Инерциальная навигация
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ΛIE(τ ) ◦ ΛE(τ )E(τ +dτ ) = ΛIE(τ +dτ ) = ΛEI (τ )E(τ +dτ ) ◦ ΛIE(τ )
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%-E8,! / -E8
-E8 . = E(τ ) E(τ + dτ ) : -E8!
IE(τ ) |
IE(τ ) |
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= ΛE(τ ) |
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I E(τ )! .3 |
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/! / .3 I E(τ )= ΛIE(τ +dτ ) |
IE(τ +dτ ) |
IE(τ +dτ ) |
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= ΛE(τ +dτ ) |
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: I E(τ + dτ ) :
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E(τ )E(τ +dτ ) |
E(τ )E(τ +dτ ) |
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ΛE(τ )E(τ +dτ ) = ΛE(τ ) |
= ΛE(τ +dτ ) |
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E(τ ) E(τ + dτ ) : =
ΛEI (τ )E(τ +dτ ) : E(τ ) E(τ + dτ )
. -E8 : ' 6
! 3 ΛEI (τ )E(τ +dτ ) = ΛE(τ )E(τ +dτ ) = 0
/ / 0 /
. / @ δ ΛE(τ )E(τ +dτ ) δ ΛE(τ )E(τ +dτ )
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(V ◦ Θ ) ◦ (V Θ ) = V + ◦ Θ + = (V Θ ) ◦ (V ◦ Θ )'
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(TtRr ◦ V Γγ Θ ◦ Gg Ww) ◦ (TδtRδrV Γ1+δγ Θ Gδg Wδw) = ψ ϑ δψ δϑ
= Tt+dtRr+dr ◦ Vψ+dψ Γγ+dγ Θϑ+dϑ ◦ Gg+dgWw+dw = |
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= (Tδ tRδ rV |
Γ1+δ γ Θ Gδ gWδ w) |
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r × v |
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Tt2Tt1 = Tt! |
t = t1 + t2' |
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RrTt = TtRr' |
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TtRr = RrTt' |
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Rr2 Rr1 = Rr! |
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r = r1 + r2' |
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Vv ◦ Tt = TtRrVv! |
r = vt' |
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Tt ◦ Vv = VvRrTt! |
r = −vt' |
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Vv Rr = RrVv ' |
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RrVv = Vv Rr ' |
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v = v1 + v2' |
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ΛIE1(τ1+dτ1) = ΛIE1(τ1) ◦ ΛE1(τ1)E1(τ1+dτ1)'
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Tt1+dt1Rr1+dr1 Vv1+dv1 = Tt1Rr1 Vv1 ◦ Tdτ1Va1dτ1 '
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dt1 |
= 1, |
dr1 |
= v1, |
dv1 |
= a1' |
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dτ1 |
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dv1 |
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dt |
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