Unstable Motion of Free Spar Buoys in Waves 



( 2 ) 

 If it is assumed that N = , equation (II- 5. 3) becomes 



(II-7.1) 



m+myy 



s (t) is given by equation (II- 5. l) with s (t) = Z (t) - J (t) 



Let us assume now that s (t) is a sinusoidal function . 

 This assumption is rigorously verified for the type 11 and 14 buoys., 

 since equation (II- 5 . l)is then linear . It is only an approximation 

 for the type 1 and 15 buoys , since equation (II- 5. 1) is then nonlinear 

 Furthermore , let us assume that s (t) does not take too large a 

 value , so that 



s (t) = s cos a~ t <; h 



-A. u 



Equation (II-7. l) can then be written as : 

 d2 y 



- — ^- + ( p - 2 q cos 2 x ) y - 



dx2 r 



y ^J' p(t) 



A I 



X = 2 T * 



p = _L ( g 



2 



P 2 ) 



4* 



f ,e 



- 4 



q = 5s 



rr¥ 



1053 



