Linearized Potential Flow Theory for ACVs in a Seaway 



and 



z' = (x - x) sinG - (z - h - z) cosG - h 



G G 



so that x' and z' are functions of x, z and the displacement parame- 

 ters x, z, which are themselves simple harmonic functions of the 

 time. However, y' is always equal to y in coplaner motion and does 

 not depend upon t. 



We may therefore write, 



Also 



at 9t i l ' j 



= 8 



ax> a h i + az> a h i 



l a t ax 1 at a z* j 



= 5 < — sinG -— cosG - (z 1 - z ) 9 1 



ill 



a x- 



+ -j x' 9 - — sin9 - — cos9 > 



a i i 



-r — = d^— h (x' , z 1 ) 

 a x ox 1 



Lax a x " 



= 5 CCv 



L ox 



a h 



a z 



a h i . Q a h i 



s9 -r — - + sinQ 



; 



azH 



aH . aH 



ay ay' 



= - 1 



aH 



- 6 i- z K*'.->-Etf' 



a xl i 

 ax 1 



a z - a h i 



az az- j 



= 8 



- sm9 - — r + cos9 



ax- 



az*J 



129 



