Derm 



Equation (II-7. 2) is a Mathieu equation [ 18 J . Its 

 stability chart is recalled in Figure 25 . The values of fi , 6 and 

 8 for the buoys type 1 , 11 , 14 and 15 are given in the following 

 table . 



Except for type 11 and 15 , the values of B are quite 

 small , and the stability map of equation (II- 7.2) is thus as a first 

 approximation the stability map of equation (II- 7.1) . 



The experimental points obtained for buoys type 1 and 

 14 are shown on figure 25 , where it can be seen that they agree 

 rather well with the theory . 



When the wave height stays constant and that the frequen- 

 cy varies , the point of coordinates (p , q) moves in the stability 

 plane (p - q plane) : when f increases , a, decreases and the point 

 moves to the left . To have an idea of the phenomenon let us replace 

 the curves (a ) and (b ) by their tangent at the origin . Instability 

 occur when : 



- (p - 1)" > 



i.e. when 



y77 



a s A 



TT 2 



^f : 



8 s 



W 



In particular for the types 1 and 14 , the experimental 

 values of the relative motion s are small in the vicinity of 2 f q . 

 Therefore there will not be any roll if the frequency is larger than 



2 V 



1054 



