hL a ~ r ~ @ o n d $i~@,"as g:ig@@ i > ~ B l % g j z @ & &>c~J~z# d&&*

fag s f $22 %Era at3&% t,lS$y af ;:i,.;~:J,i~o,;$t3;*~~ ~ ~ 2 2 baaad h~Bf *

of U L ~ ~ u t o g ; Q. ,c~ePs~o \6 d n c ~ ~ 3 % ~ ~ ~ ~ o ~ , ~ ~ i o i ; d v i L % ~ :la@

an(;%@ used b;. l i ~ck cn4 tQzt~-.tXey, nkkicll i s igoasured

$ ~ m L ~ B B :r%e$~s'ie , ~ a , , ~ ~ z $0 tba P Q % O ~ =%@* Th@

a2:loe only @%%fez 6t8rg3q; %%At8233 a f Zhe %o%or :,D%&@~

F* aoro&p&a&o Eerce, pax unit Lewth of b2@4:8o a@*-

$m ~ ~ @ ~ @ @ & $0 ~ ~ a i f a % ~ w $ w;r%ad v~s?X@@ & %Y #

fk-z + A% 1 &@P%%@R%&~ 71"@&@0%%g ~f @X@B@%& @$~&$$3$%8a&6~2&~

P a$z &@an&$; i n ck~a{@ubfa fast,

sostlcal jlana during wllrlP raooiXlalione; %%@a, i f b +- * f 8 aea8ar@& aijw&sda,

(w +Awl = VI + rb - i f

%%e @@%@anant a$? raZae%%g ;>#agalBaZ 8~ bJac\@ a h @ %@ of

#@@a%& s ~ d e 2 , %"%a @ i ~ & f l 8@&38~$ $%,

Xn %~2%%6%~Qw2 %2%@ bas&@ 3aiw8 h~~ga~a%a%$ &a$ burl~g;

&%&%I ae@%BXaC%@a@ dho x%a%a bs& o i Wze i%#%$oo~>%az L%iP$@,

~4 haa@a %as 98 ~L$LP@& wag%@@, Xf d %@ $Is@

%ha% Wte @Xm@a& a:&@@ vrSWa tSia t~%n@@ l$n@, s @ & # g p ~ &

%ha ;.%a@ s f %@F@ %kg%* %2'k:@a Bagtag g$da%Z gl~@$*$%&%isa

a r ~f ciinli r ~ a n n t i t i o n , &,a. i u d\1,g2, , g8; a

G,,, -Q . i i2 n t)]

%%@a@ ia%rdctuea affoe&%sa Pomeeu

Bs %@a & ai@e$-&f&g sy@$w of %brggwh fhs %&&@

btma @lo% &pa ,$m~~Qls% md $a &he bfg%ce f in@,

tha t ~obaiin;: ate%&& ly r i q g i w u l a r ~ ~ & ~ ~ & t ~ ~ r a@

tk%S B l r d e ssovo~ ow8y i n a g l m a %21$%$ %B asit:~$%%oaary ?~I*A

~ 4 @ g a @ $ %B 8~8%- &T~B@ R@$B%$~@ $9 QP$$ n a ~ ~ &ya%@a,

% , WOB W@ qyebf Q,

i a t;~e c to~~z~v~rc r t l v e a o c l t of %>&@ rator hub, und hog%@@

Eimvxm(u'd a@a~celc'~ab%on af %be r ~ b A @ &s 2 , . I

AT i s t j ~ ~ ~tg t%er~( i ~ a a i a vcl~peiCr , %hen ho = (& , c o e n t - j r , s fan%

Ab = 6 I @@ant - j;, stant) -n@, e inf i t +;ii, coen*

wf&% be @i$o~%i~@ s~o@l@r&$SaosaX Euraoa &gs $a %ha@@

3 % ~ cgzii:$@%c ' ~ A Z & Q aa$%an z;.c~ua$$an PB

kt= (T + A T ) * r - m & 2

prQt3s 6 - mnr"sfn\( coo 6 + ~fiA+rsin -t nrtA<rroos

8 I 6 il ds

P ~ G ~ I C ~ ? O ~ C , w: A x c ~ : ~ v e fc r gin 6 , mad ul8@

$ t a t eos 6 = I k !iuvrcfvar, il, nil1 a f : , j l i f ; i 2ile folAaxdliy die*

%~h@?or& 75, IQ , :%r% functions ind@3ctad;tz~t Clms. B k i a **I

I i \ #'? ~5 (~gf -2?&) G aon ant+% L. (ES;- + 034i) otu 1

$38 L ~ F ~ Q F 5p3 , but tks scoond is ~ u i t i : i a~ge . jimi?var,

%%$a l a ~ . $ a z ~ i @ aXwtwa faux14 SB a ikke&sg uf o i l k s oz*

der $ 1 ~ n d a k a ou~%leo uc t u uce %pitti ap;~goxiaatioa

:*@%&@&, for \ x \ l o a FdnaLton vf *tiie di@turblw volooi-

422 $n k I +?

3, . ace.. .ere can negleot

sot? =

In atll ursual sotosrs =is et-aad~ vazue of the oonini; @e

I n about 10@ and l%onae the vaXue of %PA@ fwtor foe@ '60- 2 )

P$@ qi@r$ ma&%& i x ~ & @ @ & ~ ZX@B@@ %he $I%&@@ ? ig, t e r n @ @ w ~ Y

b I

Ese tern8 wolofw , s, , are not vsrl*>&&@, a Dh@ soSutf oa &a o0 %&Q~ar B L i l e r ~ x % $ f o a l

* *

x~ \ + (%A- x.- e+;vIb + ~ ~ d a o ~ ~ f ~ ~ = - I 0,

L * rb n

bat

-+ a , r [LB, coo n% -nP, 2 1 . infi t +p'j; - \ sin fit +n~Ji, @a&*) i i.

(@ +&Iv.Z)'- -+ z k, s i n f i t @fireL- n (C,c ~2~)) co~fit doc

%ha& aEi %hose t e m ~ $hat ~ s n t a i n Yf

t a Lhe first LIBY~@%

P ~ r s avL~axbsnl L3at the ~ o n S n g angle ~ h o u l d be re8uced as

IZ; niEL be F ~ Q % % C B ~ that tha torque aF3ouf tho r o t a 2 We

tke ~@r%ical an& rotaQatur_;ir not ion E s r ssae of the sir22~1@

Q~S,BFB o f ~ ~ B ~ % Q Q $ $ B T B , tPioug1~ r10l %a t h e caee uf a aheXico~~**

o r v$%%h % ~ o roGo$a 02% t ~ o gc~ralfeX ~ z a w sota%Lz~g f t r Q ~ J ~ Q B ~ % B

+AYI~.-+ *a k[[(:;i%+~r nt- a C , - f i r c + en'$ (r,;, + r:;, # c,-

i X

+* E { F!'i, J'A 2, 1

[@ab+ ng b r ~ ) ) ~ Q G ~ L - @a@'- RT

[& +A$]@ .% Pa k I @#c'-nP P&+R)) CU

f v " , c @ f ~ ~ - n r ( G ~ + d a ) ) - 8 -'I a@.

t?@ ~ia";le%E FHad %&'-led k i a ~ ~ %?LB B ~ E L Q v a d ~ a s b'u% L L ~ B i ; ~ $ 6;da3Q1* I

i%c 0l4:n ,~LE tho@@ dile tit , unless ax+ .oof

f i gs% i rdcr ka '6. sza sf siga, %%

v%XX Ba aiotbao$ aw% %ha tor:iiie &w8. %ihzu@% W8 igl&o$@11a*

an t o f E C ~ B t i X % *

"$:f~%s f@ 80% dxao%Lot;aB&e, ga314 aa$ nBooasax &a SXQ o g d ~ g af

&@auTsay ne@&ad; %r-e~@ i@, I;nazaayaz41., ;a~oQieg s ~ u x a e of fa-

aaeurnsy, ?B so Far, nagl%;go%ed %%@ @1$@0t 0$ a38

&o ve~&$aakPb~ ~VBE~~PS: % ~ i % ~ a %IIB $%$a i~ eia$sa, a*$.& so

weu$r&l%~a &%I% ~ i d w ? % a ~ a baadin$ a t ~ s s a e e ua V&I@ b8ad@@t $f

*&:%a i u l % %:rear;~ $8 1~0Olk"c@d w&%, L",~@FB ~ ~ $ 1 2 BO fauk2$ $era@

in (xi) J the%@ tan:^^ a r e o;nsll, ifad i n mqj canc are

soriled i n ,~sac%ioc by t:l. *re~t . iaol* higaes, I% tntlroforo

saa9ias asslsss $a ax%erg& %%iia ;>ark 09 a~algaf t o

g3ga &if fekba$ir;l$~ e:r.ip;~"~aaf sns f o r aoa~dAnat@@ @;a%

%&ass fn Vao aeaoa& b ~ a ~ k a t a twa due %o %in@ blg@s&~C $&@a@%*

&%v~%oad Ln %of&&%ibzei t1a.a b h u d ~ x% w%EZ Bs uuLL@cd

%Iza% nEl $kam%s bas $a &Bs@ osntri;~otaL a~calsrs%ion

a~~xaalEcb au$,

Wkau&:ii $% Zew @@era %k1&t no ~~!ze&$ a@caraag ha@ bs@&

ob%a&t8ab da %%I@ rczsuX$s of "$*$a a@t?&oa, %t vf;kJ, xes%P%zeb

.'J $8

&a@% aP tbo %i.g$ P O F ~ B B Z k i , k ~ at:iaP9 1 e o a ~ ~ X ~ Z I * J P ~ @te&dJr

($"I $a m%e of t f 2$ or bta&a ac9ns a $ c due

@I@ $tP% o f &fie b2hcdwo ascxne mcfn; ;3x~a In g+sa&$sn (4

m?.? due t o %la KLPF knc~%%cf %cnaa, A=,,@ %@F@O ~ac$i@n (9 f ,

&u@ %a ~~991g;r~~atrl~e insgtg& t@k?2a, r,k@ neg+r&a- &$P @afggL$~~&fm*r

fb ) am@ w 3*aa%, bu% due Lo %he @dfE$~&x&"~

( a ) %a hhssisos%aP aa%"&;f~g,

due t o berrtical not ion ,

(8) %~aen%s due t o %&the hinges not being coinaideat with

(a) 2honent duo t o ro t a t i on of bLade cone axis,

fb) bfado inertia aon@~&t&~ due t o Q3c *dihciirdf

f: = - k%"q %06*

I r,', T, m& the f urceii ac~rulw froa t31m are all anal&,