Инерциальная навигация
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Λ= λ1 + iλ + jλ + kλ
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Λ = λ1 + λ |
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λ = iλ |
+ jλ |
+ kλ |
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+ ey λ |
+ ez λ |
Λ = λ1 + iλi! |
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λi = exλ |
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λi / / % .
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A = α + ia!
B = β + ib!
% / / C,
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A ◦ B = C = γ + ic ! γ = αβ − a · b! |
c = αb + βa + a × b' |
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A / / /
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a b = axbx + ay by + az bz !
× − − −
a b = (ay bz az by)ex + (az bx axbz )ey + (axby ay bx)ez '
B % , / /
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a = axex + ay ey + az ez !
b = bxex + byey + bz ez !
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◦ · − ×a b = a b ia b!
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Λ = λ1 + iλi + ελε + εiλεi!
; εi = iε / /
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! 0
ε' ! / /
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0 ε / . % , .!
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λ1 + iλi! % , . :
λε + iλεi'
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iλi + εiλεi / 3 / :
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Λ = λ1 + λ1 |
+ iλi + iλi' |
A / @ 0 λ1
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λ1! λi λi!
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. λ1 + λ1 |
! λi + λi! |
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ex = −ii |
ey = −ij |
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ez = −ik |
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iε = εi' A 0
@ / /
0 / / 0
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Λ = λ1 + λ1 |
+ iλi + iλi + ελε + ελε + εiλεi + εiλεi' |
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scal Λ = λ1 + iλi + ελε + εiλεi |
% / ,= |
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vect Λ = λ1 |
+ iλi |
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+ ελε + εiλεi |
% / ,= |
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real Λ = λ1 + λ1 + ελε + ελε |
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% / 3 ,= |
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imag Λ = λi + λi |
+ ελεi + ελεi |
% / ,= |
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main Λ = λ1 + λ1 + iλi + iλi |
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% / ,= |
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dual Λ = λε + λε |
+ iλεi + iλεi |
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% / ,= |
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Λ |
∞ |
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Λk |
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k |
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%0 ,= |
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exp Λ = e = |
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k! |
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=0 |
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sin Λ = (eiΛ − e−iΛ)/(2i) |
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% ,= |
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cos Λ = (eiΛ + e−iΛ)/2 |
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% ,= |
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tg Λ = sin Λ/ cos Λ |
% ! cos Λ,= |
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sh Λ = (eΛ − e−Λ)/2 |
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% ,= |
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ch Λ = (eΛ + e−Λ)/2 |
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% ,= |
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th Λ = sh Λ/ ch Λ |
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% ! ch Λ,= |
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˜ |
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Λ = λ1 |
− λ1 |
+ iλi − iλi + ελε |
− ελε + εiλεi − εiλεi |
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% ,= |
¯ |
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Λ = λ1 |
+ λ1 |
− iλi − iλi + ελε |
+ ελε − εiλεi − εiλεi |
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% ,'
I ! /
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+
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¯ |
¯ |
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Λ1 ◦ Λ2 = Λ2 |
◦ Λ1' |
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◦¯ ¯ ◦
ΛΛ = Λ Λ'
6 .
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◦ |
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= Λ2 |
Λ1' |
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Λ1 ◦ Λ2 |
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˜ ˜ |
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Λ ◦ Λ = Λ ◦ Λ = ||Λ|| |
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||Λ1 ◦ Λ2|| = ||Λ1|| ||Λ2|| |
. ! 0
||Λ||' > / / ||Λ|| / .
! |Λ| = ||Λ|| : %
|Λ| / . ,! / %
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2 / / / 3 /
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Λ−1 = ||ΛΛ||! (Λ1 ◦ Λ2)−1 = Λ−2 1 ◦ Λ−1 1'
; !
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