3. Mathematical formulation
3.1. Governing equations
The equation for the translation of the center of mass of the ship body is given as;
where m represents the mass of the body, f is the resultant force acting on the body and v is the velocity of the center of mass. An angular momentum equation of the body is formulated in the body local coordinate system with the origin in the center of the body;
equation(2)
where M is the tensor of moments of inertia, ω is the angular velocity of rigid body, and n is the resultant moment acting on the body. The resulting force and moment acting on the ship