During wearing maneuver the tall ship shows coupled motion of yaw and roll. In order to analyze this kind of motion, it is convenient to use the equations of motion expressed by the horizontal body axes system introduced by Hamamoto et al. [2]. The origin of this coordinate system is on the C.G of the ship as shown in Figure 5. The x axis lies along the centerline of the ship on the still water plane and is positive forward. The y axis is positive to starboard in the still water plane. The z axis is positive down. In this coordinate system, the maneuvering motion of the ship and aero/hydro-dynamic forces acting on it can be expressed easily. Both added masses and added moments of inertia which are referred in the body axes fixed on the ship, can be obtained by the coordinate transformation.

　

　

 Excluding both pitching and heaving motions, the equations of motion are expressed in four simultaneous differential equations[3]. The equations are expressed thoroughly as follows :

　

surge:

　

　

　

　

　

 where u and v are velocity components of the ship along x and y-axis of the horizontal body axes, and ψ and Ψ are the roll and yaw angles defined as Euler's angles. In the Equation (1), Xo is hull resistance in upright condition. In the terms of the right hand side of the equations. XH〜NH are the hydrodynamic forces and moments acting on the hull. XR'〜NR'are the hydrodynamic coefficients of the rudder. Xs'〜Ns are the aerodynamic coefficients of sail defined as in Figure 9.