Auto-Osoillations of Anchored Vessels 



The set of equations thus obtained makes it possible not only to 

 define the equilibrium position of an anchored ship, with the wind 

 and current prescribed, but also to follow the dependence of this 

 position on the ship's particulars and the coordinates of the hawse- 

 hole. 



In the absence of current (V = ) this set of equations 

 is reduced to a single equation which determines the angle of equi- 

 librium : 



( 6 + 6 ) - "JU 



2tt 



a{ 



C° 

 ar? 



hh 



s £ 



hh 



Sin + 



(22; 



Cos 0=0 



It follows from equation (22) that the angle is dependent on 

 the coordinates of the hawse-hole £ 



hh 



and tj , , and the lengthwise 

 position of the centre of sail area dg . The ordinate V ^h has no 

 appreciable effect on the equilibrium position of the vessel. Setting 



1^ = we shall find that angle Q is equal to zero if the hawse- 

 hole abscissa satisfies the condition 



ho 



C 



C° v o 



6 )L 



(23) 



Otherwise angle O is defined from the formula 



: hh 



/3 



2 7T ( 



+ s 



o s 



C° 



arj 



(24) 



9. Stability of equilibrium positions 



A vessel may stay in the positions of equilibrium as 

 defined above only on condition that these positions are stable. 

 Considering the stability of the vessel with respect to yawing in con> 

 formity with A.M. Liapunov's general theory [4] , the following 

 criterion of stability can be obtained : 



1089 



