Schmitke and Jones 



solving the linearized equations of ship motion. Linearization of (l) 

 to (6) results in the following two sets of three coupled linear ordi- 

 nary differential equations : 



Longitudinal 



(10) 



Pitch : I0 = Mu + Mz + Mz + (M„ + U M ) 6 + M * 6 

 Y u z w 0ow " 



Heave :mz =Zu + Zz + Zz + (Z / +UZ)0+ Z* a d (11) 

 u z w 6 o w & 



Surge : m(u-g0) = Xu + Xz + Xz + (X fl + UX) 

 to v ° ' u z w 6 ow 



e + x' 



8 



(12) 



Lateral 



Sideslip : m(v + Ur + g4>) = Yv + Yr + Y*4> + Y ,4> (13) 



Roll : I 4> =Kv + Kr+ K'<t> + K 4> (14) 



x v r <p 4> 



Yaw : Ir = Nv + Nr+ N»0 + N </> (15) 



z v r (p 



where 



J 



t 



z = (w - u e) dt (16) 



o 



and the stability derivatives M u , M z etc. are listed in the Appen- 

 dix. 



The longitudinal modes of motion characteristic of passively- 

 stabilized surface-piercing hydrofoil ships consist of a lightly damp- 

 ed oscillation governed by ship pitching characteristics, a heavily 

 damped oscillation related to heave and a simple convergence arising 

 from surge -heave -pitch coupling. These are termed the pitch, heave 



302 



