McClure and Hove 



Appendix C 



POSITIONING MANEUVERS SIMULATION 

 (Computer Program Description) 



INTRODUCTION 



This appendix presents the mathematical representation of the motion of 

 the drilling platform moving over the surface of the sea under the control of the 

 automatic positioning system. Starting with prescribed initial position and ve- 

 locity and specified wind and current conditions, the equations of motion of the 

 vessel are integrated to determine the position and heading of the vessel as a 

 function of time. 



EQUATIONS OF MOTION 



The equations of motion of the vessel are as follows: 



MU = F^CX.Y.^P.U.V.R.U) 

 MV = Fy(X,Y,>I',U,V,R,V,R) 



I3R = M^(X,Y,>P,U,V,R,V,R) 

 where 



M = the mass of the vessel 

 I ^ = the mass moment of inertia of the vessel 

 u = the forward velocity of the vessel 



V = the lateral velocity of the vessel, positive to port 

 R = the angular velocity of yaw, positive to port 



X = the eastward displacement of the vessel from the hole 



Y = the northward displacement of the vessel from the hole 



^ = the heading of the vessel, measured counterclockwise from east 



F^ = the total longitudinal force on the vessel, positive forward 



Fy = the total lateral force on the vessel, positive to port 



M^ = the total yaw moment acting on the vessel, positive when producing 

 yaw to port. 



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