14.02.2013 Views

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

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

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

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

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

_ _<br />

YC −15<br />

ZC −15<br />

B<br />

( A ≤ 10 ) ∧ ( A ≤ 10 ) ⇒ Φ : = 0<br />

22.5.10 Cartesian to Euler Acceleration<br />

b<br />

22.5-9<br />

b<br />

A<br />

Equation 22.5-56<br />

D2X_TO_D2E takes the PVA of point (b) with respect to point (a), the<br />

origins of frames (A) and (B) respectively, returning the Euler acceleration<br />

of (B) with respect to (A), assuming that the Euler roll angle is zero.<br />

− 2 ⋅ Θ&<br />

B<br />

A<br />

D2X_TO_D2E<br />

B A A A<br />

( E , P , V , A )<br />

&<br />

( ) ( ) 4<br />

hA 2 B<br />

hA −<br />

P ⋅ Ψ&<br />

& : = ϕ&<br />

− 2 ⋅ ϕ ⋅ ϕ ⋅ P<br />

⋅<br />

a,<br />

b<br />

A<br />

2<br />

A<br />

b<br />

1<br />

b<br />

2<br />

b<br />

a,<br />

b<br />

Equation 22.5-57<br />

Equation 22.5-58<br />

ZA<br />

2<br />

A A Pb<br />

1<br />

ZA hA<br />

( P V ) ⎜ ⎛ ϕ ⎞<br />

• + ⋅ ϕ&<br />

− ⎜ ⎟ ⎟<br />

− A ⋅ P<br />

ϕ&<br />

1<br />

b<br />

ϕ<br />

ϕ<br />

1<br />

2<br />

b<br />

P<br />

P<br />

2<br />

a,<br />

b<br />

hA<br />

b<br />

XA<br />

b<br />

⋅ Θ&<br />

&<br />

⎛<br />

⎜<br />

⎝<br />

B<br />

A<br />

XA<br />

b<br />

1<br />

: =<br />

⎜<br />

⎝<br />

P<br />

YA<br />

b<br />

hA<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 />

XA<br />

b<br />

XA<br />

b<br />

YA<br />

b<br />

YA<br />

b<br />

: = P ⋅ A + P ⋅ A +<br />

ϕ&<br />

2<br />

XA<br />

b<br />

YA<br />

b<br />

YA<br />

b<br />

: = P ⋅ A − P ⋅ A<br />

⎟<br />

⎠<br />

YA<br />

b<br />

XA<br />

b<br />

⎞<br />

⎟<br />

⎠<br />

( ) 2 hA<br />

V<br />

XA<br />

b<br />

b<br />

b<br />

b<br />

Equation 22.5-59<br />

Equation 22.5-60<br />

Equation 22.5-61<br />

Equation 22.5-62<br />

Equation 22.5-63

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!