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32
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Transcript of complex.gmu.educomplex.gmu.edu/ · 2017-12-05 · ',r/! ",,,,, ", xi \ Line of nodes : Figure:...

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Page 2: complex.gmu.educomplex.gmu.edu/ · 2017-12-05 · ',r/! ",,,,, ", xi \ Line of nodes : Figure: 11-15 : Size: 13p9 x 14p6 : Wadsworth ArtistlDate:eh : 3/13103 : Thornton/Marion : Revs:BJ

~ ---------------~ -

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xi Line of nodes

Figure 11-15 Size 13p9 x 14p6

Wadsworth ArtistlDateeh 313103 ThorntonMarion RevsBJ 403103 Classical Dynamics 5e 7973

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f =

ogtsltf ~r-f

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0 c)

()

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Page 4: complex.gmu.educomplex.gmu.edu/ · 2017-12-05 · ',r/! ",,,,, ", xi \ Line of nodes : Figure: 11-15 : Size: 13p9 x 14p6 : Wadsworth ArtistlDate:eh : 3/13103 : Thornton/Marion : Revs:BJ

t ~ - Crl 13) J-ll- ~l ~ fJ G4$~

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Page 17: complex.gmu.educomplex.gmu.edu/ · 2017-12-05 · ',r/! ",,,,, ", xi \ Line of nodes : Figure: 11-15 : Size: 13p9 x 14p6 : Wadsworth ArtistlDate:eh : 3/13103 : Thornton/Marion : Revs:BJ

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Page 18: complex.gmu.educomplex.gmu.edu/ · 2017-12-05 · ',r/! ",,,,, ", xi \ Line of nodes : Figure: 11-15 : Size: 13p9 x 14p6 : Wadsworth ArtistlDate:eh : 3/13103 : Thornton/Marion : Revs:BJ

frb tJT 112 ~ It kM It tAf~tul -Jc ~~-Igt tshy

o~ A cv-L -t-ll(f ~- I ~s I ~t middot oJ l Jl Jk

o~ t A cortl+ l laquot)e-f fI- fg bull (If cn-e- M ltiwoSk bel ~ )(3

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-if u-poundJr tk ~ Itr ~(~ ~ )(3

( ~v NiK fk ~~ltpoundl Cogt-SI-lt bullbull~ or - ttr~ f- ts eJ~c

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Rd = sin α

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W (bl3 IlJ rhrr~ wlt- ~ v

Jt~ruL~ ~ bL ~l ~

~~J= 4R

~ ~ ~lvk 0 -tt ~ 4I~ w ~r r I(L v-t1 ~t

tJH (l) hIt ~ WCZ u r~~f- J Jk

k p 11-1 1fJ~a Vt-N ~ ~ fk eo-

1 h-k 1 I Ik ~ IltfS

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W~ ~ ~ (O14 - 9~vgtf

~o $lvCi -p() CoS (-~s-l) ~ t)

Oo~(l-O) - rgt $

reg W - N j) c 0( ~ ~si)

~ 2 hl 0 ~~ 0( C t (ws-t)

Wl = JO~iVO( - ~ Si-

- l--lo

--

i

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-~ I c H ~(C ~trflJ ~ L c- _ ~1(S4 a

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i I i

( J _ r-0 u) U$ 0)

Il hgt1 l

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~ -1 Q - 1 I-J 1 ~ ----~

~ t cj) A~

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1 ~~l t 1 Ih As ( (fl~ ~ )

~~ I

l~ fllt S - chhcc-middotJJltgt( ~J

~~ 411 k-~$ J-k ~s t- -- ~~~ fllcry vuhr ~ Jt ~r~ ~~ j h fL ~

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ACoS ( $lt ns~~4 ASV (SLt ) o~~~

~

cjgt S e 0 A~ (9-11 ~ +4)

ACoS (n--l-t ) (654gt ~~ cgtA -+ eogt(f 1 S (st -t -t f)

e = A CoS (stt +~ -+ 4)

paso
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body

(j) e=-o

f= ~rt (c~~-A- syuJ)

e - D

reg 4gt A SlY- (-rrtJ I ~ amp0 C~+ ~ ( So s (1( tA ~

iA1 f ~ jt- -rfe UJi)

i I

C-l Q I

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Iv-lt - b IA-Jr- fI 1- fk

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wIl1gtt -10

IJ~ (-rz _r)(Z -rj)

h -

~l

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Page 19: complex.gmu.educomplex.gmu.edu/ · 2017-12-05 · ',r/! ",,,,, ", xi \ Line of nodes : Figure: 11-15 : Size: 13p9 x 14p6 : Wadsworth ArtistlDate:eh : 3/13103 : Thornton/Marion : Revs:BJ
paso
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1

-if u-poundJr tk ~ Itr ~(~ ~ )(3

( ~v NiK fk ~~ltpoundl Cogt-SI-lt bullbull~ or - ttr~ f- ts eJ~c

_ NoJ I

Rd = sin α

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W (bl3 IlJ rhrr~ wlt- ~ v

Jt~ruL~ ~ bL ~l ~

~~J= 4R

~ ~ ~lvk 0 -tt ~ 4I~ w ~r r I(L v-t1 ~t

tJH (l) hIt ~ WCZ u r~~f- J Jk

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W~ ~ ~ (O14 - 9~vgtf

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Oo~(l-O) - rgt $

reg W - N j) c 0( ~ ~si)

~ 2 hl 0 ~~ 0( C t (ws-t)

Wl = JO~iVO( - ~ Si-

- l--lo

--

i

~ Tl T l --= al ~ 0

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( J _ r-0 u) U$ 0)

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~~ I

l~ fllt S - chhcc-middotJJltgt( ~J

~~ 411 k-~$ J-k ~s t- -- ~~~ fllcry vuhr ~ Jt ~r~ ~~ j h fL ~

4gt 10 t1f shy

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ACoS ( $lt ns~~4 ASV (SLt ) o~~~

~

cjgt S e 0 A~ (9-11 ~ +4)

ACoS (n--l-t ) (654gt ~~ cgtA -+ eogt(f 1 S (st -t -t f)

e = A CoS (stt +~ -+ 4)

paso
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paso
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body

(j) e=-o

f= ~rt (c~~-A- syuJ)

e - D

reg 4gt A SlY- (-rrtJ I ~ amp0 C~+ ~ ( So s (1( tA ~

iA1 f ~ jt- -rfe UJi)

i I

C-l Q I

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ltgt~ ~ IIIpound~~ Ale cff~ ~

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CD )shy

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Iv-lt - b IA-Jr- fI 1- fk

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wIl1gtt -10

IJ~ (-rz _r)(Z -rj)

h -

~l

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I

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Page 20: complex.gmu.educomplex.gmu.edu/ · 2017-12-05 · ',r/! ",,,,, ", xi \ Line of nodes : Figure: 11-15 : Size: 13p9 x 14p6 : Wadsworth ArtistlDate:eh : 3/13103 : Thornton/Marion : Revs:BJ

-if u-poundJr tk ~ Itr ~(~ ~ )(3

( ~v NiK fk ~~ltpoundl Cogt-SI-lt bullbull~ or - ttr~ f- ts eJ~c

_ NoJ I

Rd = sin α

paso
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W (bl3 IlJ rhrr~ wlt- ~ v

Jt~ruL~ ~ bL ~l ~

~~J= 4R

~ ~ ~lvk 0 -tt ~ 4I~ w ~r r I(L v-t1 ~t

tJH (l) hIt ~ WCZ u r~~f- J Jk

k p 11-1 1fJ~a Vt-N ~ ~ fk eo-

1 h-k 1 I Ik ~ IltfS

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r) 4S ) s ~ -Ie 9 cor I

W~ ~ ~ (O14 - 9~vgtf

~o $lvCi -p() CoS (-~s-l) ~ t)

Oo~(l-O) - rgt $

reg W - N j) c 0( ~ ~si)

~ 2 hl 0 ~~ 0( C t (ws-t)

Wl = JO~iVO( - ~ Si-

- l--lo

--

i

~ Tl T l --= al ~ 0

L ~ I - -I --

-~ I c H ~(C ~trflJ ~ L c- _ ~1(S4 a

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( J _ r-0 u) U$ 0)

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~ ~ ~Ws ~dcmiddot71 $2~ 0 A(p~ (st-l ~ )

1 ~~l t 1 Ih As ( (fl~ ~ )

~~ I

l~ fllt S - chhcc-middotJJltgt( ~J

~~ 411 k-~$ J-k ~s t- -- ~~~ fllcry vuhr ~ Jt ~r~ ~~ j h fL ~

4gt 10 t1f shy

h) ~ se 4 -+ e (AgtS 4 A~( (sztd

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j)3 ~ ~ ~amp ~ t4 d--t Q t3-lgt

LO( c 4 ~ cpc1I( ~

ACoS ( $lt ns~~4 ASV (SLt ) o~~~

~

cjgt S e 0 A~ (9-11 ~ +4)

ACoS (n--l-t ) (654gt ~~ cgtA -+ eogt(f 1 S (st -t -t f)

e = A CoS (stt +~ -+ 4)

paso
Rectangle
paso
Typewritten Text
body

(j) e=-o

f= ~rt (c~~-A- syuJ)

e - D

reg 4gt A SlY- (-rrtJ I ~ amp0 C~+ ~ ( So s (1( tA ~

iA1 f ~ jt- -rfe UJi)

i I

C-l Q I

-r ~ sr IL I ~~ II JOv p+v~ (f-iIr IT~ ~k Jar raquo-~ j-J ~ u cc-S

ltgt~ ~ IIIpound~~ Ale cff~ ~

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CD )shy

~(r vJoe7

tJv -I-Lo( (y-ses

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t ~~ __Jc lhl it ~

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wIl1gtt -10

IJ~ (-rz _r)(Z -rj)

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I

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Page 21: complex.gmu.educomplex.gmu.edu/ · 2017-12-05 · ',r/! ",,,,, ", xi \ Line of nodes : Figure: 11-15 : Size: 13p9 x 14p6 : Wadsworth ArtistlDate:eh : 3/13103 : Thornton/Marion : Revs:BJ

W (bl3 IlJ rhrr~ wlt- ~ v

Jt~ruL~ ~ bL ~l ~

~~J= 4R

~ ~ ~lvk 0 -tt ~ 4I~ w ~r r I(L v-t1 ~t

tJH (l) hIt ~ WCZ u r~~f- J Jk

k p 11-1 1fJ~a Vt-N ~ ~ fk eo-

1 h-k 1 I Ik ~ IltfS

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r) 4S ) s ~ -Ie 9 cor I

W~ ~ ~ (O14 - 9~vgtf

~o $lvCi -p() CoS (-~s-l) ~ t)

Oo~(l-O) - rgt $

reg W - N j) c 0( ~ ~si)

~ 2 hl 0 ~~ 0( C t (ws-t)

Wl = JO~iVO( - ~ Si-

- l--lo

--

i

~ Tl T l --= al ~ 0

L ~ I - -I --

-~ I c H ~(C ~trflJ ~ L c- _ ~1(S4 a

G tu- t- rIo-lt (~- I- -Ifl ) 6 - I J shy

i I i

( J _ r-0 u) U$ 0)

Il hgt1 l

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1 ~~l t 1 Ih As ( (fl~ ~ )

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l~ fllt S - chhcc-middotJJltgt( ~J

~~ 411 k-~$ J-k ~s t- -- ~~~ fllcry vuhr ~ Jt ~r~ ~~ j h fL ~

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fl ~ ~ 5 9 CA If- - amp$4 ASI (Qu ~ i i

j)3 ~ ~ ~amp ~ t4 d--t Q t3-lgt

LO( c 4 ~ cpc1I( ~

ACoS ( $lt ns~~4 ASV (SLt ) o~~~

~

cjgt S e 0 A~ (9-11 ~ +4)

ACoS (n--l-t ) (654gt ~~ cgtA -+ eogt(f 1 S (st -t -t f)

e = A CoS (stt +~ -+ 4)

paso
Rectangle
paso
Typewritten Text
body

(j) e=-o

f= ~rt (c~~-A- syuJ)

e - D

reg 4gt A SlY- (-rrtJ I ~ amp0 C~+ ~ ( So s (1( tA ~

iA1 f ~ jt- -rfe UJi)

i I

C-l Q I

-r ~ sr IL I ~~ II JOv p+v~ (f-iIr IT~ ~k Jar raquo-~ j-J ~ u cc-S

ltgt~ ~ IIIpound~~ Ale cff~ ~

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CD )shy

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tJv -I-Lo( (y-ses

~ w~1 1M ~ II ~ -J-lc-~ e v (fl ~

~ ks C1laquo ~~ - lt- cent ~ raquo L J

_ -klt i ~o -hr~ ~cl-r -I+-e T--

t ~~ __Jc lhl it ~

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Iv-lt - b IA-Jr- fI 1- fk

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wIl1gtt -10

IJ~ (-rz _r)(Z -rj)

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Page 22: complex.gmu.educomplex.gmu.edu/ · 2017-12-05 · ',r/! ",,,,, ", xi \ Line of nodes : Figure: 11-15 : Size: 13p9 x 14p6 : Wadsworth ArtistlDate:eh : 3/13103 : Thornton/Marion : Revs:BJ

reg W - N j) c 0( ~ ~si)

~ 2 hl 0 ~~ 0( C t (ws-t)

Wl = JO~iVO( - ~ Si-

- l--lo

--

i

~ Tl T l --= al ~ 0

L ~ I - -I --

-~ I c H ~(C ~trflJ ~ L c- _ ~1(S4 a

G tu- t- rIo-lt (~- I- -Ifl ) 6 - I J shy

i I i

( J _ r-0 u) U$ 0)

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- D T~ frgtl shy

~ -1 Q - 1 I-J 1 ~ ----~

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~ ~ ~Ws ~dcmiddot71 $2~ 0 A(p~ (st-l ~ )

1 ~~l t 1 Ih As ( (fl~ ~ )

~~ I

l~ fllt S - chhcc-middotJJltgt( ~J

~~ 411 k-~$ J-k ~s t- -- ~~~ fllcry vuhr ~ Jt ~r~ ~~ j h fL ~

4gt 10 t1f shy

h) ~ se 4 -+ e (AgtS 4 A~( (sztd

fl ~ ~ 5 9 CA If- - amp$4 ASI (Qu ~ i i

j)3 ~ ~ ~amp ~ t4 d--t Q t3-lgt

LO( c 4 ~ cpc1I( ~

ACoS ( $lt ns~~4 ASV (SLt ) o~~~

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-h -~ st-r(1shy

~ kamptc

Fb 1gt11 ~ ~~~ltif 1 r~~n ~ (IV ~ ii-t ~ amp1 1 ~

I

Jv h) ~ w~

~2lI~ -Tl) W (1 2 -T3)(f -r) 1 ~$- 11 1= hJ t

~l (Tl -1~) ~ ( T-r3) (r~-13)kJ - IN 13 ~l

-+ ~

l- l~ t ) - T ) (T -r) gt0

cw +vr- ct~ W ()- ~kshy i 2 1 S ~~ c11e l

$fv~ ~-Ttly ~

t-I~ (1 - j) (r -)

u-l tttl hlL l ~ tshy

l-J

L t shyJ3 (Iz -fj)(T3 -11)

~ lt 0--s c )2

~l f~d ~ )( II 1l k

~~Llfl- t

Page 31: complex.gmu.educomplex.gmu.edu/ · 2017-12-05 · ',r/! ",,,,, ", xi \ Line of nodes : Figure: 11-15 : Size: 13p9 x 14p6 : Wadsworth ArtistlDate:eh : 3/13103 : Thornton/Marion : Revs:BJ

~2lI~ -Tl) W (1 2 -T3)(f -r) 1 ~$- 11 1= hJ t

~l (Tl -1~) ~ ( T-r3) (r~-13)kJ - IN 13 ~l

-+ ~

l- l~ t ) - T ) (T -r) gt0

cw +vr- ct~ W ()- ~kshy i 2 1 S ~~ c11e l

$fv~ ~-Ttly ~

t-I~ (1 - j) (r -)

u-l tttl hlL l ~ tshy

l-J

L t shyJ3 (Iz -fj)(T3 -11)

~ lt 0--s c )2

~l f~d ~ )( II 1l k

~~Llfl- t

Page 32: complex.gmu.educomplex.gmu.edu/ · 2017-12-05 · ',r/! ",,,,, ", xi \ Line of nodes : Figure: 11-15 : Size: 13p9 x 14p6 : Wadsworth ArtistlDate:eh : 3/13103 : Thornton/Marion : Revs:BJ

L t shyJ3 (Iz -fj)(T3 -11)

~ lt 0--s c )2

~l f~d ~ )( II 1l k

~~Llfl- t