LECTURE II KINEMATIcs oF Rigid &o DIEs INERTIA MATRIx AND OY ADIC CALCULATION、千 CALCULATION PRINCIPAL AXES AND ROTATIONS
RIGI0 BoDY DYNAMICS ·T叭ocAP0 NENTS千0RtG1D80 y MoTIo 千 RANSLAT(0NAL F= M R升 TIONAL D ECOU PLE PRO vIED 工ND0FRTT0A AA0A工Nb0FTRA5L|N CAN TREAT THE CoM PLEX MOTIoN of A o POINT MASS MOVING As THE CENTER oF MAss 2 B004 ROTATION ABOVT THE CENTER OF MASS ALREA0ysrv00cASE⑦工A0EPTM →C小50RC5E②F0 GENERAL 30M0T10A
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