1l rl I In -l.r genrral ,i orc relqteå 1r L* Ly Le ri ,i I ri . rt i 't Ol' wrtl -t! t - fl,e ve,ilocs È qnå a\ h, Iìntnch¡ q s Irr Iy* tx htr * I-*v wy + I¡o6. W* + fr, -t t IyeW¿ Jzfhl + Xr¿h/. t{¡ìrx ZHy 3 âZ G wr + 3 L; = ¡!j¡¡uri ìn l4ctcix Êr- [t,l fr., r*, r,J ltrl = lr)' "v rr" f lr '1 l 'i i ri LL"J Lx." J.r r'aJ tS -'\ H L = I.Lr) - Wh"te I ts *he Ïn.;Ìiq Jbnsoc ,, Tor ròt*tions qbo.tï Somg !.hi1 C C*y or noy rul bc Co Ì1) ' , iA '1 a body wtth mcrlãs denar'fY Pci), ohoke _dF oflglq ' Ò {hen parttøular ". cb'nponsrrts ùF g qre: Ìo, = J¿l¡ pc!(yaz) !y e Jj'rpci) (2"+! Jr = S¿'Ê pcñ) (r"*! Iy" =t), = - Jd'Fpcf) yz For q åtscr¿te søt' df pr^{r S + 2 urrìfbrrn dens f4= Pot tvlo^ad' f ].e.Jr^ dF c'\ C.rbe. .bo.îl Ca(her, I"x = SJSa3i p(y"n! p $"J"ay S"¿"y" = àpo' p (ll¿x)(9loyfl(Jl¿") = po (å o')q f Sl¿ vsln\¿yt = åp"' L eâfl q 3,o =¿1-=3:** = â p"u &y =-$SalF fxy = .- fslr.çig*v)(sa) P Jry = -t po' -- elt¡qqt :Ï7, th = lq, 2/g -tíq1Mq* -V, I -Vn VUq-yqzls I ) : Riå Wrîflen t/t*r^î in qyì qrbitrafy or fnurqe â t ¡ ï^= [u 'lt"' ç [r'* arcrdinal¿ 2 t .[" J*y Jr. ïyy Jy. T,Y J¿z I' ), llq¡ 6 ir,Je p^4".1 conponeals ì ,, lencførl s passlble {" fi"J ì3 qlwqy fx"À 'w.r.{. *he b"4y, So¿tn f di ogorrøl | ¡ ;;lol ï=lr,o 2L -f Lo o ^"J Ar,A",\ diogot*rlíze rne*hoås ! I z 3 qrE prlncìprl turrnl5, wi'ttr us,^^l r.^tril No* tf eypcsss ñ in *erg5, of 2 ê,, ê",ê"1 (*he pclndple qxts) we frnd we ¡-L 2,',â + 2r- *.â [= +2g,¡.â In portt,lhr, m the ro*dtio", ls qboot q prt;cìp al oìx I S ãooh J+,^'t ..^ t! -ih"t, Ë U,i ê¡ whrrl i = t, z, 0ß 3 -\ L =2;Ë Êr rotcflo", qbod* cr "f ln cipql oxìs {he dtrec,'tion ôf i *d ù cf Ìn.i,le. Thls ls ô'le wqy. +o ide"trf) /drút"e 'q prlneìp^l o\x¡s d T" ?eneral a, #2"t 23 qnd. *he cholce ùF tê,, ôr,á.1 is uvrio,ue. ,,rf L r.o-er{g qrs ejr.^l 2, = 2z / 2" -\ e; *hen ,, qncl ê. crrh'b" ony 5ù ^ iâC dìreetìons n,rtuoll7 orlh'¡*ú\ +o e; , onol !rnch o{htr s*.. A ,/ä0. ì>Â orÃf '1 i .,le ^ e2 ri r1 c^, qrls df s7r.r.o{r7 ìS EF3 'ilt*r, P. A. + Z or}to¡or".l rnona'ù org 2ê,, t,, âJ t ''lc. 'i 4 .: Q ^¡ l I rl I : I Jt :jKot"lis" ¿f Rìåee.l BoJles. 't i i rl ,lKinøtlc gneey i Stn ce l- e ?,dr à; + 1zwz éz +1gw, ã" ,i qn¿ t= ,,4 +tr;24 +wr{ l ì rt i . tt 'i I I 'l l J= å ô.È J = å t 2,*," + 7.¿d.. + âr,^1.) I l rt I I foc cr rid,ge.,\ bo.tr7 wrth 2,,4r,a" : If rúe cqn expfess (ilr.'se+' tù., td3 : in *erns oF q 'so ìfoìble of enerc^lizeå coocåt"ates w¿ qîe .-rer 4y *o wrtle clow n -The L"! rc^n$øüt S.;tofio" aF Kîâg!d Beoli¿s, Erler A'gles We hqve shown +hdl íf a b"dv has pql momeRTs Í7, ,4r,27J th,í" the k¡net;" energ) of r;t"tio'n t"kes -the simple!rt pcincì J= àça,,¡,"+ 1rwï 1?rw" r,uhcre ô= d,â * ht¿å.*,¡rê. on¿ lê,,, #.., whi¿h åJ arre - {fie pcincip"l qre fixe"l 'l% +he boåy ¡-ty 4 ox$sr r¡td¡e, T" wrÌte down *he K E f"',d 't{t¡s ü. Lgtonglô ìn qn ine,fti.¡l ff.rrne we ros-t exofigss suìtahle genero\lìz¿clt ro'or¿inalrs Ìn ^.) whtoh dìc¿¿flan +hÊ body *hot ensode t t^,, , d", is ocìerteâ P lsco ss .' Vhqt qre suì*",ble qenerutizeol coordlnofes + ¿han^rltri. *he orle¡¡h¡lion of q body with r¿s p"ot {b c4 fxed frat're? t{o* Manyl' .&tition of Ri,Åe"¿ the S irr fui.q !.rin cî *he body' hr.fÌ+". pol qxes qre fìxe.l we neeo\ only døsccìbe. l) -[he orietitian"ìce,fìan of^ ony one dF ' 2ê, ,t hr.nt q -r=,4ì fXu¿ frorne, ' *r.*î ie@ no^be6. eaglcs df c^ ã¡ohcrl r",l .oo tti*úg sysler.n. ^aI Z) r The oclølo*ío', df *h" o*h.r *wo ayes in th" plone porprndra¡tnr +o +l.e *hicå. -1 e? da a Rt.rr.s ,,,, 1 -r -) $r ) E y1( more norrrLer ob,rrs {ol^[ o,Q,t E;t"tio" of Riåqe,à. .äC¡:s. *ì'Jä *"f;y å;l]n llÍ **l"',,f1 * lo rnwd q ciåq¿4 bdv +" qn or6Érurv.. octen*aìTioq rt",.rÏa w,th 'tq,4,4J A. not rt" bv'tïqrr an ^le ô ,Í, tJ" ^ 1 *'õ' +r = L7,3, B *he Ê oxls 2â,n, ôl , Èì c^bo.rt ¡¡2 ^l qvtqle e abq,¡t +he (ô,', I ê,o, â"í, ftl B. Rotote bv l.^ on Jì % i3 ,a f; åi' Ret"tion of Rìd!ed &d'iet C. K"tdte by oíì J\ ?tt, 1, -7 !¿ 5ince we Know -the dìre.tiorr df \rúe cqh irnnedl*1{y \¡rfffe dow n q^g.,lar velo*ry ¡-S W= W= oß,, tlo*e: t7' ivrl qK + fo .(^ ê !r' ,\ e gg (- ôsìne) â' * Slnce ô= --\ [rJâ + - É¡ ù R= Cos er¡r,;lt roicilion the --¡ W, -î l' lt^ a Ver ^ '- 5ìnê !,t "âr'+ (ü. ô cÆs")å vúe eil?rer corh wriig Q,t cnå er' i¡ ferts df é, ci'.ot !r,, Af â¡.42 (ttÊ s7r,nøtrtc cose) *tren ô,' o,,,â ár, orc çcrfc¿t" goodr pltncipal qxts qhd\ R#tio", ofl K¡åed BoJ!f In +lle sf"ofctc cnse ' -\ ' ¿\- 2,r o¡ s¡¡ e [-p6he) d,,* õ ei Angohr I'tæil,* t=Iù K¡n¿tk 1z + 7s ¡ o n + (e+$coso]0" È = (-2, [sine)â,' + ?,# {'*?'CV-E*0{ = 1$l ?rf $+ô^t)>ô=$ffi tr Lz = 2, Qsin"O + IocoS$ / Encr"Y J= *q,Côir*e +å")+ åzs (.i,* Qøuf We qr¿ nôw ln q poshlro^ to t wrlte down Jtr$, L"grornX{Hvl i ,R"*"1ì0" ofl Riånø &årq The Syr,*etrr" Spt^nt^3lp oe'**lly T l- = E U("r 0, t!) \r.-..-.-Za.-ra--¿ h{r*tic.l i. tctnc For q top: -> poertrm ! à2, (Q"sinls + #)+ e"tdanl $e) = 6f i2rC'i,*ô-rri- =Bi =_ Ù qgtion: ?LP+= ãu- " d rtoes lbRcoso * ta L.CV* + Mg F+ c*tr¿ = MgRcosö 2,A = 2,Ëstrro coso Ö.î,-+íærl of ã,lr *nAt s R' "*")$tinO einê aoo 2, "sìnze + 2{9+ !cosê)core ca.st*it = Q aa 2, (Q + ! -s ê) =_co',sL,t ÉLg RS;lì0" q[ Riåg'â Boå'q 5teody Pce..sslovr Too R"{c¡t¿s c.bo.lt' z Dle c¿tlør dF rrÈfh ê fixed. ^aI Sìrt ce {hc",, Sln¿e 0 - ô=-lt = r-.t'r-3 Lz - L3CoSe d strt"o cons'fot¡f 6c O co*e1qtíl (.P+ Qcoso) is r*t.rrJ ^,, r{l + r[ cose =, t^13 = ,onç[";[ rt The" *he e e1*;ho"t becornes O = 2, !i = ?, Q".ìn ó coeo -ArC9*Qcosg ôtno +t'\Ra,ø =jI Fur tr5 larSel 2rÍco6o- ZswrJt + lAgR =o qå J¿rxsc = #" -fl¡'¡tt :