, , L l, . L , , - . , , , . L, :
F(x,y)=0, (4)
, Oz, L. , (4), Oxyz. (; ; z) - . N L , . N, , . N . N L, (4) . , (; ; z), z. , (; ;z) (4). , , (4) , L. , z F(x, y) = 0, Oxyz, , Oz, L, F (, ) = 0.
L :
(5)
.1.
, F (x, z) = 0, , F (, z) = 0, , Oxyz , .
.
1. ,
. (6)
(. 2). Oz, , . , a = b, , .
2 + 2 = 2.
2. ,
. (7)
(. 3). , z a b.
.2 .3
.4.
3. ,
|
|
= 2pz, (8)
(.4). , Oyz, .
. , , . , . , , z = 3 = 25,
(9)
, z = 3 .
, , , , . , , , .
.
, , L , . L , - , , , .
, :
(10)
b, Z = c. . .
(; ; z) , N (X; Y; ) (. 5). , 0 (0; 0; 0) N (X; ; )
.
X = cx/z; Y = cy/z. (11), , , , .
. , = b,
.
. (11)
6 . 5
.
L, Oyz,
(12)
, z (. 6). ( L X, Y Z, , , z .)
. . (; ; z) - . , Oz, Oz L N. KN . = KN. KN Y N, . . KN = |Y|, a KM = OP = . ,
| Y |= Y = . , Z N, , z .
N L, (12), Y Z N . Y Z, , z, :
|
|
, (13)
(; ; z) . , , , (13) . , (13) z L, (12). (13) (12) Y Z , z :
(14)
. , L Oyz Oz. L . , (12), (13) (14), .
.
z.
.
(14) Y Z , z , ,
.
.
5. .
,
. (15)
. , b . (15) , . , , . , z = h (| h | < ), L. ,
z, , L :
,
..7.
, L
, . (16)
(16) , |h| b . |h|=c , . | h|> z = h, , . , = h (| h | < y = h (| h | < b) . , . 7. = b
. (17)
, = b = , + y2 + z2 = 2.
.
,
. (18)
. - , , z (18) . = 0, Oxz ABCD (. 8)
, = 0 EFGH
Oyz.
z = h BFCG, :
.
. 8
= b
. (19)
z = h
. 2 3 . , , . , :
(20)
, b - , - ().
, :
, ,
. . .
, (20). (; ; z), (20), (18) . , (20) (18). k, , (18). , :
|
|
(21)
l .
. 9
, . , , (. 9). .
. , , , , , .
,
, (22)
.
. Oxz z,
.10
z = h ( | h |>c),
,
| h |. | h |< (22) z = h, , . (), . = b (22)
. (23)
. z = h (| h |>c)
R= .
.
,
, (24)
, q . , , , >0, q>0.
Oxz Oyz , ,
z = h (h >0) -
(. 11).
p = q
. (25)
(24) , : Oxz Oyz.
.11
.12.
,
. (26)
, q . ( , , , >0, q>0.)
Oxz,
(27)
(.12.)
x = h
h , , Oyz q.
, , Oyz, Oxz, (27). z = h, ( ) :
|
. 12 : h >0 h <0. h = 0, . . , , :
|
|
.
, .
, :
. , , . , , , :
k l - .
, , (. 13).
. , , . , , .
1. .. - . , 1980.
2. .., .. - . , 1980.
3. .., .., .. - , 1 . - . . ., 1986.
4. .., .. - - , , 2001.
5. .. - ., . ., 1985.
6. .., .., .. - ., . ., 1978.
1. ۅ 3
1. . 3
2. . .. 8
3. . .. 16
4. . 21
2. . .. 46
1. . . . 46
2. ,
49
3. . .. 57
4. . 69
3. . 72
1. . 72
2. . .. 75
3. . ... 79
4. . 83
5.
. 87
6. . .. 97
7. . .... 114
8. . . 122
141