Auto-Oscillations of Anchored Vessels 



2. Basic assumptions 



The discussion of yaw and drift problem for the anchored 

 ships is based on the following assumptions : 



1. It is assumed that the coupled pitching and heaving 

 motions do not affect the ship's movement in the horizontal plane. 



2. The magnitude of hydrodynamic forces is taken as in- 

 dependent of athwartship inclinations. 



3. In the estimation of inertial forces the vessel is con- 

 sidered to be symmetric not only about the centerplane but also about 

 the athwartship plane, and the center of gravity to be located in the 

 athwartship plane. 



4. In predicting the noninertial forces and moments acting 

 on the vessel use is made of steadiness hypothesis. It is also assumed 

 that the ship's movement is so slow that the anchor chain inertia forces 

 can be neglected when determining the tension of the chain. 



3. Differential equations of motion 



According to [ 1 J the differential equations of the ship's 

 horizontal motion in the body coordinate system £ Oj 77 can be writ- 

 ten as follows : 



(m+ X n ) i - (m+ X 22 ) V, /§ = F^ , 

 (m + X 22 ) v + (m + X H ) V^ |S = F77 , 

 (Y+ X 66 )0- ( X n - X 22 ) Vr, . V£ = M. (2) 



The right-hand side of equations (2) could most convenient- 

 ly be written as the sums 



Ft = -P - P, +P V , 

 * a£ h£ H 



F « = - P - R, „ - P 



' ar, h£ Tr, 



M = M - M, - M T . (3) 



a h T ' 



1083 



