Gevassimov } Per shit z and Rakhmanin 



in the nonlinear relationships between the aerodynamic and hydrody- 

 namic forces and the kinematics of the ship's motion. 



For the purpose of making a detailed analysis of yawing and 

 drifting of anchored vessels this paper deals with the discussion of 

 forces acting on the vessel in the circumstances, and the derivation 

 of relevant differential equations of motion. In the derivation of these 

 equations great attention was given to determining the tension of the 

 anchor chain as dependent on the shifting of hawse-hole. 



The aerodynamic and hydrodynamic forces are defined in 

 accordance with the known results [_lj , L^J> L 3 J • The general 

 equations of motion obtained for an anchored ship are used for finding 

 her equilibrium positions and analyzing stability of the same. It is 

 shown that the main reason inducing the ship to yaw is instability of 

 her equilibrium position due to wind. Consideration is given to condi- 

 tions in which stability of equilibrium is ensured for anchored vessels 

 while periodic yawing and drifting is ruled out. 



1. Coordinate systems and Nomenclature 



To solve the problem under review, four coordinate systems 

 are used. Two of them are applied for the description of ship's motion 

 in the horizontal plane, viz. , the fixed coordinate system XOY with 

 OX-axis directed oppositely to the wind and the origin O which coin- 

 cides with the center of gravity (CG) of a non-diverted vessel, and 

 the body axis system £0*77 with 0< £ -axis directed forward and the 

 origin in CG. The Oj 77 -axis is directed to port side. 



Figure 1 shows the directions of coordinate axes and positive 

 directions of angle reading for the two systems. The notation B 

 denotes a point of the anchor chain breaking away from the ground, 

 H Q = initial position of the hawse-hole, H^ = current position of 

 the same. 



Two more coordinate systems (Figure 2) are required for 

 the description of the anchor chain positioning in space. One of these, 

 the z' Ax' system is situated in the plane of the anchor chain sag- 

 ging. The origin A is made coincident with the anchor lying on the 

 ground. The Az'-axis is directed vertically, while the horizontal axis 

 is coincident with the ground plane and directed to the hawse-hole H . 

 The other system of coordinates h 6 is characterized by the fact that 

 the vertical axis oh always passes through the point B where the 

 anchor chain breaks away from the ground, and that the origin O is 

 at a distance of 



1080 



