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Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

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Appendix I / Utilities / Point Mass Kinematics<br />

_ _<br />

ϕ<br />

ϕ<br />

1<br />

2<br />

XA<br />

b<br />

22.5-8<br />

XA<br />

b<br />

YA<br />

b<br />

: = P ⋅ V + P ⋅ V<br />

XA<br />

b<br />

YA<br />

b<br />

YA<br />

b<br />

: = P ⋅ V − P ⋅ V<br />

YA<br />

b<br />

XA<br />

b<br />

Equation 22.5-46<br />

Equation 22.5-47<br />

E_RATES takes the VAJ of point (b) with respect to point (a), the<br />

gravitational acceleration at (b), and the orientation of frame (B) with<br />

respect to ENU LGA (A), returning the Euler rate, assuming zero incidence.<br />

Θ&<br />

B<br />

A<br />

C<br />

b<br />

≡<br />

Θ&<br />

E_RATES<br />

Ψ&<br />

C<br />

A<br />

C<br />

A<br />

B<br />

A<br />

: =<br />

≡<br />

V<br />

Ψ&<br />

C<br />

A<br />

ZA<br />

b<br />

B A A A ZA B<br />

( E , V , A , J , g , E&<br />

)<br />

⋅<br />

A<br />

: =<br />

V<br />

b<br />

XA<br />

b<br />

b<br />

⋅ A<br />

b<br />

b<br />

YA YA<br />

b − Vb<br />

hA<br />

Vb<br />

⋅ A<br />

A<br />

Equation 22.5-48<br />

XA<br />

b<br />

XA XA YA YA<br />

( V ⋅ A + V ⋅ A )<br />

b<br />

V<br />

b<br />

hA<br />

a,<br />

b ⋅<br />

V<br />

2<br />

a,<br />

b<br />

b<br />

b<br />

Equation 22.5-49<br />

−<br />

V<br />

hA ZA<br />

b ⋅ Ab<br />

2<br />

Va<br />

, b<br />

Equation 22.5-50<br />

( ) ( ) T<br />

C C XA YA ZA ZA<br />

0 Θ Ψ ⋅ A , A , A g<br />

A : = T<br />

+<br />

ϕ<br />

4<br />

3<br />

C<br />

b<br />

A<br />

A<br />

C<br />

A<br />

b<br />

C C A<br />

( 0 Θ Ψ ) J<br />

J : = T<br />

⋅<br />

YC<br />

b<br />

C<br />

A<br />

A<br />

A<br />

C<br />

YA C<br />

XA<br />

( T ( 2 ) ⋅ A − T ( 5 ) A )<br />

ϕ : = J + Ψ&<br />

⋅<br />

⋅<br />

C<br />

A<br />

A<br />

b<br />

b<br />

A<br />

b<br />

b<br />

b<br />

Equation 22.5-51<br />

Equation 22.5-52<br />

b<br />

Equation 22.5-53<br />

C YA C XA C XC ZC<br />

( T ( 3 ) ⋅ A − T ( 6 ) ⋅ A ) + Θ&<br />

⋅ A J<br />

: = Ψ&<br />

⋅<br />

+<br />

A<br />

b<br />

YC −15<br />

ZC −15<br />

( A > 10 ) ∨ ( A > 10 )<br />

b<br />

rC 2 B<br />

YC<br />

ZC<br />

( Ab<br />

) ⋅ ΦA<br />

: = Ab<br />

⋅ ϕ4<br />

− Ab<br />

⋅ ϕ3<br />

A<br />

b<br />

b<br />

A<br />

b<br />

Equation 22.5-54<br />

⇒<br />

Equation 22.5-55<br />

b

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