Download Solutions to problems in classical mechanics and more Exercises Classical Mechanics in PDF only on Docsity!
/) .l
B -- vocos9Qt
B =^ V6cos0'
2E =p^ -)
?
L ^ V69rnu -qL^ =u
2 - r / Va'j!t,1 lct{^ = a d
zva2@s(20) -e (^) +
,
,..'),v R
, ,J=
t
L / '^ .a- tr- 4
u:4q
2&- @
u.'zsu
-/*ana
-L =,Iana
x
V= v5aos^*o'):,^ p+RcoS'{'^ {='Kq;nr'x
y.: V.i*V,;,t- L gtz, y = ruolsl101,rftgtt :,
l6.jnl',#,*ue:f
i:L\ftit Lr'gtz t'->''^ or,.t,,o:r',"t
=' rir-"stt
vnc,o10[' tanx = Vosih,l€"t- - * g tz 1 :-A,^
vfucas?[ano( 2' V;sfn0 -^ *At', { ^ , ^ , ^ / /... A , /^ *tV
- (^) /o(sino -^ (os€tana) !+
,',t 'F^ 2#(t^ ihg - cose fu\or)^ I^ X = nJ',.^
' :''
,
3
, l l
'1'(7t
dx de
/ ) l t t l , L (
x
6,ih?A/z
= ua4(?d)
|hz.r, Q =
e
tan A
:jta,^. 4*-^
1-art(rtl i .) *t /. r , *^ N -+E (^) *, ' - 66f (ortf + \ / zltz
Urfut h=^ 4,^
x a?
a=
+fr
At Xo=q > d:.u=l=6ca (^) _ ga3c o'7 (^) (zo)' @F
= ffi'u
0
x =a
c +,
Cl'^ d3a'
nta ohve !(
-n4=+^ dzal
x=o
. (^) H"tn (^) z at (^) Xa: -
;r 42A:a""
x (^) Ana^htz 4.r.4rt*r"4 ./^ as"rlh-hira u ' t v
t-F \ _ dzU I- /
dxrl
c
dqtm X=
--t -, VxF ') ^ + (^) | zl 5 / 4t ?. I r ' I 'z I
' ,+ -+ -)^ ]X vxF-- | ^ I qr'. l7r l- Irx
Q,+
a) 1r aF. =^ ^t^ a1fu / 9rz = ax+b,+=^ ax+[ r 4^ 5f
=2; ?y
' (^) uz'
DFz-^ av. a-t-^ -^ av -)^ aF=--Q&. r'
;T-''' )z-'/^ ax^ a2'
?-&=or, &-= az
-) +=4 / 6V_r_' "y
_ __ (^) ax ay
1 ) (^) ,n/ lfu firaz k) Lt cznae'"va'twe' HrrLlzl YYF=o^
a
,'. can uw,l-,'t id f;leii*tlfi^
t1'@ni6=
-4l7.,aytalNx< @x=ffi'/ -)^
'' ' 'i'i" (^) t' C'r
c"/."hJl
v' w
ay
'Y
---) --+^ -)^ -) f =-/u 4^ vxF=o
,/L - ?t-)^
\ aY vz/
i(aFt., -aFx)y
aX azl
t(L - aE)
\ ax ty'
n-
q=
t) -
= -(ayrr + b-z-r"+cx) + h(n
r lz=
u-
axztbz=-# *> g=-frr4+
4-rtl
lz ( Xtz./
axy+by= ^
-(axyz+Lyz) + ft(Y,.)
,) dFz - -l
?v .,2 '
dFz (^) :X -=' = -g^ ) dx
zF., "-!= (^) Q (^7) ox
-byu -of^ -r,
tt = ,J:
aza
^r -X
o-:-x-- -e
az
OFt =0 ,/ ay
t /
I
ftJ='!rr)x +fl(y,z)= -zex+
(^) fi&')
U = - JFvdy+ f7k,')^
=-Y Inz t^ fz|ry=)
u=
-!Edz (^) +fsL,t)=-r"\W (^) +dhv)
e= -z{x-ylnz^ tC
q,oA /
--u trtr
- ' ) l. -^ tr -- a,/ (^) fz = -xvi I J
- ) r " t t , , - ^ ^
;rn1Jf= -mai- xvJ
a 4 L
4Y -^ -o^ -^ d^ v At- d^ m
\J
y= -Z n/r
(v
\nt (^) v) -v,
)=-v _
'l+L-/, V> 0 a,"'4 one yfu
4u(v=v \ ^g/
y= Yh(-ft)l
Q.7 (^) f,,= z^XsinTi'
f= zmXrs0i'
fr--v*r
''
f=+tT
/*N
atl
ri
4
m
-^3J
x
a t I J - > t1t4-e/r/A
fr=+ngi
E" '1 qua,aJir-.^ u aa(e ; l4-rr^^&U/e4-
t'?n,
