Ïd1ìÄþª¤§H=Xiri×(ω×ri)mi+R0×Ximiri(9)â%½Â§Pimiri=0§¿ @1ì´dáõ:|¤§Ä:þá§Äþª(9)C¤§H=Zmr×(ω×r)dm(10)^ÄåƯK^=$Äî.§du^½Â´ïá3ÅNIXÄ:þ§r¤kCþ3N¶IXe§r=xib+yjb+zkbω=ωxib+ωyjb+ωzkbH=Hxib+Hyjb+Hzkb(11)r±þCþ\ª(9)§ω×r=(zωy−yωz)ib+(xωz−zωx)jb+(yωx−xωy)kbr×(ω×r)=[(y2+z2)ωx−xyωy−xzωz]ib+[−yxωx+(x2+z2)ωy−yzωz]jb+[−zxωx−zyωy+(x2+y2)ωz]kb(12)^ÄåƯK^=$Äî.§Ä1ìÝω: rÃ'§¤±Äþ3ÅNIXen©þ§hx=ωxZm(y2+z2)dm−ωyZmxydm−ωzZmxzdmhy=−ωxZmxydm+ωyZm(x2+z2)dm−ωzZmyzdmhz=−ωxZmxzdm−ωyZmyzdm+ωzZm(x2+y2)dm(13)lþ¡ªw§1ìÄþ1ìþ©ÙA5k'1ìþA5©Ù^|¼êIxx,Iyy,Izz5L«§§©O´1ì7ÅNIXx,y,z¶=Ä.þÓ,|¼êIxy,Ixz,IyzL«.þÈk'§Uþ©ÙØÓ§.þÈK^ÄåƯK^=$Äî.§3ó§åÆ¥=Ä.þ½Â§Ixx=Zm(y2+z2)dm;Iyy=Zm(x2+z2)dm;Izz=Zm(x2+y2)dm(14).5Ƚ§Ixy=Zmxydm;Ixz=Zmxzdm;Iyz=Zmyzdm(15)Ïd§1ì7Ù%o=ħ3N¶IXn¶þÄþ©O§hx=Ixxωx−Ixyωy−Ixzωzhy=−Ixyωx+Iyyωy−Iyzωzhz=−Ixzωx−Iyzωy+Izzωz(16)?±¤Ý/ª§H=Iω(17)^ÄåƯK^=$Äî.§Ù¥IxxIxyIxzIxyIyyIyzIxzIyzIzz(18)dݹk=Ä.þÚ.þȧ¡.5Üþ§nÜ/V)1ìþ©Ùé^$ÄKâfN7%Äþݽn§dHdt=M(19)Ù¥M´^31ìþ åÝ¥þª(19)´3.5IXe½Â§Äþémê´ûéê·ïÄ1ì^$Ä´3ÅNIXe§¤±ïÄ´Äþ3ÅNIXeémCzÇ∂H∂t,âþýéêéê'X§3ÅNIXeª(19)¤§M=∂H∂t+ω×H(20)^ÄåƯK^=$Äî.§Óò åÝM3ÅNIXe©)Mx,My,Mz,þª¤§Mx=˙hx+ωyhz−ωzhyMy=˙hy+ωzhx−ωxhzMz=˙hz+ωxhy−ωyhx(21)ª(21)¡1ì^$Äî.§òª(16)\ª(21),1ì^ÄåƧ§Mx=Ixx˙ωx−Ixy˙ωy−Ixz˙ωz+(−Ixzωx−Iyzωy+Izzωz)ωy−(−Ixyωx+Iyyωy−Iyzωz)ωzMy=−Ixy˙ωx+Iyy˙ωy−Iyz˙ωz+(Ixxωx−Ixyωy−Ixzωz)ωz+(−Ixzωx−Iyzωy+Izzωz)ωxMz=−Ixz˙ωx−Iyz˙ωy+Izz˙ωz+(−Ixyωx+Iyyωy−Iyzωz)ωx+(Ixxωx−Ixyωy−Ixzωz)ωy(22)^ÄåƯK^=ÄU1ì7Ù%^=ÄU¡^=ÄUþmi:§ÄUTu§dT=12V2dm(23)Ù¥V´:ýéÝ,dm=mi.â,V=V0+ω×ri(24)Ý:È,V·V=V2=V20+(ω×ri)·(ω×ri)+2V0·(ω×ri)(25)òdª\ª(23)¿È©,^=ÄU,T=12ZmV2dm=12mV2o+12Zm(ω×r)·(ω×r)dm+V0·ω×Zmrdm(26)^ÄåƯK^=ÄUª¥ Rmrdm=0,1´1ì7%^=ÄUTrot,u,Trot=12Zm(ω×r)·(ω×r)dm=12Zm[(ωyz−ωzy)2+(ωzx−ωxz)2+(ωxy−ωyx)2]dm=12Zm[ω2x(y2+z2)+ω2y(x2+z2)+ω2z(x2+y2)−2ωxωzxz−2ωyωzyz−2ωxωyxy]dm(27)r=Ä.þ.þȪ\,^=ÄUúªu,2Trot=ω2xIxx+ω2yIyy+ω2zIzz−2ωxωzIxz−2ωyωzIyz−2ωxωyIxy(28)^ÄåƯK^=ÄU½ö¤,2Trot=ωx(Ixxωx−Ixyωy−Ixzωz)+ωy(−Ixyωx+Iyyωy−Iyzωz)+ωz(−Ixzωx−Iyzωy+Izzωz)(29)Äc¡ùÄþ©þLª,^=ÄUTrotq¤,Trot=12ω·H(30)dª`²^=ÄUÝ,Äþm'X.^ÄåƯK.þ̶{z1ì^ÄåƧ,ÀJ¦^.þ̶.3.þ̶e,.5ÜþÝ¥.5Èu,´éÝ..þ̶IX(ip,jp,kp)?¿N¶IX(ib,jb,kb)m3X^=ÝCp,÷v,ibjbkb=Cpipjpkp(31)üIXÝ'X,ω=Cpωp(32)duI^=ØUC^=ÄUUC,¤±3.þ̶Ú?¿N¶IXe^=ÄUu,Trot=12ωTIω=12ωTpIpωp(33)rª(32)\ª(33),ωTpIpωp=ωTIω=ωTpCTpICpωp(34)^ÄåƯK.þ̶?,Ip=CTpICp(35)ª(35)L²Ip´ÝIA,ÝIAþ|¤^=ÝCp.e1ìäk½5KAÛ/G,~X¶é¡E¥(.Ùþþ!©Ù,顶Ҵ̶,ÃIÏLÝC¦Ì¶.éu¡é¡1ì,K3顲¡S¹kü̶,1n̶Ruù²¡.eÅNIXÀJ.þ̶§d1ì^ÄåƧ{z§Mx=Ixx˙ωx+(Izz−Iyyωyωz)My=Iyy˙ωy+(Ixx−Izz)ωxωzMz=Izz˙ωz+(Iyy−Ixx)ωxωy(36)^ÄåƯK.þ̶~6.1:fNäkXe.5ÜþÝ,I=100103510250503550300(37)¦3.þ̶e.5ÜþÝI^=ÝCp.|^Matlabf·-eig.m¼ê¦)[Cp,Ip]=eig(I)(38)¦.þ̶e.5ÝÝ,Ip=94.0366000219.8462000336.1172(39)I^=ÝCp,Cp=0.9862−0.07540.1473−0.01030.86050.5094−0.1651−0.50390.8479(40)^ÄåƯK^ÃåÝ$Ä{´©ÛE¥(aÊUì§ØÄí ¸é¥(^K§¥(gqØ)åݧ¤±åÝMx=My=Mz=0.c¡?Ø3.þ̶e{z1ì^ÄåƧ¥§ÒåÝu§d^$Ä´ÃåÝ$Äéuc¡?ض顥(§¦=Ä.þIxx=Iyy,u´^$ħ§Ixx˙ωx+(Izz−Iyy)ωyωz=0Iyy˙ωy+(Ixx−Izz)ωxωz=0Izz˙ωz+(Iyy−Ixx)ωxωy=0(41)dª´|5éá§|dd§|±)¥(3í ÷;1§^$ÄÄA:^ÄåƯK^ÃåÝ$ÄFigure:6.2^=¶é¡^ÄåƯK^ÃåÝ$Äb¥(3Ýω§Ñy^$Ädª(41)¥1nª7顶^=Ý~êC,=ωz=Cωz=Constant(42)ª(41)¥1§ª§˙ωx=Izz−IyyIxxωyCωz˙ωy=Ixx−IzzIyyωxCωz(43)òþª¥1¦±ωx§1¦±ωy,, üª\§ωx˙ωx+ωy˙ωy=0(44)½¤ωxdωx+ωydωy=0(45)édªÈ© C§ω2x+ω2y=Cωxy=Constant(46)^ÄåƯK^ÃåÝ$ÄÏd¥(Äþhx,hy©Ou§hx=Ixxωxhy=Iyyωy(47)3oxy²¡SܤÄþhxyu§hxy=IyyCωxy(48)dªL²hxyCωxy´ÓÄoÝܤ§ω=~Cωxy+~Cωz(49)¥(oÄþHu§H=~hωxy+Izz~Cωz(50)§ÃåÝ¥(^$ħÄþH3m½§¿Ýω^ÄåƯKg^¥(½5½5´¥(ÌN½Náu§U!*ÿ§ÙU±½°Ý±3.5m§½Ü½=Äþéuäk^= /E¥(§^ÄåÆïįK´µ¥(fN§Ð©^=Ýω0(NIXoxyz±Û«'X§¥(g^=Uäk½5XJ(NIX¥(.þ̶§ à åÝ^3¥(þ§d1ì^ÄåƧ|§Ixx˙ωx+(Izz−Iyy)ωyωz=0Iyy˙ωy+(Ixx−Izz)ωxωz=0Izz˙ωz+(Iyy−Ixx)ωxωy=0(51)-i,j,k´¥(.þ̶nü ¥þ§^=ÝωnA©þωxo,ωyo,ωzo§âª(H=I·ω),±y²¥(ÄþÝH§H=Ixxωxoi+Iyyωyoj+Izzωzok=Constant(52)^ÄåƯKg^¥(½5¤±ldª±wѧ¥(7/¥1§3=ÄL§¥ÄþÝH3.5m´ð½½ö`§¥(fN§Ï åÝu§§ÄþÝÅð`²´§e=Ä.þ3ÅNIXþØUþ!©Ù§Äþ¥(g^=ÝØXJÊUìëIX´.þ̶X§¥(g^Ýω0d.þ̶,¶Ü§~X顶oz,Kk§H=I·ω=Izω0k(53)dªL²§¥(7.þ̶^=ЩÝω0§Äþdu¥(fNÄþÝ3.5mS±ØC§Ïd¥(±.þ̶g^¶