~ ?yvD ?Dy
? 6 ?
w
q
~ ?yvD ?Dy
Ba±s
N
R
T
A
0
x
M
x
xx?+
.
),()(
= μ ???
 uW
!f
baxf
x
y
o
),,(:
00
yxA?
,),( 1 ?iB?yxM
?;)1( 9v￥Z_Bá wL￥?_D x
,)2( sAM =
j
.,,, |μ|MQ
H |?|Bá
H
￥Z_D wL?_?
ss
AM
j
~ ?yvD ?Dy
).(xss =
??9f
),,( yyxxN?+?+
!
?m
NTMTMNMN +<<
j
,0
H? →?x
22
)()( yxMN?+?=
x
x
y
+=
2
)(1
,1
2
dxy
′
+→
sMN?=
j
,ds→
22
)()( dydxMT +=
,1
2
dxy
′
+=
dyyNT=
,0→,1
2
dxyds
′
+=#
,)( 1??9f
xss =Q
.1
2
dxyds
′
+=#
±s
T
N
M
T
R
A
0
x
x xx?+
x
y
o
~ ?yvD ?Dy
=a w
q# 9

T
w
q
^
í
wL ??é
? w?￥

1
M
3
M
)
2
α?
2
M
2
S?
1
S?
M
M
′
1
S?
2
S?
N
N
′
α?)

? w?
v?v
?M]


? w?v
1a w
q￥?l
1
α?
)
~ ?yvD ?Dy
)
α?+α
α?
S?
S
)α
.
M
′
.
M
C
0
M
y
xo
.
s
KMM
=
′
α
￥
ü ( w
q1

! wL C
^;á￥
.
0
^?M
,sMM?=
′

.α?
′
→ ML?1MM
?l
s
K
s
α?
=
→? 0
lim
wL C ? M )￥ w
q
,lim
0
i￥Hq/
ds
d
s
s
αα
=
→?
.
ds
d
K
α
=
~ ?yvD ?Dy
2a w
q￥9

T
?i,
(1) °L￥ w
q))1
,;
(2) ?
ò?)￥ w
q????￥?
, O
??l w
qv,
,)( =¨ V?
! xfy =
,tan y
′
=αQ
,
1
2
dx
y
y
d
′
+
′′
=α
.
)1(
2
3
2
y
y
k
′
+
′′
=∴
,arctan y
′
=αμ
.1
2
dxyds
′
+=
~ ?yvD ?Dy
,
),(
),(
=¨ V?
!
=
=
ty
tx
ψ
.
)]()([
)()()()(
2
3
22
tt
tttt
k
ψ?
ψ?ψ?
′
+
′
′′′
′′′
=∴
,
)(
)(
t
t
dx
dy
ψ
′
′
=Q
.
)(
)()()()(
32
2
t
tttt
dx
yd
ψ?ψ?
′
′′′
′′′
=
~ ?yvD ?Dy
è?
2

'B?￥ w
qKv
tL cbxaxy ++=
3
,2 baxy +=
′
,2ay =
′′
.
])2(1[
2
2
3
2
bax
a
k
++
=∴
A ?,
,
2
H?
a
b
x?=,Kvk
,)
4
4
,
2
(
2
1
tL￥???
a
acb
a
b?
Q
.Kv
tL??)￥ w
q∴
~ ?yvD ?Dy
? m
?i)lb \ T
).
(
1
),(
,
￥??
1?E??
q ??1?
,V
P w ?m

??-W¤ ?B
×aa°?
R
ü ?^?
3
Y#1
?￥ w
ql ??M
?
H ?¤h)ME?°? ???
R
R
è
~ ?yvD ?Dy
.
1
)1(
,
],0[
6
1
0
3
R
A
R
l
R
l
OOA
OAlOA
xxx
Rl
y
￥ w
qí
1
H?
li O?1
,
￥ w
q
S
￥é￡

1 ?

T1Yè¨ ?Q
tL
<<
∈=
x
y
o
R
),(
00
yxA
)0,(
0
xC
l
~ ?yvD ?Dy
x
y
o
R
),(
00
yxA
)0,(
0
xC
￡ ?m
￥μ?àV
U°?x
.,
^?E?
^

ABOA




,
,
2
1
2
x
Rl
y =
′
.
1
x
Rl
y =
′′
,0,0,0 =
′′
=
′
= yyx )
.0
0
=k#
S?￥ w
q
L=1 p,
0
xl ≈
l
~ ?yvD ?Dy
2
0
2
1
0
x
Rl
y
xx
=
′
=
μ
2
2
1
l
Rl
≈,
2R
l
=
0
1
0
x
Rl
y
xx
=
′′
=
l
Rl
1
≈,
1
R
=
￥ w
q1#?
A
0
2
3
2
)1(
xxA
y
y
k
=
′
+
′′
=
2
3
2
2
)
4
1(
1
R
l
R
+
≈
,1<<
R
l
Q,
1
R
k
A
≈¤,
4
2
2
R
l
{ ?=Q[
x
y
o
R
),(
00
yxA
)0,(
0
xC
l
~ ?yvD ?Dy
?a w
q?D w
q??
?l
D
)(xfy =
M
k
1
=ρ
.),(
,.
1
,
,
).0(),(
)(
)￥ w
q??N?1 wL? ?mT?
1??1??[
P?￥B§ |B?
)￥ wL￥EL
?
)￥ w
q1
?
! wL
M
D
k
DMD
M
kkyxM
xfy
ρρ==
≠
=
, w
q?D
. w
q?ρ
x
y
o
~ ?yvD ?Dy
1. wL
B?)￥ w
q??D wL??)￥
w
qo1?
,
.
1
,
1
ρ
ρ == k
k
'
?i
2. wL
B?)￥ w
q??v, wL??)
￥ w
ql ( wL
ü ); w
q??l, w
q
v ( wL? w ).
3. wL
B?)￥ w
q? Ví
}9???
í wL (?1 wL???í￥=Qí
).
~ ?yvD ?Dy
′′
′
+
+=
′′
′
+
′
=
=
y
y
y
y
yy
x
CyxM
xxfxfy
2
2
1
)1(
,
),(),(,0
)( ),(:.4
β
α
βα
1
￥US￥ w
q??5 wL??1
? O=¨?
! wL￥Z?1
222
)()(,RM =?+? βηαξ?￥ w
q?Z?1
! wL

[ w
q?
 Oy1,),(,
)1(1
2
32
2
2
yxM
y
y
K
R
′′
′
+
==
2
32
22
)1(
)()(
y
y
yx
′′
′
+
=?+? βα
~ ?yvD ?Dy
#<°??￥ MLD w
q?￥??y1 wL,CMM
′′
′
+
′
=?
′′
′
+
=?
∴
y
yy
x
y
y
y
)1(
1
2
2
α
β
β
α
=
′
y
x
y
2
22
2
)1(
)(,
y
y
yx
′′
′
+
= βα¤h ?
..0
0;00
Q|D'j￥
H wL
^
H wL
^?￥?
ββ
β
′′
>
<
′′
<>
′′
yyy
yyy
),( βαC
)(xfy =
),( yxM
x
y
o
~ ?yvD ?Dy
′′
′
+
+=
′′
′
+
′
=
y
y
y
y
yy
x
2
2
1
)1(
β
α
'
L
L
′
.
￥v 7L
?1v yL7e wL
￥?1 wL?￥E
￥ w
q? ?·m wL
L
L
LL
L
′
′
~ ?yvD ?Dy
è
$

'B?)￥ w
qKv
tL xxy +=
2
3 ¤?,2,12 =
′′
+=
′
yxy
2
3
2
3
))12(1(
2
)1(
22
++
=
′
+
′′
=
xy
y
K
Kv
Hs
Kl' w
q1 Vn?
2
1
=x
??) w
qKvb
[
tL xxy +=
2
è
w
q??b
)￥ w
q#? p?? ),0(
sin
cos
b
tby
tax
=
=
~ ?yvD ?Dy
3 ???￥?
?,
2
),0(
π
=tb
ta
dt
xd
tta
dt
dx
t cos)(,sin)(
2
2
==
′′
==
′

tb
dt
yd
ttb
dt
dy
t sin)(,cos)(
2
2
==
′′
==
′
ψψ
ba?=
′′
=
′
=
′′
=
′
)
2
(,0)
2
(,0)
2
(,)
2
(
π
ψ
π
ψ
π
π
#
,
)]()([
)()()()(
:
2
22
2
3
a
b
tt
tttt
K =
′
+
′
′′′
′′′
=∴
ψ?
ψ?ψ?
w
q
b
a
K
R
2
1
,== w
q??
~ ?yvD ?Dy
è
x
y
o
Q
P
.
,
.70
,/400
,)(
4000
2
a ?
f??VU￥?e?
H
p¤
$ Xf??8×
e
ü)
1?
e¤
f??ê1
ü
f
tL
=
=
vO
x
y
3 ?m,
s ?s
,PQF?=
jf??? oT
???,
.
2
ρ
mv
F =∴
O?)
tLE?￥ w
q??
~ ?yvD ?Dy
00
2000
==
=
′
xx
x
y
,0=
.
2000
1
0
=
′′
=x
y
¤ w
q1
.
2000
1
0
=
=xx
k
w
q??1
.2000
ü=ρ
2000
40070
2
×
=∴F ),(4.571)(5600 $ X
d ≈=
),(4.571)(70 $ X ? $ X ? +≈∴Q
).(4.641 $ X ?=
',f??VU￥a ?1 641.4 $ X ?,
~ ?yvD ?Dy
è
.
)0,0(
2
￥ w
q?￥Z?
?￥v yLZ?#
 p
tL xy =
3
2,2 =
′′
=
′
yxy
￥ w
q??1??
tL
￥? ),(
2
tt
)41(
)1(
2
2
ttt
y
yy
x +?=
′′
′
+
′
=α
2
411
2
2
2
t
t
y
y
y
+
+=
′′
′
+
+=β
+
+=
+?=
∴
2
41
)41(
2
2
2
t
ty
tttx
v yL￥?
Z?1
~ ?yvD ?Dy
1?

' t
ty
tx
3
2
1
4
2
3
+=
=
),
2
1
,0(,0 w
q??1
H? =t
2
1
2
)41()1(
:
0
2
0
2
2
3
2
3
=
+
=
′′
′
+
=
== xx
x
y
y
R w
q??
￥ w
q?Z?1?#
tL )0,0(
2
xy =
4
1
)
2
1
()0(
22
=?+? yx
0
22
=?+ yyx'
~ ?yvD ?Dy
1al2
¨±sD￥ ?
,ù? wL w
￥?
é￥
Ds| ——±s+D,
'à
Q,±s, w
q, w
q?,
wL? w?￥
í
—— w
q ;
wL￥í
}9 w
q? ( ).
~ ?yvD ?Dy
± I5
??

't?)
w
qKv$
,cos2 tx = ty sin3=
~ ?yvD ?Dy
± I53s
2
3
2
])(1[
||
y
y
k
′
+
′′
=
2
3
22
)cos9sin4(
6
tt +
=
2
3
2
)cos54(
6
t+
=
1
P Kvk
2
3
2
)cos54( t+
Aμ Kl
2
3
,
2
ππ
=? t
N
H Kvk
~ ?yvD ?Dy
°z A b5
a w
q))1
,￥ wL1@@@@@@@@ w
q))M?￥
wL1@@@@@@@@@@
a
tL 34
2
+?= xxy  

)￥ w
q1
@@@@@@@@ w
q??1@@@@@@@@@
a wL )1ln(
2
xxy ++=  

) ￥ w
q 1
@@@@@@@@@@@
?z  p wL )ln(sec xy = ? ),( yx )￥ w
q# w
q?
?
~z  p wL
=
=
tay
tax
3
3
sin
cos

0
tt = )￥ w
q
?z ￡
ü wL
a
x
ay cosh=  ?B?) w
q??1
a
y
2

5
~ ?yvD ?Dy
?a wL xy sin= )0( π<< x

'B?)￥ w
q?
?Kl$ p??)￥ w
q??
Ba wL
 w
qKv￥??1N wL￥??
k p·
wL
x
ey = ￥??i p??)￥ w
q??
~ ?yvD ?Dy
Baa°L? a
2
1
,2  a
=a xxk sec,cos =ρ= 
?a
0
2sin3
2
ta
k = 
?a )1,
2
(
π
) w
q??μKl′
B 3
2
3
),
2
1
,2ln
2
1
( =ρ? 
5s?