美国麻省理工大学:《Aerospace Dynamics(航空动力学)》英文版 lecture 13

LECTORE *13 AXISYMMETRIC ROTATION S B00¥cNEs SPACE CowES PRECESSI0N,NUτAToA GrEDMETRIC IATE RARETATIONS

ATTITUDE MOTION -TORQVE FeEE MANE 0ISCUSSED THE ROTATIONAL MOTION FRDn 1 ERSPECTvE。FE”6o0 FRAME 一NE0T0F1A0 A WAy TO CONNECT THE MOTION To THE INEATIAL FRAME So WE CAN DESCRI BE THE ACTUAL MOTION TYPICALLY DoNE 6y DESC RI BING MOTION oF NEHICLE ABoVT THE R SINCE THIS工sFNE0 wE工 ERTAL FRAME(凡=) CONSIDER AXISYMMETRIC Bo0IES PLATES TVBES CAN DE VELoP SIMPLE FAIRLy INTUITIVE GEOMETRIC INTERPRETATIONs FoR THE RESULTING MOTION CLASSIC PR0LEA工心CL35 CAL MECHANIcS

2 AXISYMMETRIC WITH PRIMARY SPIN ABovT T已3-升*15 工工 EvLERS Ec. M RE DucE千 工心+(x3-工)42 0 工2+ 工、=0 3 CoNSTA REWRITE: M1+入w2 RELAT NE S八AATE" SOLUTION oF THE FoRM EAy T SHow λ+以5N乩 2(t)=如)-山s 4 o o, CONST ANTS工八 THIS PROBLEM ARE) AND TIME七。山HCX山=0,山·a t…,大m()m TIME

1-3 So 12 CORRESPONOS TO THE PROTECT ION OFTHE 工 NSTANTANEO5LY工 NTD THE Bor0 yFRAME B0DY FRAME IS ROTATING IN 3-0 E w Is ALso MOVING工小s0 →0N凵)TH小GTAT了5 FIXED ISTHE WHAT CA Y ABOUT THE RELATIVE MOTIOAS 0FTE6o(s)队0Eb? CAN AN5 WER THIS By STνD》| NGTHE MOtIoN oF PRoTEcTED ONToTHEe,,ez PLANE 12 BoOy PRINCiPAL AxEs TCALL STANT 01 RECTI0 THAT W1 PoINTs(5zEoF山,以 CoMfONENTS ) NIL CHANGE AS A FVNcTIDA OF TIME. DEFINE 入(七-七) NOTE AN BE日TMER R-比 CDS → GIVES RELATIVE SPIN BATE

-3A 囚,=心。c05λ+山2。SWt 处。TAN( λ(七-t) uzS(x-A。) S比cost K= TAw Cos t sNA七。 到N)(CD5M)-Cs(5w 2● 此+uoCo5

SUMMARY W SIN 12 山a.C0s 2+u STANT NOW COJSIDER ANGULAR MO MENTVM 甙 FIXED BuT As Y RoTATES EXPECT THE PROTECTION DF 工 THE BoDY FRAME,,与 WILL CHANGE WH TIME 工 工2工2山zCs八 工3 Hu= I 叫,·Ha5 h H3 NSTE M STILL DEFINES ANGLE FRoM T·H、,+H1 e2 RE ON 0 LATER

-5 FoR THE GEOMETRY LET 8BT牦 Le BeTJEEN THE I AND THE 3-As OF THE Boy FRAME (e3) eE們 E ANGLE6mEN Body cone THE H AND THE 3-AXs THE 600Y FRRME.(E3) TE小EHNE: TRN0= Ha Space cone 3 KEY ERUATON N TAN 3 F工,-3(R)E 8>8 工、<工3(05c)"HENe<¥ e GWEs B00y Ax15 ORIENTATION WRT 工ERT1AL0RECT0N,0工 s OFTEN CALLED THE NUTATION ANGLE

1- ·NE- FAIRLY EASYT0 OW THAT e3 ALL LIE工 N ONE PLANE O SINCE H FIXED, THIS PLANE ROTATES ABoUT PATH OF W工3-0 CREATES A B00Y CoNE AND A SPACE CONE ONE:-ATTACHEO To 23 oF Booy+ ALIGNED 5 MMETRY升×s - AT AN ANGLE)FM已节 PAce D ATTA CHE D TO H So FIXE0 工 NEKTIAL SPACE AT AN ANGLE [8-01 FRoM H To , H IS AT THE LINE OF TANGE心CmT6 CoNES →B00y开 TT ITUDE M07 ON CAN BE VISU鹿zE BY RoLLING ONE CONE(6009)Or THE OTHER

RECALL FRoM BEFORE 工>工3+合>8 H(RE H (0s 工,中自< zI h BODY CONE Space cone ROLLS ON FIXED SPACE CoNE < Bod cone X2 ALWAYS忏 Space cone LINE oF 1 ANGENACY OF T毛 2c0E5 cone

ER丌10A0FE、AM0丹BrR 工 S CALLED PRECESS|oN BUT WE HAVE TWO OIFF ERENT TYPES oF QR6ESs0NH歌E DFFERENTiATE BETWEEN THEM ByHow esA0升REM0v心R丁T七CH ONHER 0 ETERMINE06y入“ SINCE X () THEA工F 工;(0s) 入 WHEN Ao DIRECT PRECESS/O THIs D( FFERENCE TS NoT SoMETHING THAT CAN NORMAUY8Es巨EN
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