Murthy 



VIII. FREE OSCILLATION IN WAVES 



We will now consider the case of an ACV moving at a constant 

 speed in a seaway composed of regular waves with their crests nor- 

 mal to the course of the craft. It is assumed that the craft has been 

 operating for a long time so that all the transients would have subsid- 

 ed. The craft would then undergo periodic oscillations in pitch, hea- 

 ve and surge with the same frequency as that at which the progressi- 

 ve waves are encountered. It is assumed for the purpose of this ini- 

 tial study that the seaway is composed of a single system of simple 

 harmonic waves of a particular frequency. An extension to motion 

 in an irregular seaway can then be made by using the methods of 

 spectral analysis. 



The velocity potential of the water will now be composed of 

 several terms as follows : 



*(x,y,z;t ; S, 0, e ) = «• + /3* flioo + R,., 1 *' 



[ 4 *0001 



1001 0101 



where 4> and ^* nlni are the steady potentials for motion in 



calm water discussed in Section 6; 



4> is the potential of the incident wave; 



3\ ~~i i- s tne potential of the wave diffracted from the side 



1001 u II . - 

 hulls; 



4> is the potential of the wave representing the disturban- 



ce of the incident wave by the air cushion; 



and <x is the encountered frequency of the regular waves. 



VIII. 1 Incident Wave Potential 



It has been shown in Reference 1 that the velocity potential of 

 a regular wave of amplitude a , circular frequency a and progres- 

 sing along the negative x-axis may be written in the form 



a 

 X 



(f) (lf) eXp [-kz + i(kx +% t + 7)] 



where the wave length 



160 



