Joosen 

 Ht - VH,^ + 0,^H,^ + 4>yiiy^ + c^.^H,^ = (2.5) 



where H(x, y, z, t) = is the part of the ship under the water surface at the time 



t . 



The following dimensionless quantities are introduced: 



Li ^ L* Li Y D 



''i=^^i' yi=e-2^i' ^1=^-2^1' ^^T' 



(2.6) 



The displacements and rotations of the ship are supposed to be small and 

 consequently the problem can be linearized. 



, -7 - icot L y -i<i)t (2 7) 



41^ ^ a^^e , Zg = a- ^0 e . V^-'/ 



H can be written in dimensionless form as 



H(^,77,^,t) = e{T)- f(^, 0} - ^do-^o^) f^e'^"* + 0(ea) . (2.8) 



Because of the linearity of the problem it is possible to split up 0(xj, y^, z^, t) 

 in a time-dependent term and a term independent of t: 



0(x,,y,,z,,t) . e^£-,,(^,,.,„^,) + e2|.^,(^,,^„C,)e-i-^ (2.9) 



After substitution of (2.8) and (2.9) into (2.3)-(2.5) and omitting higher order 

 terms the conditions for $j and ^^ are obtained: 



A^j = , Aip2 = (2.10) 



-e^L ~^2 + ^/^o ^2f j^, + 2iey^2^^ + ?2?^ = (^-H) 







(2.12) 



170 



