Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 51 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

cÈÏ Ëã
55
¯ºÒÏmËËÓÒ«mË}º¯ºm

(,) ( , ) (, )
′′
== = = =
→→ →
=
→
=
→→
=====
∑∑ ∑∑∑∑∑
ee e e ee
i t it si s
s
pt p
p
si pt s p
ps
pi st sp
ps
si st
s
δσ σ σσ σσδσσ
1
3
1
3
1
3
1
3
1
3
1
3
1
3

|äËÒä º ¹ºãËÓÓ©Ë ÏË° °ººÓºËÓÒ«
σσ δ
si st
s
it
it
==
=
∑
1
3
123;, ,,
«mã«°«
°mº®°mºääÈ¯Ò©¹Ë¯Ë²ºÈ
S
ººÓººº¯ºÓº¯äÒ¯ºmÈÓÓººÈÏÒ°È}¯ºä
sÈ®Ëä˹˯m©¯ÈÎËÓÒËã«ãÒÓˮӺ®}ºäÒÓÈÒÒ
332211
η
ξ
η
ξ
η
ξ
++
mÈÏÒ°Ë
{, , }
′′′
→→→
eee
123
Ò°¹ºãÏ«ÏÈmÒ°Ò亰Ò äËÎ}ºä¹ºÓËÓÈäÒäÈ¯Ò©¹Ë¯Ë²ºÈÒº¹¯ËË
ãËÓÒË°ÒämºãÈz¯ºÓË}˯È
ξ
ησ
ξ
ση
ξ
ησσ
ξ
ηδ
ξ
η
ss
s
si i
i
st t
ts
i t si st
sti
itit
t
ii
ii
==========
∑∑∑∑∑∑∑∑∑∑
=
′′
=
′′
=
′′
=
′′
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
()( )

ºãËÓÓºË ¯ÈmËÓ°mº º}ÈÏ©mÈË ÒÓmȯÒÈÓÓº° °ää©
332211
η
ξ
η
ξ
η
ξ
++
¹¯Ò ÏÈäËÓË
ºÓººº¯ºÓº¯äÒ¯ºmÈÓÓººÈÏÒ°È¯Òä}ºº¯È«äºÎË©¹ ¯ÒÓ«ÈmªÒ²ÈÏҰȲ
ÏÈº¹¯ËËãËÓÒË°}È㫯Ӻº¹¯ºÒÏmËËÓÒ«mË}º¯ºm
c È Ï  Ë ã                                                      55
¯ºÒÏmËËÓÒ«mË}ˆº¯ºm



              → →                              3         →       3             →            3        3                   →    →            3     3                              3
            (ei′ , et′ ) = δit = ( ∑ σ si e s , ∑ σ pt e p ) = ∑ ∑ σ si σ pt (e s , e p ) = ∑ ∑ σ pi σ st δ sp = ∑ σ si σ st 
                                            s =1                p =1                       s =1 p =1                                     s =1 p =1                             s =1
                                                                                                         
                                                                                                                                   3
                  |ˆäˈÒä ˆº ¹ºã‚ËÓÓ©Ë ÏË°  °ººˆÓº ËÓÒ«                                                                 ∑ σ si σ st =δit ; i , t = 1,2,3  «mã«                               ˆ°«
                                                                                                                                  s =1

°mº®°ˆmºääȈ¯Ò©¹Ë¯Ë²ºÈ S ºˆºÓººº¯ˆºÓº¯äÒ¯ºmÈÓÓºº­ÈÏÒ°È}¯‚ºä‚
       
       sÈ®ËäˆË¹Ë¯ m©¯ÈÎËÓÒËã«ãÒÓˮӺ®}ºä­ÒÓÈÒÒ ξ 1η 1 + ξ 2η 2 + ξ 3η3 m­ÈÏÒ°Ë
    → → →
{e1′ , e2′ , e3′ }  Ò°¹ºã ς« ÏÈmÒ°Ò亰ˆÒ äË΂ }ºä¹ºÓËӈÈäÒ äȈ¯Ò© ¹Ë¯Ë²ºÈ Ò º¹¯ËË
ãËÓÒË°ÒämºãÈz¯ºÓË}˯È
       
                       3                   3        3                   3                        3       3           3                      3     3                        3
                     ∑ ξsηs = ∑ (∑ σ si ξi′)(∑ σ st ηt′) = ∑ ∑ ξi′ηt′∑ σ si σ st = ∑ ∑ ξi′ηt′δit = ∑ ξi′ηi′ 
                      s =1                s =1 i =1                    t =1                     i =1 t =1          s =1                   i =1 t =1                      i =1
       
ºã‚ËÓÓºË ¯ÈmËÓ°ˆmº º}ÈÏ©mÈˈ ÒÓmȯÒÈӈӺ°ˆ  °‚ää© ξ 1η 1 + ξ 2η 2 + ξ 3η3  ¹¯Ò ÏÈäËÓË
ºÓººº¯ˆºÓº¯äÒ¯ºmÈÓÓºº­ÈÏҰȯ‚Òä}ºˆº¯È«äºÎˈ­©ˆ ¹¯ÒÓ«ˆÈmªˆÒ²­ÈÏҰȲ
ÏȺ¹¯ËËãËÓÒË°}È㫯Ӻº¹¯ºÒÏmËËÓÒ«mË}ˆº¯ºm
       

Страницы