" "  N 9, 2005


 

.. , ..

 

19 2005 .

 

. . , . , . , , ( ).

 

 

, [1,2] . . .

, z , : z=f(r) , ( ), z=j(r) , , n(r) .

, (.1). [1]

 

                                          (1)

 

, n(y) , f(y) j() . 1.

 

. 1

(1)

                                         (2)

,

 

                                         (2a)

 

, . . = 0.

:

 

                                         (3) 

 

d1=arctg(1/f¢(y1) 1 , - 1, q1- , , (.1) (3)

 

                                         (4)

 

 

                                         (5)

 

, :

 

                                         (6)

q2 , q2 >0 , b() , b(0)=0.

n(y), (2) ( 2) (4), (5), (6) , , f(y) j() . , ( ) (), .

. [2] . , . , .

 

, ,                                     (7)

 

no2=n2(0) , f2k, j2k , 2k (k=1,2,3,) , . 2>0 (n(y) ).

(6), , :

 

                                    (8)

b2-1 (=1,2,3,) .

(4). sinq1, cosq1, f¢(y1) 1 :

,

,    ,    ,

,    .

 

* ,

g1(a)=2f2(a-1)-n1, g3(a)=4f4(a-1)+2f2k2+n3, g5(a)=6f6(a-1)+4f4k2-2f2k4-n5,

 

g2=g12, g4=2g1g3 , g6=2g1g5+g32.

 

(7), (4)

                                         (9)

a2=no2-a2.

(9) , (1=0) a=no a=0.

g2+c2>0 , (9) 1, .. 12 a2:

 

                                         (10)

, ,

 

(5):

 

                                         (11)

 

h2=h12, h4=2h1 h3 , h6=2h1 h5+h32 ,

 

, ,

 

,

,     ,     ,

,    .

 

(11) 22:

 

                                                 (12)

, ,
 

 

(10) (12)

 

, i=1,2                                (13)

 

(2). (7), (2) :

,                                       (14)

n2(p)-a2=0 . (7) ,

.

:

 

                                         (15)

 

, ,

 

.                                (16)

 

R2k, Q2k (k=0,1,2,) (7) (16). ,

 

Ro=a2 /p2, R2=c4+p2c6 , R4=c6 ,

Qo=p/a , Q2= -1/2p3/a3(c4+p2c6) , Q4=3/8p5/a5(c4+p2c6)2-1/2p3/a3c6 .                           (17)

 

(14), (2) :

 

                                         (18)

(2)

 

                 (18)

I2k :

*, ,

,  . . .

1, 2, (13), (15) (16), arcsin(y/p) (p2-y2)1/2 a (18) (18) a, :

 

a2=no2-a2.                                       (19)

,

 

,

 

,

, ( i=1,2),

.

 

:

 

 

(2). Y(a)=j(y2)-f(y1). (7), (10) (12) ,

 

                                         (20)

, ,

.

(2)  

 

I(a) = Y(a),                                         (21)

 

  I(a) (19), Y() (20).

(21) , =no, . (21), =no c2k:

 

,

,                                         (22)

,

 

2, 2, 4, 2,4,6 .., .

(22) :

 

.                                         (23)

:

 

                                         (23)

2 . (23)

 

                                         (24)

(23)

 

                                         (24)

 

1 2 (10) (12).

(22) 4. :

 

,                                         (25)

 

 

, ,

 

 

                                 (25)

 

(22) ( 6 ), 6 ..

, . , f(y)=f0 + f2y2 j(y)=f0+1+ j2y2, f2=j2=0.1, 1 10. 2 n(y) , - . 2 n(y), 1 , 2 .

 

.2

 

. n(y) - . (. 3) n(y) . , .

 


.3

 

h1 q , 2=h1 . 젠 h1 , . h1 n1=no .

, , i-1 , .. nj, hj , j=1,, i-1. i- , .. ni, hi.

, q1=iqo . , k. , k < i, q1 , k < i. i- yi+1.

 

,                                         (26)

 

- , qk

,

 

d=arctg(1/f¢(y) . Si i :

 

,                                         (27)

ji= j(yi) , ,

.

Li i- .

, j(), , -

yi£ y£yi+1.

i+1

 

                                         (28)

 

(26) (28) (27), qi

,

 

,

DF .

ni  

, q=nkcosqk =nk+1cosqk+1=

 

 

,

 

, .


,

m

, ,

P=Wsinbi , R=Wcosbi+V , U=2-Wsinbi.

 

ni

i-

.

i+1 ..

[1]. ,

 

.4

 

4 n(y) 500 () 1000 .

- , (24)-(25). , , , y. .

 

.

 

1. .., .., , ., ., 1974 .

2. .., .., 頠 , , 1997, 42, 12, .1452-1458.