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

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

Appendix I / Utilities / Axis Transforms<br />

_ _<br />

The Jacobian elements with respect to P ZA ,<br />

a,<br />

b<br />

3<br />

a,<br />

b<br />

B<br />

A<br />

ZA<br />

ZA XA<br />

( 1 ) ∂ P : = − P P<br />

P ⋅ ∂ T<br />

⋅<br />

3<br />

a,<br />

b<br />

B<br />

A<br />

22.4-15<br />

b<br />

ZA<br />

ZA YA<br />

( 4 ) ∂ P : = − P P<br />

P ⋅ ∂ T<br />

⋅<br />

B<br />

A<br />

b<br />

( ) ( ) 2<br />

ZA<br />

ZA<br />

7 ∂ P : = 1 P P<br />

P ⋅ ∂ T<br />

−<br />

b<br />

b<br />

b<br />

b<br />

b<br />

b<br />

Equation 22.4-105<br />

Equation 22.4-106<br />

a,<br />

b<br />

hA 3 B<br />

ZA<br />

YA ZA<br />

( P ) ⋅ ∂ T ( 2 ) ∂ P : = P ⋅ P<br />

b<br />

A<br />

hA 3 B<br />

ZA<br />

XA ZA<br />

( P ) ⋅ ∂ T ( 5 ) ∂ P : = − P ⋅ P<br />

b<br />

A<br />

∂ T<br />

B<br />

A<br />

b<br />

ZA ( 8 ) ∂ P : = 0<br />

b<br />

b<br />

b<br />

b<br />

Equation 22.4-107<br />

b<br />

Equation 22.4-108<br />

b<br />

Equation 22.4-109<br />

Equation 22.4-110<br />

ZA<br />

XA<br />

( ) ⎜<br />

⎛ ZA 2<br />

3 ∂ P : = P ⋅ ( P ) ⋅ ϕ − ⎟<br />

⎞<br />

b<br />

b<br />

b<br />

⎝<br />

⎠<br />

hA<br />

B<br />

Pb a,<br />

b A<br />

1<br />

⋅ P ⋅ ∂ T<br />

1<br />

Equation 22.4-111<br />

ZA<br />

YA<br />

( ) ⎜<br />

⎛ ZA 2<br />

6 ∂ P : = P ⋅ ( P ) ⋅ ϕ − ⎟<br />

⎞<br />

b<br />

b<br />

b<br />

⎝<br />

⎠<br />

hA<br />

B<br />

Pb a,<br />

b A<br />

1<br />

⋅ P ⋅ ∂ T<br />

1<br />

P<br />

a<br />

, b<br />

⋅ ∂<br />

T<br />

B<br />

A<br />

P<br />

P<br />

ZA<br />

hA<br />

ZA b b<br />

( 9 ) ∂ Pb<br />

: = − 2<br />

hA<br />

b<br />

P<br />

P<br />

a,<br />

b<br />

Equation 22.4-112<br />

⋅ P<br />

ZA<br />

b<br />

Equation 22.4-113<br />

Expressing the transform components in terms of the direction cosines,

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

Saved successfully!

Ooh no, something went wrong!