《航空航天动力学》英文版 lecture11 KINEMATIcs oF Rigid &o DIEs

LECTURE II KINEMATIcs oF Rigid &o DIEs INERTIA MATRIx AND OY ADIC CALCULATION、千 CALCULATION PRINCIPAL AXES AND ROTATIONS

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QUICK REVIEW AN GULAR MOMENTUM Of A PART ICLE i A BOUT 千帖 CENTER OF MA55工s出 QUAL to T MoMENT OF THE PARTICLE's LWEAR MOMENTUM ABOUT THE C.o.M. ( NOT NECESSARY, UT SIMPLIFIES) M;=F;×(M y甘·Ex(;) LOCATION 6● A6SOLVTE 0 F PART∪CLE VELOCITY WRT C.o.M Of PARTICHE i FoR RiGid BoDY WITH CoNTINUOUS MAS5 OISTRIBVTIDN PARTICLE M MAss dM of SMALL Volume dv d =(x 6 USE TRANSPORT THEoREM +WⅩ

Su&STITVTE TD GET: M F×(×)A CONSTANT AND ORIGIN OF F IS 甙「Fx(x) Q B

3弃 WNERTIA DEFINITioWS EXPANSION oF THE INERT(A RB, REF POINT AT DRIGIN OF CARTESIAN C0oR0N升 TE SYSTEM NoLUME ELEMENT AT =X+yj+ z ANGULAR VELDCITY DF B00Y TN TERMS oF 2品 CARTES:AN CoMPONENTS: 时yj+zk 宁 NoWEXPAN「xCK x (zw-Y吨z)i +(X F义(x) Xw"zwx 人 2 ywy -Zwz [y以+(x+x2》wy-yw] Z×x-2 Wz

-38 DE FINE THE MoMENTS oF INERTIA As: x·∫+2)4w,x-x…-/y 工 (x2+2)成州;工a-工zx--/xzA uo 工 y 工 工 yz dM ENH:「=x(动F)d响 Q L工kw+工xyMy+工xz […+王ww+x] +I2x wx+ Ix wy+Ix 2]k ≡Hxi+A YJ 十H2 F\N心t川G工 其其 1-xy」…… REQOIRES MAwY TRIPLE TNTEGR升Ls MATRIx NOTATION 工 xZ 风 工Yx工w工 Z X 工心 ERTIA MATRIX

TYPICAL EXAMPLE: Box Caxbxc) 夏·FND工x AT CO,M 工 +2)“(+2)4z 8 Z dz )()] C M= ta c (2+c2) MANH以kEK丹 MPLES TN THE T灯BkS

1o-30 KEY PoINTS o FoR PLANAr BoOIES WITH ORIGIN INTHE PLANE (y) YZ 工x+工 u∞N♀z 2FoR 3-D BODIES WITH A PLANE oF SYMMETRY THE cRoss MoM ENTS of TWERTIA ACROSs THE PLAn∈AREz∈Ro PLANE OF SYMMETRY x-Y 工 Yz “ MASS EVeNLY0s( RI BUTED ON BoT材 SIDES oF THE PLANE 工 F FURTHERMORE,N∈0 F THE C0OQ0NATE AXES TS THE SYMMETRY AXIs OF A BoDy DF REVOLUTIoN, THEN ALL CRoSS MoMENTS OF 工 NERT IA AR52ERD

L0-3E TRANSLATU人·FC00R自AAS FTE心HAU∈HrN∈ RTIAS ABOUT。A∈ SET OF AXES AND NEED TT ABoUT 舟sECo川0sET u O PARALLEL TO FIRST OFFSET (kLy x=x+xc Y +Y Z+ ze RuLτ工swE? RALLEL AXIS THM 工 十M KK 工 KK WhERE d Is THE DistANCE BETWEEN A GIVEN PRIMED AND VNPRIMED AXIS (:+22) Iyy (x+z2) 工 (x+Y2) 工N工*y MXY;工 工 x Z 士yz'-Yc2c

6-3 ROTATION oF CoOR DINATES L0-3. TNTRoDUCED THE TNEKTIA MATRIX XZ 工 YZ 工 山 0vE×-- Z COORDINATE SYSTEM(Fx CoRIGW AT C oM) WH工 F WE HAVE月sEco0fR.ME(F2) xy-z′( SAME OR)TAT工sR∈HED FRoM THE FIRST THROUGH A GENERAL RotAt ion R2. (sEE 2-to) y REcALL THAT 21￥ 2 工 N FRAMEΔ H,=工 GLVEN H、,FDH R2. 2 认,=T2W 工 2 RrH 工 2-