ECTURE +2 RIGId BoDY DYNAnIC 工Ap1CAT105FA。R工 GENERAL ROTATIONAL JYNMICS EULER'S EQuATIoN of MOTIoN TORQVE fREE SPECIAL CAsEs PRIMARY LESSONS 3D RoTATONAL MOTION MUCH MORE COMPLEX THAN PLANAR (20) EULER'sE。.A.PR∞N10 E STARTING Pot FoR ALL A/s s/c DwAnIcs soLuTIONs To EULERs ERvATrows ARe DAPL巨,B叭 T WE CA DE VE LDP Goo0 GEOMETRIC VISVALIZATION TOOLS
1- Now CAN DEVE LOP THE FULL SET OF RoTAT IONAL 0YNAuICs: TRW/sPoRT THM =R王 X H b:pN昕TEsB0Y AN GVLAR VEbOcIT of FRA心E B。 Y URT INERTIAL ND山, E ASSUME THAT WE ARE USIN丹FME FRTE600y训M肝我 CENTERED升 THE CENTER OF MAss AND FIXED TO THE BoDy INERTIA VIAL UES FIXEO 工 K VECToRs of RECALL,工F sWxi+uyJ十 BoDy FRAME 乐小 xi+Wyj+ SUMMARY M= H °+x() GENERAL FORM OF ROTATIONAL DYNAMICS
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b背-6 STA BI LITY OF TORQUE FREE MOT(o M CA小 GAIN A LOτ0⑩sGBY CoNSIDERING SPECIFIC TyPes F MGTIDNS Awo THEN SEEING How THE VEHICLES MOTION WBULD RE SPONO TD SMALL PERTURBATIONS MOTION SIMILAR 工小T升LADT0N 升8LE CONSIDER ROTATION ABOUT OJE PRINCIPAL AXIs w= W. X, Y, Z N Bo0Y. FRAME. NOw A00 A SLIGWT PERTURBATION To THIS MOTloA ASSUME TORQvE FKEE PERTURBAnoN 「W4则山LA TO HOPEFWULY SMALL CHANGES To Wy wZ →性0千0FD升sAYT0EDcT 5Uxlt), dwy(t) Wzlt) NOTE: PERTURBED: MOTION MUST 5ATISFY EULER'S ERVATIONS
0→7 PERTURBED, TORQUE FREE EULER's )0:工x(山+5)+(工n-工) z 工 +(工xx)(+) +(工w-工x)(w+k) Y POINTS: 。 CONSTANT J以κ,dy,z LINEARIZE EoM By DRoPPING PRo DUCTs of dus EG.了 +wJw 心z+ 山EAR忆EF0RM X CON ￥Y yx 2=0 工 工 J认、 COMBINE:(oFERENTIATE FIRST ONE) : 工孓 Wy
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峰-9 6 BSERVATIONS 一工 F INITIAL SPIN ABOUT AN INTERME01ATE Ax15 ERT A yY 工xy>工 THEN SPIN UN STABLE 5P|NA&orM升/AxEs0FeT ARE STA BLE (oNLy NEUTRAL) EXAMPLE URTHER THDUGHTS: ROTATIONAL KINETIC ENERGY T=2W61wg 8 or=左工xM 工 NoE*化 E RNAL MOMENTS,HFED 士以 工 工5工*×A山AA工ERT14, THEN TRr工 THE MAXIMUMⅦ Lve Pos58LE MAXIMUM千 MIN VALVE
