Davis and Oates 



Expanded Equations 



The expanded equations, including the expressions for the basic forces and 

 variations due to speed perturbations are as follows: 



Heave 



- [Cl^^,/Iy)-(L)] ^°^ r^L) -[CL^^_^^(hR)a^R)] COS r^^^ - Cl^. (71) 

 Surge 



2mu+PCl = Cj (1 + k)ri - n(u - u^) 



o o L -^ 



- CD(R)(hR)[l + 2(G-G^^R))] -KD.^^^(h(R))[a^^j^^(l + G-G^^K)) + a^^j^J' 



- C^ Ivl . (72) 

 Pitch 



- Cd , (hF)"^(F)(drag) + C, (h) + C, (h(e))^ + (izz-ixx)<^^- ^^^^ 



(F)(total) ^.-iv t=/ o a ^' 



626 



