434. Alex Goodman 
z = w- U6. (A9) 
o 
Also, since w/U = @ (for small angles), Eq. (A9) can be restated as 
z = U(a-@6). (A10) 
o 
As stated previously, the primary condition that must be satisfied for pure pitching mo- 
tion is that © = 0. Equation (A10), therefore, reduces to 
Ze at UE) (A11) 
Substituting Eqs. (A5) and (A7) into Eq. (A11) results in 
CTR eA a's 
— + — cos ¢.] cos wt + — sin ¢, sin ot| 
U X, a, s ay s 
one ay i, 
= (1 = ay cos +) ‘Sin wt + a, sin ¢, cos at| : (A12) 
Equating sine and cosine terms results in 
wx wx a5 a 
a cos". = §sin'p)- =)'= (3) 34) 2 (A13) 
(=) Ls Dy a 
cos $, t\7,]sin ¢, = (3*) . (A14) 
Solving Eqs. (A13) and (A14) for sin @, and cos ¢, results in the following relation- 
ships: 
1 
sin ?s = RR oR eae (A15) 
=) [a+ FA | 
= Dra enn 
2 
amar ona 4 
ag ( % Cr} (A16) 
cos ¢, = Srrcreree renew a BP e 
Ait = 
A boundary condition that must be satisfied is that sin @, cannot be greater than one. 
Therefore, 
