Auto-Oscillations of Anchored Vessels 



which corresponds to the longitudinal component . 



P a t of the aero- 

 dynamic force for = <p = . The tension increment A T is 

 estimated by the hawse-hole shifts AX' in the course of drifting or 

 yawing of the vessel. The curve of T against A X' plotted with 



allowance for the chain line characteristics is presented in the dimen- 



To 

 sionless form in Figure 4 for the case when K_ = ■»,. TT =0 . In all 



WHh 



other cases the relationship of A K = f( AX') is easily determined, 

 using the same figure, by shifting the origin along the curve to the 

 point where the latter is intersected by the straight line K = K . 



7. The final form of differential equations of motion 



Taking into account the results given above and conver- 

 ting the equations (2) to the form where the coefficients for the 

 second derivatives of variables £ , r\ , and are equal to unit, 

 the set of differential equations of motion for an anchored vessel in 

 the presence of wind and current can be presented in the following 

 final form which will be convenient for further analysis : 



£ - P t V 0+P t , H{ +P t ,V Cos( a + 0) Cos( a + 0) 

 £ 1 V £ £ I I £ Z o o i o ' 



- P AKCos( + <P ) = P V 2 Cos( + <p ) - P V 2 Cos , 



£3 U U 



J?+P Vt|8+P„^|^|-P„V Sin( a + ) Sin( a + ) + 

 r?ls 17 3 I I 17 3 o o I o I 



+ P A A X Sin( + <p ) = - P B V 2 Sin( + tp ) + P , V 2 Sin , 

 tj4 »? 5 TJo 



0+ P^ j V^ Vr, + P I j8 |+ P ARSin( + <p) = 



= P A ^ Sil1 P ~ P C V2 l ^ l Sil1 Z 3 - P « ^ V2 Sill ( ^ + * ) + 



f(4 p D 'I (3D 



+ P V 2 Cos( + <p) +-P AKCos( + *>) 



>(18) 



In equations (18) the values of CG velocity. projections V£ and 

 V jj are determined from formulae (4) and the following designat- 

 ions are used : 



1087 



