Ship motion equations (6 DOF)

The 6-DOF ship motion equations describe rigid-body response in the three translations (surge x, sway y, heave z) and three rotations (roll phi, pitch theta, yaw psi). In linear seakeeping they are a coupled set, sum over j of (M_ij + A_ij) times eta-double-dot plus B_ij times eta-dot plus C_ij times eta = F_i(t), for i = 1 to 6, where M_ij is the rigid-body mass-inertia matrix, A_ij the frequency-dependent added mass, B_ij radiation damping, C_ij hydrostatic restoring, and F_i the Froude-Krylov plus diffraction exciting force. Lateral symmetry decouples them into a symmetric set (surge, heave, pitch) and an antisymmetric set (sway, roll, yaw) in head and following seas. They are solved by strip theory or panel methods.