Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 35 стр.

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cÈÏ Ëã
39
{Ë}º¯©ÒãÒÓˮөËº¹Ë¯ÈÒÒ°ÓÒäÒ
~ÈÈÈ

Ëj wjéjssnsvméjuun wvxzévnt lkn xqxznu rvvélqtjz ³xzjéj¹´
},,{
21
→→
ggO
q³tvkj¹´
},,{
21
→→
′′′
ggO
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uyswnén}vljkéjjíqn³tvkn´rvvélqtjz·néno³xzjén´nxsq
→→
′
=
′
OOg
1
q
′
=−
→→
gg
21
1
2
cËËÓÒË

′
→
g
2

′
O

g
2
→

′
→
g
1

O

g
1
→
èqxytvr
jÏ °mº®°m ¹È¯ÈããË㺯ÈääÈ ÓȲºÒä °ºº
ÓºËÓÒ« m©¯ÈÎÈÒË mË}º¯© Ù°ȯººµ
ÈÏÒ°È˯ËÏÙÓºm©Ëµ
.2
2
212
21
→→→
→→
′
+
′
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′
−=
ggg
gg
ºÈäÈ¯ÒÈ¹Ë¯Ë²ºÈ
22
10
−
−
=
S
È
0
1
2
1
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β
β
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vã˺mÈËãÓºm©¯ÈÎËÓÒ«ÙÓºm©²µ}ºº¯ÒÓÈ˯ËÏÙ°ȯ©ËµÒäËmÒ
+−=
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212
21
22
1
ξ
ξ
ξ
ξ
ξ
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12
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sincos
212
211
→→→
→→→
+−=
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+=
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eee
eee
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ϕϕ
ϕϕ
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β
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c È Ï  Ë ã                                                      39
{Ë}ˆº¯©ÒãÒÓˮө˺¹Ë¯ÈÒÒ°ÓÒäÒ



    ~ÈÈÈ                        Ëj wjéjssnsvméjuun wvxzévnt€ lkn xqxznu€ rvvélqtjz ³xzjéj¹´
                                     → →                                                → →
                                   {O, g1, g 2 } q³tvkj¹´ {O ′, g1′ , g ′2 } rjrwvrjojtvtjéqxËjpzq{vé
                                   uys€wnén}vljk€éj jíqn³tvk€n´rvvélqtjz€·néno³xzjé€n´nxsq
                                    →      →       →       1→
                                    g1′ = O ′O q g 2′ = − g1 
                                                           2

    cËËÓÒË                                                                                   jÏ °mº®°ˆm ¹È¯ÈããË㺯ÈääÈ ÓȲºÒä °ººˆ
                                                                                               Óº ËÓÒ« m©¯ÈÎÈ ÒË mË}ˆº¯© Ù°ˆÈ¯ººµ
                                                                                               ­ÈÏÒ°È˯ËÏÙÓºm©Ëµ
                                                         →
                                                                                                
     g 2′                                                                               →                         →
    O′                                                                                                                               g1 =                − 2 g 2′
                         →                                          →                                                                                                  
     g 2  g1′                                                                                     →             →           →
                                                                                                                                     g 2 = − g1′ + 2 g ′2 .
    O                                                                                                                                      
                                                                                               
                                                              →                                 ‘ºÈäȈ¯Òȹ˯˲ºÈ
  g1                                                        
 
                                                     0 −1       β1   1
                                             S =          È    =   
 èqxytvr                     −2 2        β2   0
           
vã˺mȈËã Óºm©¯ÈÎËÓÒ«ÙÓºm©²µ}ºº¯ÒÓȈ˯ËÏÙ°ˆÈ¯©ËµÒäË ˆmÒ
           
                                                                                   ξ1′ =       −ξ 2 + 1
                                                                                                        
                                                                                  ξ 2′ = −2ξ1 + 2ξ 2



Ë¯Ë²ºäË΂º¯ˆºÓº¯äÒ¯ºmÈÓÓ©äÒ°Ò°ˆËäÈäÒ}ºº¯ÒÓȈÓȹ㺰}º°ˆÒ


                                                                                                                                                                 → →                            →      →
      cÈ°°äºˆ¯Òäm˺¯ˆºÓº¯äÒ¯ºmÈÓÓ©Ë°Ò°ˆËä©}ºº¯ÒÓȈ {O , e1 , e 2 } Ò {O ′ , e1′ , e2′ } 
ºã‚ÒäÁº¯ä‚㩹˯˲ºÈã«°ã‚È«¹º}ÈÏÈÓÓººÓȯҰ
      
      
      jÏ˺äˈ¯ÒË°}ÒºËmÒÓ©²°ººˆÓº ËÓÒ®
      
                                                                               →           →                    →
                                                                               e1′ = e1 cos ϕ + e 2 sin ϕ
                                                                               →            →                   →
                                                                                                                                
                                                                              e 2′ = − e1 sin ϕ + e 2 cos ϕ
                                                                                                       
                                                                     cos ϕ           − sin ϕ                                 →             β1
¹ºã‚ÈËääȈ¯Ò‚¹Ë¯Ë²ºÈ                                                                           ÒË°ãÒ OO ′ =                        ˆºÙ°ˆÈ¯©Ëµ}ºº¯ÒÓÈ
                                                                     sin ϕ            cos ϕ                                                β2
                  
                  

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