Инерциальная навигация
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Tt+dtRr+dr ◦ Θ + = (TtRr ◦ Θ ) ◦ (TδtΘ )' ϑ dϑ ϑ δϑ
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Tt+dtRr+dr ◦ Θ + = TtRr ◦ Θ TδtΘ = TtRrTδtΘ ◦ Θ = ϑ dϑ ϑ δϑ ϑ δϑ
= TtTδtRr ◦ Θ ◦ Θ = (TtTδt)(Rr) ◦ (Θ ◦ Θ )
ϑ δϑ ϑ δϑ
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Tt+dt = TtTδt!
Rr+dr = Rr!
Θ + = Θ ◦ Θ
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Tt+dtRr+dr ◦ V + ◦ Θ + = (TtRr ◦ V ◦ Θ ) ◦ (TδtV Θ )'
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Tt+dtRr+dr ◦ V + Γα+dαΘ + ◦ Gg+dg Ww+dw = ψ dψ ϑ dϑ
= (TtRr ◦ V ΓαΘ ◦ Gg Ww) ◦ (TδtV ΓδαΘ Gδg Wδw)' ψ ϑ δψ δϑ
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ΛIE(τ +dτ ) = ΛIE(τ ) ◦ ΛE(τ )E(τ +dτ ) '
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Tt+dtRr+drVv+dv ◦ Θ + = (TtRrVv ◦ Θ ) ◦ (TδtVδv Θ )' ϑ dϑ ϑ δϑ
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Q = exp(iϑ/2)
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RrTt = TtRr'
TtRr = RrTt'
Rr2 Rr1 = Rr! r = r1 + r2'
ΘQTt = TtΘQ' TtΘQ = ΘQTt'
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Vv ◦ Tt = TtRr Vv ! |
r = tv' |
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Tt ◦ Vv = VvRrTt! |
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Vv Rr = RrVv ' |
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Vv ◦ ΘQ = ΘQ ◦ Vv ! |
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τ+ ρ = Q ◦ (τ + ρ ) ◦ Q−1 + t + r + τ v!
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ρ = eiϑ/2 ◦ ρ ◦ e−iϑ/2 |
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TtRrVv ◦ ΘQTdτ Vadτ Θexp(iωdτ /2)'
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Tt+dtRr+drVv+dv ◦ ΘQ+dQ = Tt+dτ Rr+vdτ Vv+Q◦a◦Q−1dτ ◦ ΘQ◦exp(iωdτ /2)'
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t + dt = t + dτ !
r + dr = r + vdτ !
v + dv = v + Q ◦ a ◦ Q−1dτ !
Q + dQ = Q ◦ eiωdτ /2'
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ΛIE(τ ) = TtRrVv ◦ ΘQ / / .3
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dt = dτ !
dr = vdτ !
dv = Q ◦ a ◦ Q−1dτ ! dQ = iQ ◦ ωdτ /2'
F / / dτ ! / .
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dt/dτ = 1!
dr/dτ = v!
dv/dτ = Q ◦ a ◦ Q−1! dQ/dτ = Q ◦ (iω)/2'
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