HW4soln - EAS 4101 S08 HW solutions 02/22/08 4th Homework...

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EAS 4101 S08 HW solutions 1/10 HW#4 02/22/08 4 th Homework 1. (1.2 Anderson) Starting with Equations (1.7), (1.8), and (1.11), derive in detail Equations (1.15), (1.16), and (1.17). () ( ) ()( ) ) ' cos sin cos sin cos sin ' ' TE TE uuu lll LE LE TE TE ul u l LE LE TE TE u l LE LE Np d s p d s ds dx ds dy p d x d y p p p d x d y θτ θ θτ θ ττ ∞∞ =− + + = + + + + ⎡⎤ ⎣⎦ ∫∫ Divide by 1 qS qc = 0 '1 1 11 lu TE TE u l LE LE cT E np p f f LE pp N dx dy qc c q q c q q cc c d x c c d y ⎛⎞ −− + + ⎢⎥ ⎜⎟ ⎝⎠ + + This is Eq. (1.15). ( ) ) ( ) 0 0 ' sin cos sin cos ' ' 1 1 TE TE uu u ll l LE LE TE TE u l LE LE TE c u l LE TE c u l LE TE ap p LE Ap d s p d s p d y d x p p p d y d x A dy dx qc c q q c q q c d y c + + + =−+ + + + + + 0 1 c ff d x c ++ This is Eq. (1.16).
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EAS 4101 S08 HW solutions 2/10 HW#4 () ( ) ( ) ( ) ( ) ' cos sin sin cos cos sin sin cos ' ' TE LE u u u u u LE TE ll l LE TE TE TE TE L E ul u l u l LE LE LE LE TE TE LE u l u l LE LE Mp x p y d s px py d s M pp x d x x d y y d y y d x M p p p p xdx xdy p θτ θ θτ θ ττ ∞∞ =+ ⎡⎤ ⎣⎦ +− + + + =− + + + + ∫∫ ( ) 22 2 0 2 '1 1 11 1 lc
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HW4soln - EAS 4101 S08 HW solutions 02/22/08 4th Homework...

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