Goldstein solution chapter 8 (2, 20,26,35)

AbhishekSrivastava122 13,110 views 27 slides Jan 11, 2015
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About This Presentation

Goldstein solution chapter 8 (2, 20,26,35)


Slide Content

Sohn 8.2

Trans or me 0) Lagrange 2 afin en dy
he AF (aye _ 3
bee re A O

pro war proved But Dea Lpargean des var
e ale of mol Ceom)
Leb ur apply da Same Jomformaliiz À Canario
moments. E Hamilbaiis . ww cn? ur”

we know pb

” Be

. q)

24): 2 =)

Ceerl44))

mo dr Hamibionar

Her) = aR -L(19,+)

me Parera

Way) = UP)

\ 1): 4. 2£
y wn) AE

p, + A Lou

- 1'(94)

- pr

pro

wear) = Al 4,

au? & rn

wep) 2

pe Ag

-1 72€
PP... DE

Ha - 27
Ob

ES x BE

ae

xx
T

fom

y

L 2% _af

D at

—®

wns Ba Hans formed Marilyn Eguatee are

g, - 20! — ® :
Zr
| 2
Loan — ©
4 E 4;

4 a an
ow ty ol
joe he OPI

A ©) ue EX tas

choo De 4,
ab

. F
aM. 2 pri, - UD
en Spe 0

ens
no... a
a gt
1 DÉ
oz 4 ar
À ay. xa? nasal
ig a,
yr st y >,

n edlueı, F>
jou wae chute. 2 Pe U CAC

M ovgindl Som: je:

sk hs 2

Pr. Zu, E
pr Fi ES (ha ©)

IS
2 pr @)
fe © bar
a (2h) = -
b r# (2) e (e -2£)
: =
s+ HE 2 + 20
Sel, a %)
> y+ ZF A
wilde) * Be
el: ee
24

>) be = - 2H
OU

Mi ghw dut nur Hamil ntion reia ts
old Samt Hamil nian.

Solution BLO

eRe

sing + DSinO
sep} + (Aas 6 )

ai
Yap + J ue)
ECC Sinp)P + (Aso 6)

ne

pep ) .
¿yo . eat
¿ y ml la cg hr 106) + (asing À pass)
qn] ip cian re tt o
+ os Tg weite sal sing sind À 6 Î
unfair
A bobbie £099

yo mg) * mg (amp +108) \

now de Lhe Eon ithe ae
à am luniform So Pr rs w ‘a ae

v rer 6
m) ee EP OY + alu é lo (6-08) ]

T

y

se
bo ye omg jamet

we dh pete À

188]

mi Se mgt re

N
ue

Solitim 80 (lont-—) &

2, re 0

mid = ly wadwted eed) -

D iQ DE Île - made Ge" we

So
> "só jte" - pate ole}
> Ind“ era veto 000-4)
ÓN
IR
> y. le puvetesŸ" zu
ve ¿podio y oda
ur] Be)
6- 2 = me”
6
1-6)
a ite ae ff meen \
a |
7

PH
0 26
21 L
-L fe mal winlo-0)} — glint 3
à A = 1% - pat voto-ni)\ Swatasilto9) + mph Sin
> me migas pel |
mal Sin
> mib- mar into) - mg kSin8
pow pur unten fair y Canonical montt
url Hemi pia
we mio - mgt 26
2772 ow) Ar des # ne à olfunda? Zerm
we : He one which

y de tre
mip + malo da (o- wt)
Je pt 2 À Le angles memandten jan Lh pet Y
LT da ela cal dermis Me angeles part iles
ide, from inutisl part À yotaling front

Sohdlim 8-24

a A,
neh
a

bn pen de gly hy il à
ga A Beg of À abroad EE VA
Liu à éguhbian condibión (whan Phar do no
fra on Ha ma

se A-=*R

: Ride
à HE a
dr %
D s EX
at 7
a ww
=
x AT on

2 ku x
det

pS

de cedido y men de y dem Af

ow Le
y a wang inate? Se the yolnbal Enugg
ge By x Y
Ve pare te Ca) u

Im extern um
ig with bs

th kinks Eve e

$e kn
i” —@
noo Legprye”
- . 2 -
ave paie ant que —D
ung u
> ” o
1 >? o
laid nio
ment Ll
mi Berge: item”
n> Mk aden us
FE aad à á
\ je an” — Es
tl E)

4

© A

= fa ÓN

. a

pe su th prim date wet ABLE Afar,
y shall he comarcal. Ju

gn dr sé
Vasile Ah i

A

oe
OR
A ar at
Pr
mu 7 ht 2 mi
a rs Bin rá = mit
24, * :
a [ed
= Ky 7 qua + eats?
oponga Best
a 20
re
> Hz ‘ d
aie * Jus Lo 00)
poso em col ee
Ly. =
pO
a "cr? nn)
pre e ney e A u
s ge
eb — >)
O (40)

pue Henidhhien > ore!

. 5 i

Sl un Sec (art. _ 7 LD)

B= Jib Cregg + PE
= e

- rt + Lht +1 h (a-9"

soe ten de € doe E tr HE spl

se &/ à lansaved.
Le tm vaig Ub

in Hi Core 2?

ly JE 20
ped Gee

Sima =H
22» MH -0 (md)

b) Date dicos à mau berbimt Oz 4- byrwt

Se B= 2 -bSmwe
pet - blo aout ——6
B = 4 + bw sinwt

had,
Layrengean

Le Ent pd h,la-a)”
cr PO
Lagrange

ue u
Le in lbromwt) = Sei (Geb Sinwt)

2
=

= tha 51504)”

Se band mente

= U -
Pn % mio + bw Gat)
Hanidse mar.
; a
n= Be -L
mtb bu ent) o nes
u id
Pon 4 8
Le Le (ot b Sint)

nl kÇa-ë-b See)

=

Solution 326 (tor) Gy
>

zm Py (Po. - pistas +) - >
H fe (e bu las lo zm Te (ons) |
4m (a 00d Sous)

ate We

Que Po _ Pp bwaowe - Pr LL RO Sint
m

2m

- Lhe D) Sie)

3 vo
D Me fo -Pyhoësué -Sh(O rbsinot)
am

- um (a0 bin)

iy nian Hail de met be a Cancer ved
Lhe Hani

e O) GS)

du. “on + ;
e +2 2H
dé a Sue ra

Up = fe us hp

afer
= m(5 +bb awe -iouet)(& = bi” sinwt)
= mb (6 - bw" sinwt)
OH. & = Alm Cerisner) lala o -bsinot) | &
ae E

pu got

Eu)

so ~ Rl Ort

sine) (nerve EL?)

U = lobo
sé = p, (ae bin)
x (-buow t)(w)
er Lager 1 )
seat eo - (Rit Rr) b Sinw & + kat

——
inw +)- Re
ae fm te +)-@

(> pv rt) pwr Sinto € = RbW Grswe l(& +h Sinwe)
+mive

+ bot (a- ("+ bSinwt) )
= 27 EA of he Sohbe vec

So UL yn(pr bw ae) b W'sinw t
le
= (heh) bw aout (Hb Sine)

kb à Lowe

at = (mir bet Snot 4 Jia (o | lose simio

x

+0 REA - Hl last
L

ae
DM 2 (mows) Sinwe + bw {rer He) nor
de "as —
e

+ be pa - & (Riek) Y Gree
a 5 ze

A ge ¿e Samy Sin y losion Yun À de

se so za divida! bfeiinh a, bard o

Sid la 0 whith em pessild boat

d e > Bw bah = b ander
TA

340209 6-2

Soluhin 626 (brr--)

sh Hao we mu u ®
azi=cre ;
pr are
>... ? qrbwmwt = ©
D 47 -bumeæt (x)
QE
bas 4
cro

> ka -(Ritke) = °

> bash
kop
> oF Lb D 4-bSinwt = b
3 ab tb Swe

D à= baut (#9
aa

wur we on tah Y

1e

PO Zu tuppicar? will be nonzono [©
y tet Hi vide nie do erlitt
Lime dpa nat

uA
pre

qos u
Shh A à dro Ae fret x

$ = rfi) «(G+ bSnwe)

~ ¿Rola Ob saugt

CI E
a 2) al wos
dee 75

D om - bot Sinwt) - (RAR DO = (KR) bin wt tara
N ) C yb a
D M -) )-Ck+k

Solution 8.35
©

ven = mii
4 Le ner we A

(Co) Equabion 4 modern :
trom Exe Lagrange? EJ”

:
af) -
lon) Fr =a
at >
> aos er) SE =)
paques] - [re]

de

= yt Ne
à metre") res Fomine re

eros 8 à.
3 met (ves Et ax) ae
> í- ua ri —O v

LO à A Yalin y roto

(D com given
x = -wx% YX
ur mylar the Second divo on Lhe sight sica
ur get
BS Hw
Yu à an Eyuatin Jay - L
aim pré lin he Caer Lf do Ñ
jaumons osullti abou ov gin, 2
pow He extn lam - Ik 2
ar an old pre per A be bec
pasties tha à egpivalnt amp ger

al

ni a

À Lines #

CC) Canonical momertum

- Be
ai
s pon ©
= Of met a te
pP a E ree

Sedutim 8-35 (bn! =.)

we (on BE
so 4 maj

Le ur vi vod y ate cd

ns
dH. BOF
du. ah ep Qe + SH

2H. —®

de OP
De at

ote, te
>? me tom @

J
=:

m
ce Leit.
¿mis Ji erm’) et

un Sodufim 835 (don. -—)
030 -D «yt

sy ye
yx a mate

mel
mel (x

xB

now

Solution 8:35 (cont --)

So pulling ©8888 m © ve ge

ET . e
Pl me? ) + mo Lee

dt
a ne oe y qe vr +
WET pe ) + ame? ve’
et fan ae jr 58210
> met hä La rer 2,8] -B
pow fom ada Lagrange? 9”
dar al
Gl)" ax °°
>, + re > E
= yet’ )- [-Srre )-
> Em Pe
> ti =
e 3
a mp x) = 2
2 paris ®
a see? ®
0

now pull valıı ge rr@ A
we 2er a
ce pelt ae A
re ews Ye ) tL YE + Wa sre |
= met | gat ays rye ewe ey uty ert

en ena ex
mé / bye 45)

ELLE z
de
I = a =
rt y ERE?
or) eee
Stanton à uned 4 E
¿Hacia Hamclh nian de nat toners ed

y a eatin J MÈRE POY

Yavi rones -®
m solubior of Ari equal wel be of Ah Jor
ee Ot put + 4 €
Mo

> re

> ara Niro

Solufin 2-35 Clm4*___ )

dz] 2 Vs
a pon van . A
lu
y EA
a( x =
> me A= Ve
nee

2

==
RA

O

ct rad So br a HE me.
sive am je de au osc lhbrg

Jue we

pe e
“dn pret EO 45e Sof 6) > ©
PE Dee a BPE ”
Ja Vie
. ler wid Le
Do HAT à “ar
b à pue +
% (ars
y = LICE -
exp J% IH y+
A

9,
Sp port ie sol y
nee u 2
e eo» 4>® Dar un

gap 14)20 4 am