Variational Approaches to Steady Ship Wave Problems 



where pg is a homogeneous solution, as is 4^2> 3^<^ ^2 ~ Vs* 

 Since B is also a measure of the total lift, this formula shows that 

 the homogeneous solution for the constant surface elevation influences 

 the lift, as we have easily verified by the reciprocity (4.8). [ 26] 

 It should be noticed that, in this case, the condition A = in (A. 18) 

 insures the continuity of the planing hull. 



Kotchin's function (A. 17) is also given in the form 



H(e) = - y^ (|)^x^ dS - J <j>,^ dy + 2L*(c}),'$d) , (4. 27) 



where "^^j has the boundary values 



and (4. 28) 



g^d = ^dx = - *ex °^ L 



^(jis called the diffraction potential. [23,26] Here, the second term 

 of (4,27) may be omitted as in (4.25). 



For a submerged body, there is no integration along L and 

 H may be written as 



H(e) = - J J (4>e + \)^y dS. (4. 29) 



Finally, for a pressure distribution, 



H(e) = 2p£*(p,5.), (4.30) 



where 



Cd=-|*ex. (4.31) 



V. CONCLUSION 



We have presented two variational principles for the boundary 

 VcLlue problena associated with the waves of a ship advancing at a 

 constant speed: The first is Flax's principle, which makes use of the 

 stationary character of the drag. This principle is useful only for 



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