Understanding and Prediction of Ship Motions 



Wave Elevation observed Time ~ 



Roll Motion observed 



r8°P 

 [I' 



L8°S 





\-ApJ 



V t/ v/ 



Vf V V 



Wave Elevation 



observed rou /m 



Ti 



lOsec 



i^^.- R°P observed T— 20% x by Founer irans afWW U), o by h .from R„ -h , * R., 



Motion r" ^ \ '^ r, 



I ^8 S I I : 1 I i 



Figure 16 



such as an analogue computer can be used in addition to the general purpose 

 computer. 



3. ON THE EFFECTS OF NON-LINEAR DAMPING 

 ON CALCULATION OF THE SPECTRUM [11] 



When the irregular input, for example the sea waves for the ship, can be 

 considered as a Gaussian process, the output of a linear system, such as the 

 linear oscillation of ship, is also a Gaussian process and can be expressed 

 using the spectral expression. 



y(t) 





dZ(co) 



E[dZ(co) dZ(co')] = dSyy(aj) ?,(co-co') 



Syy(a;) = |H(a;)| S^^(a;) 



When a non-linear component is included in the response character, the output 

 is no longer Gaussian, and cannot be expressed by the spectral form which 

 premises the superposition theory. 



Even for that kind of case, the autocorrelation function as 



115 



