Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 55 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

cÈÏ Ëã
59
¯«äÈ«Ò¹ãº°}º°

~ÈäËÈÓÒË
¯ÈmÓËÓÒË ¹¯«äº® ÓË m ãº® °Ò°ËäË}ºº¯ÒÓÈ «mã«Ë°« ÈãË¯ÈÒË°}Òä
¯ÈmÓËÓÒËä¹Ë¯mº®°˹ËÓÒsȹ¯Òä˯ m¹ºã«¯Óº®°Ò°ËäË}ºº¯ÒÓÈ°ä
¹ºÓºäºÎËÒäËmÒ
ρ
ϕϕ
=+P
sec( )
0

nº¯ä©ÏÈÈÓÒ«¹¯«äº®ÓÈ¹ãº°}º°Ò
{¹¯ºÒÏmºãÓº®Ë}ȯºmº®°Ò°ËäË}ºº¯ÒÓÈ
{, , }
Og g
12
→→
°Ë°m¯ÈÏãÒ
Ó©ËÁº¯ä©ÏÈÈÓÒ«¹¯«äº®ÓÈ¹ãº°}º°ÒcÈ°°äº¯Òäº°ÓºmÓ©ËÒÏÓÒ²
°
 ¯ÈmÓËÓÒË
¹¯«äº®
¹¯º²º«Ë®
˯ËÏ mË
ÓË°ºm¹ÈÈ
ÒËº}Ò
r
x
y
1
1
1
→
=
Ò
r
x
y
2
2
2
→
=
º°}ºã}Óȹ¯Èmã«Ò®mË}º¯ÈÓÓº®¹¯«äº®
arr
xx
yy
→→→
=−=
−
−
21
21
21

º ËË ¯ÈmÓËÓÒË m mË}º¯Óº® Áº¯äË Ë ÒäËmÒ
rr rr
→→ →→
=+ −
121
τ
()
ÒãÒ
rrr
→→→
=− +
()1
12
ττ

vººmË°mËÓÓºm}ºº¯ÒÓÈȲÒ°}ãÒm¹È¯ÈäË¯
τ
¹ºãÒäºÓÒÏ
°ãËÒ²Áº¯äã
xx
xx
yy
yy
xxyy
yy x y y
xx y x x
−
−
=
−
−
−−≠
=∀ =
=∀ =
1
21
1
21
2121
121
121
0; ( )( )
;,
;, .
 
 
~ÈäËÒäºªÒ¯Ò°ãÈ«äº©º¹Ò°ÈÓ©°ãºmÒËä
det
xy
xy
xy
1
1
1
0
11
22
=

vãË°mÒË

iã« º
º
º© ¯Ò º
}Ò
r
x
y
1
1
1
→
=
r
x
y
2
2
2
→
=
Ò
r
x
y
3
3
3
→
=
ãËÎÈãÒ ÓÈ
º
Óº®¹¯«äº®Ó˺²º
ÒäºÒ
º°Èº
Óº
º©Ò²}ºº¯
ÒÓÈ©
ºm
ãËmº¯«ãÒ¯ÈmÓËÓÒ
det
xy
xy
xy
11
22
33
1
1
1
0
=

c È Ï  Ë ã                                                      59
¯«äȫҹ㺰}º°ˆ 



~ÈäËÈÓÒË ‚¯ÈmÓËÓÒË ¹¯«äº® ÓË m ã ­º® °Ò°ˆËäË }ºº¯ÒÓȈ «mã«Ëˆ°« ÈãË­¯ÈÒË°}Òä
                           ‚¯ÈmÓËÓÒËä ¹Ë¯mº® °ˆË¹ËÓÒ sȹ¯Òä˯ m ¹ºã«¯Óº®°Ò°ˆËäË}ºº¯ÒÓȈ °ä
                           ¹ ºÓºäºÎˈÒäˈ mÒ ρ = P sec(ϕ + ϕ0 ) 
                  
                  
                  
                  
nº¯ä©ÏÈÈÓÒ«¹¯«äº®Óȹ㺰}º°ˆÒ
                  
                  
                  
                                                                                                                                            →      →
           {¹¯ºÒÏmºã Óº®Ë}ȯˆºmº®°Ò°ˆËäË}ºº¯ÒÓȈ {O, g1 , g 2 } °‚Ë°ˆm‚ ˆ¯ÈÏãÒ
Ó©ËÁº¯ä©ÏÈÈÓÒ«¹¯«äº®Óȹ㺰}º°ˆÒcÈ°°äºˆ¯Ò亰ӺmÓ©ËÒÏÓÒ²
          
          
                                                                      →   → →    x 2 − x1
° ¯ÈmÓËÓÒË  º°}ºã }‚Óȹ¯Èmã« Ò®mË}ˆº¯ÈÓÓº®¹¯«äº® a = r2 − r1 =               
         ¹¯«äº®                                                                                                                                                                       y 2 − y1
         ¹¯º²º«Ë®                                                                                                                                                   →        →            →        →
         ˯ËÏ mË
         ÓË°ºm¹ÈÈ
                                   ˆº ËË ‚¯ÈmÓËÓÒË m mË}ˆº¯Óº® Áº¯äË ­‚ˈ Òäˈ  mÒ r = r1 + τ ( r2 − r1 ) 
          Òˈº}Ò                         →                      →          →
         →            x1           ÒãÒ r = (1 − τ ) r1 + τ r2 
         r1 =                     
                      y1
                                   vººˆmˈ°ˆmËÓÓºm}ºº¯ÒÓȈȲÒ°}ã Òm¹È¯Èäˈ¯ τ¹ºã‚ÒäºӂÒÏ
         Ò
                                   °ãË‚ Ò²Áº¯ä‚ã
          →           x2           
         r2 =                
                      y2                                                    x − x1    y − y1
                                                                                    =        ; ( x 2 − x1 )( y 2 − y1 ) ≠ 0
                                                                          x 2 − x1 y 2 − y1
                                                                            y = y1 ; ∀x ,  y 2 = y1                     
                                                                           x = x1 ; ∀y ,  x 2 = x1 .
                                   
                                   ~ÈäˈÒ䈺ªˆÒˆ¯Ò°ã‚ȫ亂ˆ­©ˆ º¹Ò°ÈÓ©‚°ãºmÒËä
                                   
                                                                                                     x                y         1
                                                                                                 det x1               y1       1 = 0 
                                                                                                     x2               y2       1
                  
                  
                                                                                                         →           x1         →           x2              →           x3
    vãË°ˆmÒË                     iã« ˆºº ˆº­© ˆ¯Ò ˆº}Ò r1 =                                                       r2 =                  Ò r3 =                    ãËÎÈãÒ ÓÈ
                                                                                                               y1                     y2                          y3
                                   ºÓº®¹¯«äº®Ó˺­²ºÒäºÒº°ˆÈˆºÓºˆº­©Ò²}ºº¯ÒÓȈ©‚ºm
                                   ãˈmº¯«ãÒ‚¯ÈmÓËÓÒ 
                                                                                                     x1               y1        1
                                                                                                 det x 2              y2        1 = 0 
                                                                                                     x3               y3        1
                  

Страницы