Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 80 стр.

UptoLike

Составители: 

Рубрика: 


Ë} ÒÒ}ÈÁË ¯©m©° Ë®äÈËäÈÒ}Òlnj
ÙkÓÈãÒÒ˰}È«˺äË¯Ò«ÒãÒÓË®ÓÈ«ÈãË¯Èµ

äÓºmkp
ÒãÒ
Ax By C A B++= + >00,
º˰
Gxy Ax By C(,)
=++

°
 { Ë}ȯºmº® º¯ºÓº¯äÒ¯ºmÈÓÓº® °Ò°ËäË }ºº¯ÒÓÈ º}¯ÎÓº°
¯ÈÒ°È
R
° ËÓ¯ºämº}Ë
x
y
0
0
m ¹È¯ÈäË¯Ò˰}ºä Ë äºÎË
©ÏÈÈÓÈ}È}
xx R
yy R
=+
=+
0
0
02
cos
sin
,[,)
τ
τ
τπ
º˰
FxR
FyR
x
y
() cos
() sin
,[,)
ττ
ττ
τπ
=+
=+
0
0
02
ÒãÒÎË¯ÈmÓËÓÒËä
()()
xx yy R−+=
0
2
0
22
Ë
Gxy x x y y R
(,) ( ) ( )
=− +
0
2
0
22

|¹¯ËËãËÓÒË

ÒÓÒ« ÓÈÏ©mÈË°« jsmniéjq·nxrvp ˰ãÒ ËË ¯ÈmÓËÓÒË m Ë}ȯºmº®
°Ò°ËäË}ºº¯ÒÓÈÒäËË
α
k
k
m
xy
pq
kk
=
=
0
0
Ë
p
k
Ò
q
k
Ëã©ËÓË
º¯ÒÈËãÓ©ËÒ°ãÈÈÒ°ãÈ
α
k
ÓË¯ÈmÓ©ÓãºÓºm¯ËäËÓÓº
|¹¯ËËãËÓÒË

Ò°ãº
Npq
km
kk
=+
=
max{ }
[, ]0
ÓÈÏ©mÈË°« wvé¹lrvu jsmniéjq·nxrvmv yéjktn
tq¹ }ÈÏÈÓÓºº m º¹¯ËËãËÓÒÒ  Ë äÈ}°Òää ÒË°« ¹º m°Ëä
k

ã«}ºº¯©²
α
k
0
Ëjqunt¡qpÒÏ¹º¯«}ºmÈãË¯ÈÒ˰}Ò²¯ÈmÓË
ÓÒ® ÏÈÈÒ² ÈÓÓÈãË¯ÈÒ˰}ãÒÓÒ ÓÈÏ©mÈË°« wvé¹lrvu
jsmniéjq·nxrvpsqtqq
¯Òä˯

ÈãË¯ÈÒ˰}ÒË
ãÒÓÒÒ
¯«äÈ«
zmȯÈÓÈ«¹È¯ÈºãÈ
ҹ˯ºãÈ
ÙiË}ȯºmãÒ°µ
xy++=320
yx−=
2
0
xy −=
10
xyxy
33
0
+−=
(N=1
(N=2)
(N=2)
(N=3).
˺¯ËäÈ

º¯«
º}Èã
Ë¯ÈÒ
˰}º®ãÒÓÒÒÓËÏÈmÒ°Òºm©º¯È°Ò°Ëä©}ºº¯
ÒÓÈ
 Ë }  Ò Ò    } È Á Ë  ¯ ©   m © °  Ë ®   ä È ˆ Ë ä È ˆ Ò } Ò   l n ‘ j 
ÙkÓÈã҈Ò˰}È«˺äˈ¯Ò«ÒãÒÓË®ÓÈ«ÈãË­¯ÈµäÓºmkp



                              ÒãÒ Ax + By + C = 0 , A + B > 0 ˆº˰ˆ  G ( x , y ) = Ax + By + C 
                              
                              
                         ° { Ë}ȯˆºmº® º¯ˆºÓº¯äÒ¯ºmÈÓÓº® °Ò°ˆËäË }ºº¯ÒÓȈ º}¯‚ÎÓº°ˆ 
                                                                                     x0
                                ¯È҂°È R ° Ëӈ¯ºä m ˆº}Ë                         m ¹È¯Èäˈ¯Ò˰}ºä mÒË äºÎˈ
                                                                                     y0
                                ­©ˆ ÏÈÈÓÈ}È}
                                
                                  x = x 0 + R cos τ                          Fx (τ ) = x 0 + R cos τ
                                                    , τ ∈[0,2π ) ˆº˰ˆ                           , τ ∈[0,2π ) 
                                  y = y 0 + R sin τ                          Fy (τ ) = y 0 + R sin τ
                                 
                                ÒãÒÎË‚¯ÈmÓËÓÒËä ( x − x 0 ) 2 + ( y − y 0 ) 2 = R 2 Ë
                                 
                                                              G ( x , y ) = ( x − x 0 ) 2 + ( y − y 0 ) 2 − R 2 
            
            
            
 |¹¯ËËãËÓÒË            ÒÓÒ« ÓÈÏ©mÈˈ°« jsmniéjq·nxrvp ˰ãÒ ËË ‚¯ÈmÓËÓÒË m Ë}ȯˆºmº®
                                                                        m
                         °Ò°ˆËäË}ºº¯ÒÓȈÒäËˈmÒ                         ∑ αk x p  k   y qk = 0 Ë p k Ò q k Ëã©ËÓË
                                                                              k =0
                         ºˆ¯ÒȈËã Ó©ËÒ°ãÈÈÒ°ãÈ α k Ó˯ÈmÓ©ӂã ºÓºm¯ËäËÓÓº
            
            
            
 |¹¯ËËãËÓÒË              Ұ㺠N = max { pk + q k }  ÓÈÏ©mÈˈ°« wvé¹lrvu jsmniéjq·nxrvmv yéjktn
                                            k =[ 0,m ]
 
                         tq¹ ‚}ÈÏÈÓÓºº m º¹¯ËËãËÓÒÒ  Ë äÈ}°Òä‚ä ҝˈ°« ¹º m°Ëä k
                         ã«}ºˆº¯©² α k ≠ 0 Ëjqunt¡qpÒϹº¯«}ºmÈãË­¯ÈÒ˰}Ò²‚¯ÈmÓË
                         ÓÒ® ÏÈÈ Ò² ÈÓӂ  ÈãË­¯ÈÒ˰}‚  ãÒÓÒ  ÓÈÏ©mÈˈ°« wvé¹lrvu
                         jsmniéjq·nxrvpsqtqq
            
            
            
 ¯Òä˯                         ¯«äÈ«                                  x + 3y + 2 = 0                                     (N=1
 
  ÈãË­¯ÈÒ˰}ÒË
                                                                                                                                
 ãÒÓÒÒ                          zmȯȈÓÈ«¹È¯È­ºãÈ                      y − x2 = 0                                        (N=2)
                                                                                                                                
                                 €Ò¹Ë¯­ºãÈ                               xy − 1 = 0 
                                                                                                                              (N=2)
                                                                         
                                                                                                                                  
                                 ÙiË}ȯˆºmãÒ°ˆµ                         x 3 + y 3 − xy = 0 
                                                                                                                              (N=3).
            
            
            
 ‘˺¯ËäÈ                º¯«º}ÈãË­¯ÈÒ˰}º®ãÒÓÒÒÓËÏÈmҰ҈ºˆm©­º¯È°Ò°ˆËä©}ºº¯
                  ÒÓȈ