~M Leif\Ster LA. o~ ~\o-~aw CPo.~ SlApport- : J\J\AAAeLJ ~da.~0Y\") I C.recl~ts : Sc..hClV)\.(-e lJ 'I:bk" .) . - - R.ob:A. J &-ezJ 0
-- --- - - - --- - - - - - - PLAN O. Mobl~inv~CM fr:rr CQ,{-e~es ~ (VeA )( : lA --) S~t-..I At\Swer \. 'l. \A.e&'t; crY) : I ~ x I ?- w~ is d.eterMihed b~ (. 'X-I)CJ.EA ,. x Uy Z I=-' XI +, 2.1- IY I C0.) ( E .~. . }(. 2:. . If S ) IS/~1 := lsl/~, ;s O\..fi-ee. G.-std J 2. Eu..1e- C.~CAC..{.erisJic ~ ,eoJ:eyoftS
@ . BI ( Le,~ lA ~ ex Hn;1R. ~~... ~ . ECI-) [:efns is t-he CQ. -~~~ {fw.d:ioo ~i\JCcJbIA~ wi~ M~ltipl\~CN) (e. tp) lo.J c.) = L. $(0.." b) fJ(bJ c.) b (9J ".~ f:(/A)J a..,c~A'\ ~d. ~ d as. ~[-f: . [:)iven ~ . ~ E £ CA) ~ c..., b) = is r P\~)o) I . lA ~ MObi~ ;~i<M it. 5-' eki~j \,Je wri~ ~:: ~ -\ ( ~e M obi\AS ~c;Y)) So \fa" c." ~ 5~ lo)j'(I,,,c.) cf(;..,c:) = ~ /(,., b)~(b.,c) . :: ~_~-Leaw<.) (~ 2.
XClMp \-es . lA::; (1 ~:l~~)" ~ 2..) : r~ (6 ~') et4 is H~ 3 = [fvtlJ r: ~d. M: ~M' ~ . Lck ~ be ~ w\~ '[[)N 1.,) - - - J N dbjed:s: ~e -Hl\ik .crn1;~ ~ ord.-er- rreserri~ i"jedifNlS. ~ Jeo.,b) = C.:.) (~). ~ I fA&.~Io) ... (-I)~ . Posd- (?LT., I ) : ~ { 1 i~ G.r\o 3~)O) 0 ~e-wiS.e. I ~ c..lo5siec:J Mobi ~ = J f'('o/e..) jJ-(p.,o) i~ 0./'0 L 0 ot:MetiMse . 3
Proper-ties . Anj is skeletal .... wt~. Mob;~ ir"/EnicM CtA-t bA:t- no~ e"~ skelefzJ. co.J- ~ M. ;nveJ3iO'V) . There -h:rr ~ ~ are foovtu.b.s vAlid. se\f~ ~~ cC- sk~Le:b..J ~: - pos~ (r<~): j-tlo.Jb"):: ~ (-I)" }{~I\S ~=a..<--- <~~b1} - (43 wi& t10 YkSY)-&-i'rioJ. ,deNJ~ts - c:o.l3 wi ~ a.~ e.pi- M(SY)O ~~t:;rt s~ 4
it- ~oJ ~? is Wha,{:;- One ~we.r; fm&;~ ~ rep~W;~ ~~ ~ 0\.. SUIV' '*- re.p-esen~es. Mo bi ~ I~ lA has Propn ;I")versi CIY\ O/\J. : )( ': L. r;.. H\~.I-) lA ~ Se:J:- ~ a.. erA eN) ~en rQ.= ~JXb\r(b~~). ~ f (~~l(c;,b-))rOo,o..) fhxk: RHS (~S(C,lb)i(b,lo.) : ~r.: re. o( c~ 0..) :: ~ C' = r" . 0 $"
. ~ -; s W ~at fvt-? - 500cl , 0 ne. o.i\Swer : frlb 14!n1S . CoU-~~ E.~- ~ Le*- d.,.::: no. o~ ~er~ '*- n I~ ~~). C~Lt~CIY\J" w,~ (10 HK~ Rx Ne "" o.t\c:l ~~id.~ .,~ S : 1DN n I ~ Sn . --men ~ L. c:l~ 1DN(~",n) St\ "" So dn:: ~ ISnt I r(Pa.l~) :: L, m~. (-I)n-M(~) O'M''1 L.J... - - n ' ( '..! ... -L ) - . ,- 1!-r2' ". . . . b
). THE c.AR-DfNALIT"f OF A CDLIfv1/ ~i' ~ Q.eca [(: we .. re -h> 3&1erz:J:, 2I2- -i:t1e ~: folLDw\'~ i~ X ~Xt.. ) ~X 3 ~ I XJ , = I ~ I -4- lx31 - (XI \ - t X:t +)( 7
. 'vJei~hii~ Le~ lA '" b2. -H(\il£ C'Q,t-eg~. Defn: A we;~hts" on is lA ~ .fw.ac&,y, ~ SLI.<:.M ~ 1<.8: ob lA ~ JG:...b) k":: 1. Q '010 :z.. ) . ( EB.: , ~ k I: -'J ,,2.~1c. UJ1 i tt ue weiBh&~: i: I. '" hCAS ~3 K:: llMI . . MonOi6 M has l.(,ni~ue we;8M-;~: Prorer6es: MobilAS ;f\vers;OV) ~ . le lA ~ if- ~ ~ ~ lA. = i: rf.o., b) . \A.n\ tttAL wei~hf:)"8 J OJ ,) or > I we;6~f.;"8. . lA ~~ heAve . I~ lA~ rE ~> lE d.oes. ~ h\ ~ tA wei8~~ 11
~fnes:s Compnerrt-w ise. .; Set- is X:/A coyV)poneJ11:wiSe~ A ~dvr if ELk (x) noS t-he follow,~ ct~raM-Cowf(.eOCIV} r9P~~: . . . . . . . , ... , .. J, ..' ' .:J .~/. . 11 . . X is c& ~ ~ 0\. su.fV' [ E~ (,t.i "0..~f: fo; ~ . -~X ] ~lf~. E.~. : lA C/w f{Q.tness m~: x ) )Y" 2. (J..£. x" Me.. it'jtct1 v'~ ~3 man~& M ~ is -H--e.e ~2 I~'-\ XIA & Xv o..re ;tject)ve .; \I irva{X(,I.) n iM(X,,) ~ ~ 9
Re-sui t- ThM: Suppose. tho-.t- lA is CCu.t~-~~ and. ~d.M,'~ Ol wei8~~ 1<.'. Let- X: Ht ~ 1=i'~Se;t- -n,e/) be CCtv\ pO'f}~W .,se ~. '~l. I !AM xl:. ...@ ~'k~ ~ /fA. P(""Oc~; Bj CA.~d.o.nl ~J )( is (A S~ rCfre~bks. ~ the c~ oC ~ o~ )( s~s~ i~ @ CALL r€fres&\tzJol. ... CQ1ia; 115 ... is cltsecl W1d..-er SUM.S. 0 E.:).: - MO+;,,~~ ~.e; ~eKl)(a+JC,X31:1Xs.'+'x~J-IX.' S;M;l~ - 'jfb1.era1 i(\d.tA.S'<In - ex~;CJY') ~ ~ . I siN =- ISI/fMf . 'F1-e.e. M~d. ~cl-\~ °. 1 1o
- 2. Eu Cf.{An.ACT£1:- r ST (C Le}- lA be ~ Roi~ co.bz3~' A co~'&~hB~ Ot1 lA is lA Wt2-ig~~~ /Acrf. 0\') O\f\ A J wei~h.f.;~ )f 1<..8 ;S leMMCA: ~8 ~Q..Ccwe\8~~ Ot'\d 0\. Z~. 0 ~ 2:~o.: 0. Cl J'v1c;loi IJ.S ;n,,€~iCW\.I E.~.: IC. lA ho.s . . . jA= . . --- . 1<Cl.. 1<." I ~lA\ 1<.. '" De~; lA h~ EtA.\.er cMwod-erisac. iC it- O\dMtts ec:wei8kk~. --;-Vt~ "'- wet8~~ OV\J.. CA ~[/A) = ~~o.: ~~ t~ tfA A +w- ~ ~~~kH"3 1<.8 and. cowe.!5~':!1 1<... 11
u- Xo.~ p l.e.s .,~ lA is cJ.\screte ~ {{A) I cr10 141. == . le. lA ~r& ~ ()OY)-rn viol' eI'\d.os no 1( C&/A) = t(lA) ~ w~e 'IS/A:: INIAl J4 . dr is ~SSi~i~ . Jf- 8~h d4rec.l:eJ ~ is 0. c.ircu.it-~ -t-Mcrt == lG-ol-I&-,\ ?((~(K) where F Gr is +=re.e CA-t CM Gc-. . CRot?A.) If lA is ~ p~s.et ~ t (lA) -:: Z 0.0 < .. - - < ~ 11 . I { v~t\s (-I) 1\ n SiMi\o.r -forMt.Alos CO~ o~ ~ et. ca..t-. . 1 ~ M ~ ~(M):: ';i~f \s . CA MOnO')cJ. . ~-t::o~ ~r-ees . wi~ For ~tJ.roidsl 12
f-i,~ {(J4) ~ /( (1K ) /A~(g ~C2r\ ~(;\)=.X.(~) ~(/A):: 1 0 1 ~ -,~ lA ho.s 0\ r/f ~ - ~ (lAat') = ~ (it) ~ (ITt4:) = TT~(J4:) ::: ~ ~(/A:'\ . 'C (~I\:) . F ibra-ti CM fzrr MUl.o. ~ a: )(:/A :> ~ CAn4 1<- ~ wei8~1'\3 CJY\ It tit., is ~(~(hGx)) =. {:'ko.t(~). 13
ur~.er €><~f''' p}...es ~ M . Lek X: M~ $e:e- be o.n ~c:::;l-;01 I\I1~J CA. Wri~ eLk lx.) = s//JVt. -"'eI1 S . aY') 0\. sc1:- ~ lsll~) Isi /IML == . R~- ~ Wlf"e Si: ~: ho.v-e. CornM ., f~1 {f:ri~IA~ ~ihrtJ~1 jt ~d"l 1 - ~1L {tVI~.1 fz>lcLs ~ s~(Aare Tk5 Ut.ecsrj: h~\Ie CofflM MP 1 1 =:> l co.~oviE!S {tnoo~\A~~ orb;fblch . l~ ~ttl £ arlo\~Y.s 1 J<Q '" . Eth ( $'-' /' t $/': . ~ cf:>, S-c: ~1. )- - . ;I.-) - - .~. ~ -.. X ~ - '(i$"') ;:. ~(f}+~{II) -'K/f;"-o) So JX:a"l= '-t(...r. ': 2 -1((1:"'-') 14-
CoY1c.lus.iCSY1 ThiS f-\1.e r;8hr is ~fA,kt- c.k~'~c- k CDi:e-rt'S w~ J.eK~). Lo..t- Le03:- .I re rmp~ W\i ~ oC ~ € 1A1.er FinJ. a. ~ &c,h,.r1\A-el. 0... (.,~~~~ist\C. c£. ~~ovies) b-
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