l.1 LEcτURE蛙 CORIOLIS DEMYSTI FIED FRAMES EULER ANGLES ROTATIONS 2-4,2-5,2-1
2-1 CoRIoLIS ACcELERAT0 EMYSTIF∈p CONSIOER CASE oF CONSTANT ROTA ToN.No AT0 N OF MME⊙AGUA,ANDc°srAT RADIAL VELOCITY ( As sEEN IN THE RomTIwG 仅AAE F+2只xF+两x) 了Ns乩LE式NB △T SGE So THERE IS No AccELERATION oF PARTCLE P As5N到τ帖60ME BUT THE N6S0LVTE ACCELERATION IS THE DIFFERENCE ETWEEW THE 2 VELoCMES (A8SoLUTE DIIOED 6y At. (AND THIS IS Now-ZERo) ASSUME△七SMAL △e以t s|AMt~4七 COS Wa 七~A SEE WLLIMS 0 EN HARToG"峨 ECHANICS·302
2-2 EuFR。MA60vE NEED To CALCU LATE THIS 0 FFERENCE工201 RECTIONS TANGENTAL/RADIAL △r=V△ AT INITIAL Por NOTE: CHANGES IN VELOCITY THAT ARE VISIBLE 8: FURTHER 0工 N RADIUS, So TANGEA軋L 5∈0Aν5TB∈ GREAT∈ r BY Ar ② T NEW AAGL幽6,TNE RE了s A CMANGE IN THE DIRECTION oF ME ATION RELATIVE TO THE BooY C→A→C+4 DIRE CTION PARALLEL To C12 =(+④) ( JCos w, +-Wo(r+)sHu,山)-y-r AV ENTRIPETAL PA PERPENDICULAR C12 w=①+⑥-r s山+w(r+btv)cou-「w V十wwa=2Ⅵ M
23 So TT IS ExPuCIT THAT THE TANGENTIAL ACELERATION IS THE CoRIOLIS ACELERATION (TAS c小s1sT。F2C。 WTRI BUT0As As毛 CHANGE0uR∈ T IN OF THE M7N RELATIE To B(I.E. 6 FRAME ROTATEs) AoT工A色 CHLNGES R霹0Us,McH EFFECTS THE ROTATIONAL SPEED AB50 LURE ACCELE LON了svEcτ D SUM oF RELATIVE ACCELERATIN CENTRi PeTAL CORRECTIONS MA0ET●5ER轩Ms △DRLs BY OBsERVER工 N A ROTATING ERAME CoRIOLIS TERM 2WX tL12出s sine L VELOCIT C。A/AENT PERPEN OICULAR To W NOTE DIRECTION oF CpRLoLiS ACcELE RATION ALwAYs5 PERPENDICULAR节BoTH讠良AD SMALL. BUT ALWNYSTHERE CHANGE了A0 REGTON鲁
2-3A CoRRECT BY A ROTAT(NG OBSERVER WHEN ONE FRAME IS K0τTG Respec AoK,山MHUE r: OFFSET Fr 十 ORIGIN OF A+2(×) FRAMES 2 日5 UME ORIGINS f TWO fRamEs ARe ColIc KEY POLNT: NEWTON'S LAWs HOLD IN AN NE RTLAL FRAME;s0C升 R17 BT工 N THE Roτ ATNG FRAME,THsE×1ms R M 宁T085RVER工 N TE ROTA1八sY5TE,工T 俐v5ER5A5卫 F THE PARTICLE工 S BEING c∈0PoN6)AN斤 FECTIVE FoRce (示xyr) 义(x EFF
2-8 THE AH00T10A升 L FICTITIOUS” FoRces ARE NEED ED Ex PLA(N THE TRuE 8 BE HAVIOUR f THE PARTLCLEWMICk 15山 OT SIMPLY US CENTRIFUGAL FoRc∈ AcTS RADILy R 2M W x ORIOLIS FORCE Acr⊥oz,8 τ o THE RI GHT AcTuAL PA
2-4 THREE CASES PARTICLE MOVES GRoovE AROUNO TRACK AT CaSTANT RELATIVE SPEED V CORIOLIS ACLELERRT\ON E GRv毛N0 W RADIAL GRooVE NOW VERTICA CR10L1s丹 CCELERATION 2WV V,- PoNENT oF RELATIVE VELOCITY L T0.×S0FR04T(0A
FRAMES oF REFERENCE WE HAvE THE BAsIc EXPRESS (oN FoR THE TNERTIAL (A 650LVTE) ACcEUERATIoN 下E0T0TR工 T OUT ON SOME FRAMES cYL小RcAL 5?H∈RCAL GENERAL
2 CYLIND RICAL Coo ROINATES 只%;z) HAVE WITH COMPONENTS IN THE FIXED z XY, Z FRAME SELECT SECoNd FRAME yz So THAT kEY了佣H肝伲鼠M 了5zER0 THIS STeP Is AccoMPLISHED BY KoTATING ABOVT THE z(=Z)AxIS 8y fRON →x,Yy ASIDE: HOW CAN WE RELATE COMPONENTS WRT x,v2zA0DxYz′? →NEDτ4T0 W MATRICES NDTE:0EN0TEβy THE FACT THIS S THE REPRESENTATION of t WRT FRAME 4 AS OPPosE0 To ( AT FRAME 2
2- So Now WE HAVE A NEW SET of Coo RDINATES TO DESCRIBE THE As THE poINT P(Tip of THe vETo& u)Move THE FRAME WILL ROTATE TO MAINTAIN THE ALIGNMENT GWEN PREⅥosL FRAME 2 WILL ROTATE A BOVT FRAME 1 TH ANGυ LAR RATE 中K 々k THE ACCELE RATION WRT THE IWERTIAL FRANE T5 TMUS USE u"+WXut2wX u+wx(w MATRIx NOTAT STILL ZERo BECAUSE oFTHE GLIGNMENT MAKE SURE ALL OF THE MATKIX COMPONENTS ARE WRITTEN WRT THE SAME FRAME水
