Unstable Motion of Free Spar Buoys in Waves 



if s < 



A 



where F(s) = == 



2h, 



if < s «s h. 



if s > h. 



Let us assume that the wave amplitude be sufficiently 

 small so that s ^ h always . It is then possible to determine the 

 expression relating half the amplitude s of s (t) to half the ampli 

 tude j . of the wave by means of the optimum linear operators the- 

 ory [ 11 ] .For the type 1 buoy , one obtains : 



(II-6.3) 

 s . 



> (m+m zz ; a- 2 - pg S(o) C k H Qo (k)l + a 2 Nzz 



- ir — I 



I 



V 



-I 2 



pgS(o)-cr (m+mzz) - 



3TTh 2 PgS( ° )s A 



+ <r Nz 



(?>' 



For the type 12 buoy one has 



if s < h^ 



F(s)=^/s - 



dy-hP + 3(h 2 -hJ2 



if h 1 < s < h 



h 2+ 2h, 



if s >. h. 



1041 



